The game to play: expanding the co-opetition proposal through the strategic games matrix

The game to play: expanding theco-opetition proposal throughthe strategic games matrixEliezer Arantes da Costa and Celso Pascoli Bottura

Department of Machines, Components and Intelligent Systems,School of Electrical and Computer Engineering,State University of Campinas, Campinas, Brazil

Joao Maurıcio Gama BoaventuraFundacao Instituto de Administracao, Sao Paulo, Brazil, and

Adalberto Americo FischmannSchool of Business, Economics and Accounting,

University of Sao Paulo, Sao Paulo, Brazil

Abstract

Purpose – Using Brandenburger and Nalebuff’s 1995 co-opetition model as a reference, the purposeof this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enablescholars and managers to identify which games may be played in response to the different conflict ofinterest situations faced by companies in their business environments.

Design/methodology/approach – The literature on game theory and business strategy arereviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel gamesare described and modeled.

Findings – The co-opetition model is not sufficient to realistically represent most of the conflict ofinterest situations faced by companies. It seeks to address this problem through development of theSGM, which expands upon Brandenburger and Nalebuff’s model by providing a broader perspective,through incorporation of an additional dimension (power ratio between players) and three novel,respectively, (rival, individualistic, and associative).

Practical implications – This proposed model, based on the concepts of game theory, should beused to train decision- and policy-makers to better understand, interpret and formulate conflictmanagement strategies.

Originality/value – A practical and original tool to use game models in conflict of interest situationsis generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on theSGM to suggest in which situations they could be useful. Two innovative games are described to fit fourdifferent types of conflict situations that so far have no corresponding game in the literature. A testapplication of the SGM to a classic Intel Corporation strategic management case, in the complex personalcomputer industry, shows that the proposed method is able to describe, to interpret, to analyze, and toprescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.

Keywords Game theory, Conflict, Management strategy, Computers

Paper type Conceptual paper

IntroductionA number of articles have been published on the application of game theory to businesssituations (Arend and Seale, 2005; Ghemawat, 1999; Parkhe, 1993; Smit and Ankun, 1993).However, an essential problem always surfaces when this theory is applied to the business

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Received 21 September 2007Accepted 20 August 2008

International Journal of ConflictManagementVol. 20 No. 2, 2009pp. 132-157q Emerald Group Publishing Limited1044-4068DOI 10.1108/10444060910949603

world: what is the right game to play now? This is precisely, the issue of this paper seeks toaddress, and which has already been discussed by Brandenburger and Nalebuff (1995),who emphasizing the need to choose the right game to play, hold that a player can playboth cooperative and competitive type games at a given time, through behavior they call“co-opetition.” Nevertheless, the cooperation-competition dimension employed by theseauthors proves insufficient to explain all the games that could be played in each particularconflict of interest situation. This study therefore addresses this matter in further depthand expands on the original concept of co-opetition.

The main objective of this study is to provide scholars and managers with a tool,based on the tenets of game theory that allows identification of which games can beplayed in each conflict of interest situation faced by companies in their operatingenvironments. Although cooperation and competition have frequently been featured inacademic articles and books on negotiating strategies, especially when they involvegame theory, as in Lado et al. (1997), we were unable to find anything in the literaturethat addressed our proposed objective.

Brandenburger and Nalebuff’s (1995) proposal may be summarized by Table I.Our research problem will be broken down into four questions as presented in

Table II.

Theoretical backgroundDifferent types of concepts of strategy contentsBefore we further focus our discussion on the types of strategy used in this study,based on game theory, it will be useful to present a broader perspective of the variousconcepts of business strategy and where each of these approaches can be found.

Question Answer

Which is the right game to play? Competition and/or cooperationTable I.

The co-opetition proposal

Issues Questions

1. The co-opetition model presumes competitionand cooperation are the two models ofbehavior to decide what game to play

RQ1. Are competition and cooperation the onlytwo models of behavior that executivesshould consider before deciding whatgame to play?

2. The co-opetition model does not consider thepower-ratio among players to decide whatgame to play

RQ2. Does the power ratio among playerssuggest different games to play?

3. A review of the literature found no modelscapable of indicating which classical gametheory games may be applied to each of thedifferent conflict of interest situations faced bycompanies

RQ3. According to the classical game theory,what game should managers play in anygiven situation of conflict of interests foreach different business situation they face?

4. A player who chooses the wrong game to playis expected to incur negative consequences

RQ4. What are the possible consequences ofchoosing the wrong game to play in atypical situation of conflict of interestsamong players?

Table II.Research questions

Expandingthe co-opetition

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Through an analysis of articles about how different authors define strategy, we providean overview of the different strategy concepts they use. Next, we present an analysis of“strategy contents.” In this section, the different ways in which various authors haveinvestigated the definition of strategy are grouped by similarity. Hax and Majluf (1996,p. 1) hold that, for the purpose of analysis, strategy contents should be separated fromstrategy process. Hax and Majluf (1996, p. 14) also identify nine dimensions for theconcept of strategy:

(1) determination of the long-term objectives and the allocation of priorityresources;

(2) selection of the business where the organization operates;

(3) search for and application of advantages for the company;

(4) identification of the different management levels;

(5) integration of decision patterns;

(6) definition of contribution to stakeholders;

(7) establishment of strategic intent;

(8) development and strengthening of essential competences; and

(9) use as a means for investing in the resources needed for developing andsupporting the competitive advantages.

Hofer and Schendel (1978) also studied the concept of strategy and established that themain components of strategy are:

. scope and range;

. resource application;

. competitive advantage; and

. synergy.

To classify the different categories, the assumption used in this paper is that authorsemphasize their concepts of strategy by the form they use to define it. Therefore,through the authors’ research one can recognize four broad categories for strategycontents. It should be noted that, although they are different, these four types,described below, are not incompatible with one another, neither are they mutuallyexclusive, strategy:

(1) as a means for attaining objectives;

(2) oriented toward competitive advantage;

(3) focused on resources and competences; and

(4) based on interaction with the opponents.

Some authors provide definitions that use more than one category. In these cases, thecomponents were classified into more than one of the categories they had identified.One example is Quinn (1992, p. 5), who says that a well-formulated strategy helpsorganize and allocate an organization’s resources in a unique and feasible posture,based on the respective internal competences and weaknesses, thus anticipatingchanges in the environment and unexpected moves by an intelligent opponent.

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Quinn bases his position on concepts (1) and (3). Fahey and Randall (1998) also usemore than one type of concept, taking concepts (1) and (2) to explain that strategyshould confront and solve three sets of basic choices: scope and range, competitivedistinction, and goals. These four categories for the concept of strategy contents can besummarized as follows:

(1) Strategy as a means for attaining objectives. One group of authors conceivesstrategy as a means through which objectives may be fulfilled. This is like acausal relationship, where the cause is the means for using the organization’sresources and the effects constitute the attainment of results or objectives.Chandler (1962), for example, says that strategy can be defined as thedetermination of the basic long-term goals and objectives of an enterprise andthe adoption, of course, of action and the allocation of resources necessary forcarrying out these goals. Christensen et al. (1978) have a similar perspective ofstrategy, defining it as a pattern of decisions in a company that:. fashion and disclose its objectives, intentions and goals;. produce the main policies and plans to attain these goals; and. define the business area where the company wants to operate.Other authors with a similar approach are Ackoff (1973), Andrews (1971),Ansoff (1984), Drucker (1977), Fahey and Randall (1998), Henderson(1979), Hofer and Schendel (1978), Johnson and Scholes (1989), Learned et al.(1965), Lorange and Vancil (1977), Miles and Snow (1978), Rhenman (1973),Rumelt (1974) and Steiner (1979).

(2) Strategy oriented toward competitive advantage. The literature presents anothergroup of definitions that relate strategy with competitive advantage. In thiscase, the basic assumptions are that strategy should be oriented to attainingand maintaining a company’s competitive advantage. Porter (1985) introducedthis new concept and a number of other authors followed suit. Hax and Majluf(1996, 1991) recognize that the connection between strategy and competitiveadvantage was one of Porter’s great innovations, and they too adopted thisconcept. They thus define strategy as a means to attain and maintaincompetitive advantage. Henderson (1991) changed his earlier definition ofstrategy to line up with Porter’s concept, and redefined strategy as a deliberatesearch for a plan of action geared to developing and implementing competitiveadvantage in a company’s business. Even Andrews (1971), who initially definedstrategy as a means to reach goals, revised this definition. Several years later,Andrews (1987) reformulated his definition by including the concept ofcompetitive advantage. Fahey and Randall (1998) and Pfeffer (1998) alsodefined strategy on the basis of this category.

(3) Strategy focused on resources and competences. Another group of researchersstress that strategy should be centered on the organization’s resources orcompetences, and presume that competitive advantage is a function of theorganization’s resources or competences. Various authors in this line of thoughtuse the concept of resource-based view (RBV) – based on Wernerfelt (1984),who credited the original idea to Penrose (1959) – whereby a company is seenas a set of resources. In a way, the RBV theory is an attempt to delve deeper intothe study of competitive advantage by developing models that seek to explain


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how the resources of an organization can generate sustainable competitiveadvantage (Barney, 1991; Collis and Montgomery, 1995; Peteraf, 1993). Anotherconcept that is similar to the notion of resources is that of competences, firstproposed by Hofer and Schendel (1978). These authors held that distinctivecompetences should be the most important factors in a strategy. As far as, theoriginality of the concept of “competence” is concerned, Andrews (1987, p. 45)attributes the term “corporate competence” to Stevenson (1976). Prahalad andHamel (1990) later coined the term “core competence,” which becamewell-known in the field. Hamel and Prahalad (1994) stressed the need for astrategic architecture that would provide a guideline for the construction of thecompetences needed to dominate future markets.

(4) Strategy based on interaction with opponents. Another group of authors definestrategy by associating it with interaction with the opponents. These authorsemphasize the actions and reactions between organizations and theiropponents. In other words, they hold that it is impossible to conceive astrategy without considering the actions and reactions of one’s opponents. Theorigin of this concept goes back to von Neumann and Morgenstern, who in 1944,published a landmark book entitled Game Theory and Economic Behavior. vonNeumann and Morgenstern (1947, p. 74) defined strategy as a complex planethat specifies the choices that one should make in each possible situation, foreach possible pattern of information available, according to the rules of thesupposed game they are playing. For Schelling (1960), the term “strategy”focuses on the interdependence among decisions involving competitors andtheir reciprocal expectations in terms of each other’s behavior. It would seemthat similar ideas were published before Schelling, such as those of Newman(1950), who relates strategy to the predicting of reactions. He defines it as beingthe adjustment of a plan in order to predict and anticipate the reactions of thosewho will be affected by this same plan. This concept is also used by Dixit andNalebuff (1991, p. ix), who stated that strategic thinking is the art of outdoingadversaries, knowing they are trying to do the same thing to you. Otherauthors, including Brandenburger and Nalebuff (1996), Dixit and Skeath (1999)and Simon (1947) follow the same idea.

Strategic analysis based on game theoryThe present paper is based on the concept of “Strategy based on interaction with theopponents,” which has benefited greatly from the results of game theory, as will beexplained further ahead. We employ this approach since, in our opinion, it is the mostadequate for analyzing competitive strategies, considering that competitors – orpartners – are always present in any business undertaking and that their actions anddecisions can, and actually should, interact with the company’s decisions and results(Basar and Olsder, 1999).

Strategic analysis based on game theory as applied to business managementAttempts to apply the concepts and results of game theory to the business environmenthave been described by many different authors (Sebenius, 2006). Dixit and Nalebuff(1991) and Dixit and Skeath (1999) describes the competitive movements of companiesas if they were moves on a game board, and discusses the possible reactions of opponents

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when they predict and anticipate the moves of their adversaries. Porter (1980, 1985)mentions the application of the classical theories on equilibrium strategies of gametheory to interpret situations of strategic confrontation and the choice of moves made byeach competitor. Smit and Ankun (1993) describe the application of game theory todecision making in investment strategies in situations of competition. Oster develops theconcepts of competitive rivalry by applying concepts of game theory to the analysis andinterpretation of the rational strategic decisions of companies. Oster (1994) defines andapplies the concepts of “payoff matrices,” “dominant strategies,” “credible threats,”“threat points” and “strategic core” to the business environment, to model the behaviorof undertakings among numerous companies, and discusses the feasibility of the manypossibilities of partial or total coalitions. Ghemawat (1999) mentions a number ofsituations of competition between companies in which game theory is very useful foranalyzing and deciding among several different available competitive strategies. Hewarns, however, that decision makers often do not follow the “paths of rationality,” sincebusiness people often make their strategic choices based much more on psychological,political or diplomatic reasons, such as the need to justify past decisions, or because ofselective perceptions of reality, or due to unjustified hostilities, or simply as the result of“intuitive moves.” The author mentions several cases in the literature to illustrate these“anomalies.”

Fundamentals of classical game theoryThe meanings of certain technical terms used in this paper are the same as thoseapplied in the context of game theory: a game can be conceived as a situation of conflictof interests between two or more intelligent autonomous agents, and it can bedescribed by a mathematical model. The problem of conflict of interests between twoor more autonomous agents, decision makers, or controllers (henceforth simply“players”) is known as a game. The players are presumed to interact upon a singlesystem, and each intends to optimize some specific criterion, such as measures ormeasurable results of the system.

The aim of specialists or researchers in a problem of a game is to find a “solution forthe problem in the game.” In other words, they seek out a point, a so-called equilibriumpoint, in such a way that players understand they have reached the best resultspossible in that specific game situation. A saddle point is a particular case of anequilibrium point, generally applicable to zero-sum games. In game theory, the termstrategy has a slightly different meaning than it does in the business environment: it isequivalent to a set of “rules of decision” that should be followed by all players involvedin the game in order to attain or obtain an equilibrium point (Basar and Olsder, 1999).Basar and Olsder (1999), Costa Filho (1992), Cruz (1978) and Matalobos et al. (2005) alldescribe typical situations of cooperative and competitive games and indicate ways toobtain “equilibrium strategies” for various types of games. As examples of thesetypical game situations, the following games were chosen for this paper:

. zero-sum games, in which strategies are applied seeking the existence of a saddlepoint;

. non-cooperative variable-sum games, where one seeks to apply the Nashequilibrium strategy;

. cooperative variable-sum games, in which the Pareto strategy is applied; and


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. apart from game types (1), (2) and (3), which differ with regard to player posture,one finds hierarchical or non-hierarchical games, which differ from one anotheras far as players’ power ratios are concerned.

In hierarchical or unbalanced games, the stronger player decides on its strategy andannounces it to the remaining player, to whom they try to apply the Stackelbergstrategy; there are a leader strategy for the stronger players, who makes the firstmoves in the game, and a follower strategy for the weaker player, who simply reacts tothe leader’s strategy.

The concept of “player”. In this paper, the word “player” means an intelligentautonomous agent, or simply an agent, representing any being that has the followingcharacteristics (Gonzaga, 2006; Wooldridge, 2002):

. is aware of itself, of its individuality, its outside environment, its possibilities andits shortcomings;

. is aware of other players with which it has a certain degree of interaction or sometype of conflict of interests;

. is capable of making intelligent decisions and implementing actions seeking toobtain “better” present and future results for itself;

. is able to take into account the present and future consequences of its decisionsover the interests of the remaining players;

. can take into account the present and future consequences that the unpredictabledecisions made by other players involved may have on its own interests; and

. is able to learn, with time, to make better future decisions based on its positiveand negative past experiences.

In general, a player can be represented by a manager, an executive, a company, adecision maker, a commander, or any stakeholder – that is, a person, a group ofpersons, a company or a governmental (or non-governmental) organization.

The concepts of equilibrium point and equilibrium strategies. An equilibriumstrategy for a game can be understood as a “solution” to the problem of the game. Itleads toward decisions that should be made by the players – considering each one’sobjective functions – and express, to some degree, the solution for the conflicts ofinterests among these players. The application of one or another equilibrium strategydepends, among other factors, on the structure of the game, the number of participants,the attitude of cooperation or rivalry between the participants, the structure ofinformation available to each player, and the existence or nonexistence of a“privileged” player that is in a position to impose its own strategy on the other players.

The generic notations used here to formalize the discrete dynamic games in time aresummarized below:

. Pi, with i ¼ 1, . . . , N, is the designation of the ith player;

. k ¼ 0, 1, . . . , K is the index that defines each K þ 1 stage of the game (for thesake of simplicity, we will omit index k for dynamic single-stage games);

. xk is the vector-state of the game at the beginning of stage k; the sequence{x0; x1; . . . ; xk; . . . ; xK ; xKþ1} describes the evolution of the game, given x0, itsinitial state;

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. uik is the decision-vector taken by player Pi in stage k; the sequence

{ui0; u

i1; . . . ; u

ik; . . . ; u

iK} represents all the decisions taken by Pi during the

game;. zi ¼ J iðx1; . . . ; xKþ1; u1

0; . . . ; uik; . . . ; u

NK Þ is the objective function for player Pi;

. xkþ1 ¼ f kðxk; u1k; . . . ; u

ik; . . . ; u

Nk Þ is the transition-equation of the game, from

stage k to k þ 1; and. ui

k ¼ g ikðh

ikÞ is the control function, where g i

kð. . .Þ is the strategic function of thegame, and hi

k is the set of information available to player Pi in stage k.

Using the terminology presented above, the formal concepts of equilibrium point andequilibrium strategy are described as follows. To facilitate the explanation, we willassume a simple game with only one stage and two players, P1 and P2, whose decisionvariables are designated as u 1 and u 2 and whose strategic functions are g 1(. . .) andg 2(. . .), respectively. An equilibrium point for a given game is defined as a set ofdecisions ðu 1; u 2Þ, such that, through these decisions, players believe they have foundthe possible optimum for their objective functions, respecting the limitations of thegame and operating according to the postures of competitors and the power ratiosassumed by them, as we shall see further ahead. The equilibrium strategy of a gameis a set of rules ðg 1ð. . .Þ; g 2ð. . .ÞÞ that leads to the game’s equilibrium point. In thisregard, an equilibrium strategy is a “solution” for the problem of the game. It leads inthe direction of the decisions that must be taken by the players, considering thedifferent objective functions of the players and taking into account the conflicts ofinterests among them.

Discussion and the proposed model

RQ1. Are competition and cooperation the only two models of behavior thatexecutives should consider before deciding on what game to play?

As noted above in our literature review, certain games are characterized by at leastthree distinct behavior types, namely:

(1) zero-sum games, in which players take on an individualistic posture and applythe saddle point strategy;

(2) non-cooperative variable-sum games, in which players take a competitiveposture and to which the Nash equilibrium strategy is applied; and

(3) cooperative variable-sum games, which feature a cooperative player postureand application of the Pareto strategy.

For the sake of simplicity, we have adopted three mutually exclusive posture types,characterized by the following statements:

(1) “I would like to destroy my competitors if possible; if not, I would like to weakenthem as much as possible so that they can pose no threat to me in the future.”We will call this the “Rival posture.”

(2) “My competitors exist and they have the right to exist because there must beopportunity for all. Although I recognize that there will always be conflicts ofinterest between us, I will act in such a way as to obtain and maintain my vital


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space for my survival and growth.” This attitude will be referred to as the“Individualistic posture.”

(3) “I need to survive and so do my competitors; therefore, it must be possible tofind some form of coordinated action among us to arrive at a conciliatorysolution that is best for all.” This attitude will be known as the “Associativeposture.”

For the purposes of this analysis, these three possibilities must be recognized as trulypresent and distributed among the various types of players. They effectively conditionthe analysis of the postures, behaviors and actions that are taken in each conflict ofinterest situation and in each type of game. The three degrees – or levels – of playerposture assumptions characterized above are described here as rival (warrior attitude),individualistic (combative attitude) and associative (cooperative attitude), respectively.They are illustrated in Table III, which shows typical situations where theseassumptions are applicable. It also shows the results the players hope for, their ethicalassumptions, and their basic postures.

This paper does not question whether this choice is a subjective or an objectivematter that can be explained by economic reasons or, more specifically, by the survivalof the company; Lewicki et al. (1996) delve further into this question. For the purpose ofthe present conceptual model, we will simply underscore that they are present insituations of conflict of interests, without making any moral or value judgmentregarding the choices made:

A1. There are at least three important, distinct and mutually exclusive types todescribe the competitive postures any given player can assume toward theother players: rival, individualistic, and associative.

RQ2. Does the power ratio among players define different games to play?

As mentioned before in our literature review, different power ratios among playersentail different types of games. In this study, we seek to characterize the typicalpostures a given player may take on regarding its relationship of forces whenconfronted with its main opponents. Again, for the sake of simplicity, we have adoptedthree levels of typical power ratios, characterized by the following statements:

(1) “I am stronger (or the strongest) and I can impose my interests on myopponents.” This will be known as the stronger power ratio.

Players’ postureassumptions Rival Individualistic Associative

Typical situation Predatorycompetition

Loyal competition Alliances agreementspartnerships

Expected results Eliminate or reducecompetitors

Win and survive The best possible forall

Ethicalpre-suppositions

Do anything tosurvive

Win, yes, but with dignity We are all in the same

Typical definingstatement

Everyone is againstme

Each man for himself, and maythe best one win

One for all and all forone

Table III.Players’ competitiveposture assumptions

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(2) “I am like any of them, and my main opponent and I have equivalent strengths.”This will be referred to as the balanced power ratio.

(3) “I am very weak and I can’t make my opponent act according to my interests; ifpossible, I prefer to wait for the strongest to decide, and then make my owndecision.” This can be called the weaker power ratio.

The power ratio assumptions described above are illustrated in Table IV, which showstypical situations where these assumptions are applicable, as well as results desired bythe players, their ethical assumptions, and each one’s basic postures.

For the purposes of these analyses, we will not enter into the question of objectivity;that is, there will be no attempt to ascertain whether the power ratio assumed by aplayer has any objectively calculated reasoning behind it. Brandenburger and Nalebuff(1995, 1996), for example, discuss this aspect at length. For purposes of this paper,however, we only need to recognize that these three assumptions are present insituations of conflict of interests, without adding any connotation involving moraljudgment or questioning the values associated with the posture taken on by a player ina specific situation of confrontation:

A2. There are at least two types of assumptions of power ratios that players canassume in any given game: balanced and unbalanced power ratios, both ofwhich serve to characterize the types of games to be played. Games withassumptions of unbalanced power ratios are always played by two types ofplayers in opposite positions: one type of player, with a stronger power ratio,is the stronger in the relationship, and another, with a weaker power ratio, isthe weaker.

Proposed model: the strategic games matrixThe strategic games matrix (SGM), which we describe in this section, is a descriptiveand conceptual model meant to support managers and decision makers in the varioussituations that arise in the management of conflicts of interest situations. It helpsdetermine the right game to play and the strategy for playing each game. A preliminaryversion of the concepts and structures used in this matrix was first presented by Costaand Bottura (2004), later expanded and applied in Costa et al. (2006a, b), Costa andBottura (2007) and Costa (2008). The SGM is also useful to explicitly warn executives,in each situation of conflict of interests, that, before deciding “How I am going tocompete,” they must first decide, “What game should I play now?” In this regard,

Players’ power-ratioassumptions Weaker Balanced Stronger

Typical situations Beginner or terminal Free market Monopoly, control,and regulations

Expected results Survive Win Keep the position ofsovereignty

Ethical pre-suppositions Do anything to survive Win, yes, butaccording to the rules

I make the rules andI profit from them

Typical defining statements I am very small I am one of them I am the strongest

Table IV.Players’ power ratio

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SGM is simultaneously a descriptive model, since it allows one to classify, identify, anddescribe the possible games to be played in different situations of conflict of interestsamong the players, and also a prescriptive model, in that it points executives andstrategic decision makers to the best competitive, cooperative, or other types ofstrategies they should assume in these situations. To construct the SGM, the two majordimensions in any game under analysis are described as follows.

The major dimensions for analyzing a strategic game. There are several importantdimensions that could be used to construct a conceptual map of the attitudes orbehaviors that players may explicitly or implicitly assume in conflict of interestsituations. We chose two dimensions for our conceptual model, suggested on the basisof distinctive characteristics present in the equilibrium strategies for classical games.

For the purposes of this paper a player, as characterized above, can be seen as adecision maker that, individually or as a team, after considering the risks andopportunities involved, makes decisions and implements them. Players operate in thisway while being aware that their decisions may entail risks and uncertainties, and that,positively or negatively, their decisions will influence the results of all the otherplayers, which have other interests at stake. Players also take into account that thedecisions of their opponents – or partners – are beyond their control and will influencetheir own results.

Studying the different situations of conflict of interests among players, we chosetwo determining conceptual factors that characterize and distinguish the games andtheir respective strategies. These two factors are the:

(1) possible attitudes, or behaviors, that are typical of the players when facing theircompetitors; and

(2) relationship of forces between a player and the opponents, against whom theplayer engage into some type of conflict of interests.

These two determining concepts are precisely the two dimensions of the SGM:

P1. The bargaining power of players in a given game, represented by theassumptions of power ratios, as well as their attitudes of competition, are thetwo distinct dimensions that, individually and jointly, determine the differenttypes of games to play.

The structure of strategic games matrix. A matrix – called the SGM – is obtained bycombining the three player posture assumptions with the three power ratioassumptions. The matrix has nine cells representing nine typical strategic situations,as shown in Figure 1.

The nine cells of the SGM are referred to, respectively, as: hegemonic, leader,paternalistic, retaliatory, competitive, cooperative, marginal, follower, and solidary, asshown in Figure 1. These names seek to mnemonically represent each of the typicalconflict-of-interest situations that the players may face. Each of the nine cells of thematrix represents a typical situation of strategic games. Four classical games in gametheory correspond to the five central cells of the matrix.

But there are no classical games corresponding to the four cells located in thevertices of the SGM. Two new games should therefore be added to the classical gamesmentioned, in order to complete the mapping of all the cells of the matrix:

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P2. The three types of competitive posture mentioned, combined with the twotypes of power ratios mentioned in P1, result in six different types of gamesthat players can engage in.

Mapping of the classical games and their equilibrium strategies in the SGMFour of the classical games of game theory can be characterized by the five central cellsof the SGM, representing typical game situations. Here, the classical games are calledcooperative-, competitive-, retaliatory-, and leader/follower-type games, all shown inFigure 2 and described in the topics that follow.

In this section, we will briefly discuss the equilibrium structures of the four gametheory classical games, corresponding to the five central cells of the SGM, as shown inFigure 2.

Nash equilibrium strategy – competitive type games. The strategic positioncorresponding to the central cell of the SGM, which we refer to as the competitivegame, describes a type of game where we find free market or perfect competitionsituations, with many suppliers and many buyers, and where no single playeris able to dominate the others. In non-cooperative variable-sum games, in whichplayers decide to take on a competitive strategic position, they seek to optimize theirobjective function and ignore what the other players are doing or plan to do(Nash, 1950).

If this solution exists, it is characterized by the situation where no player is ableto improve its results by individually changing its own decision. For all theplayers involved, this set of decisions is called a Nash equilibrium point, as definedbelow.

For a non-cooperative variable-sum game with N players and a single stage, a Nashequilibrium point is defined as u* ¼ ðu 1; . . . ; u i; . . . ; uN Þ [ U , if for every u i [ U i,

Figure 1.The SGM

Hegemonic Leader Paternalistic

Retaliatory Competitive Cooperative

Follower SolidaryMarginal

Rival Individualistic

Play

ers’

pow

er-r

atio

ass

umpt

ions

Players’ competitive postures

Associative

Wea

ker

Bal

ance

dSt

rong

er


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with i [ N, it simultaneously obeys the following N inequalities for the values of theobjective functions of all the players:

J 1ðx; u 1; . . . ; u i; . . . ; uN Þ # J 1ðx; u 1; . . . ; u i; . . . ; uN Þ

· · ·

J iðx; u 1; . . . ; u i; . . . ; uN Þ # J iðx; u 1; . . . ; u i; . . . ; uN Þ

· · ·

JN ðx; u 1; . . . ; u i; . . . ; uN Þ # JN ðx; u 1; . . . ; u i; . . . ; uN Þ

P3. A game where the competitive postures are individualistic and where the powerratio assumptions are balanced can be explained by the Nash equilibrium strategy.

Pareto equilibrium strategy – cooperative type games. In this type of variable-sum game(mapped here to the right central cell of the SGM), the cooperation among players canlead to results – for all the players – that are better than the results any one couldobtain if it tried to optimize its objective function without prior knowledge andcoordination with the others’ decisions. These are cooperative games: when playersdecide to share information about their respective conditions and restrictions, theiralternative courses of action, and their objective functions, they are able to find a pointknown as the “Pareto optimum point,” which is the best possible for all the players.

This point, if it exists, is characterized by the fact that none of the players can improvetheir results without worsening the results of the other players. These are known as“win-win” games. The environment for cooperative games implies, however, that there mustbe an explicit or implicit agreement among the players for none of them to exacerbate their

Figure 2.The four strategic gamesmapped on the SGM


Play

ers’

pow

er-r

atio

ass

umpt

ions


Associative

Wea

ker

Bal

ance

dSt

rong

er

Retaliatory:Minimax

Competitivenash

Cooperative:Pareto

Followerstackelberg

Leader:Stackelberg

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individual interests in detriment to the interests of the others. This type of game thereforerequires an atmosphere of goodwill and loyalty among all participants.

For a variable-sum cooperative game with only one stage and N players, the pointu* ¼ ðu 1; . . . ; u i; . . . ; uN Þ [ U is defined as a Pareto optimum, if there is no otherpoint u ¼ ðu 1; . . . ; ui; . . . ; uN Þ [ U , such that J iðu

iÞ # J iðuiÞ; ;i [ N .

This condition requires that J iðuiÞ # J iðu

iÞ; ;i [ N , only ifJ iðu

iÞ ¼ J iðuiÞ; ;i [ N , with a strict inequality for at least one i [ N:

P4. A game where the competitive postures are associative and where the powerratio assumptions are balanced can be explained by the Pareto game optimumstrategy.

Minimax equilibrium strategy – retaliatory type games. This strategic position – locatedin the central left-hand cell of the SGM – applies to a type of games called “win-lose” or“lose-lose” games. Here, each player, explicitly or implicitly, assumes that any gain forone of them automatically implies losses for the others, characterizing a retaliatorycompetitive position. To formalize this strategic position, the concept of zero-sum gameis used. A zero-sum game is defined as a game for which:

i[N

XðZ iÞ ¼

i[N

X�J i

�x1; . . .xKþ1; u

11; . . . ; u

ik1; . . . ; u

NK

��; 0

(In fact, it would be sufficient for the result of this operation to be any constant insteadof zero).

A saddle point is a solution for a zero-sum game, if it exists, for which each playerbehaves in a way it considers is the most favorable to optimize its objective function,considering all the possibilities that the others can fulfill. This point has the peculiarcharacteristic that any deviation from it by any player makes the result worse for it interms of its objective function.

Applying this concept to a game with only two players (N ¼ 2), a saddle-point isdefined as a pair of decisions, ðu 1; u 2Þ, that satisfies the following inequalities:

J 1ðu1; u 2Þ # J 1ðu

1; u 2Þ # J 1ðu1; u 2Þ for every u 1 [ U 1 and u 2 [ U 2:

Generalizing this concept for N players, a u i [ U i strategic decision by each player Pi

is defined as a saddle-point solution if, for every admissible set{u 1; . . . ; u i; . . . ; uN } [ U , all the following relationships are valid:

u 1; ... ;u i21;u iþ1; ... ;u Nmax J iðu

1; . . . ; u i21; u i; u iþ1; . . . ; uN Þ #u 1; ... ;u i21;u iþ1; ... ;u N

max J iðu1; . . . ; uN Þ

A strategy that leads to a saddle-point, as defined above, is called a Minimax strategy. Itshould be noted that the calculation of the saddle-point for player Pi depends exclusively onPi’s objective function. This is because, in this strategy, player Pi does not take into accountthe other players’ objective functions, since it cannot rely on their goodwill or theirrationality. This strategy also applies to real situations where a Pi player believes the otherplayer may show erratic, irrational, unpredictable, or even malicious behavior; that is, in


proposal

145

which adversaries can make moves to jeopardize Pi’s objective purposes, even if, by doingso, they are also hurting their own interests:

P5. A game featuring rival competitive postures and a balanced power ratioassumptions can be explained by saddle-point type games with the Minimaxequilibrium strategy.

Stackelberg equilibrium strategy – leader/follower type games. These strategies, whichapply to a type of unbalanced game where one player (the leader) has a stronger powerratio assumption and another player (the follower) has a weaker power ratioassumption (Cruz, 1978), both with individualistic postures, are called Stackelbergstrategies. These strategies correspond to two opposite positions found in the upperand lower center cells of the SGM.

Let us consider a game with an unbalanced power ratio between a player M, called aleader, and another player P, called the follower, with strategic decisions l and m, andobjective functions R(l, m), and J(l, m) associated with players M and P, respectively.Let us also suppose that, due to the structure and rules of the game, the player M firstchooses its strategic decision l, and then player P chooses its strategic decision, afterlearning of player M’s decision.

If the pairðl; uÞ [ ðL;U Þ exists, it defines a Stackelberg equilibrium point, with thefollowing properties, there is a:

. transformation T: L ! U such that, for every l [ L, J ðl;TlÞ # J ðl; uÞ forevery u [ U; and

. l [ L, such that Rðl;TlÞ # Rðl;TlÞ, for every l [ L, where u ¼ Tl.

It should be noted that, to obtain a Stackelberg equilibrium point, the follower must bea rational decision maker that always makes optimum decisions within its limitations.For this game structure, a pair of Stackelberg strategies can be determined – one forthe leader and another for the follower.

This game is generally applicable to situations of conflict of interests between onevery strong and one very weaker players, both with individualistic competitivepostures:

P6. A game featuring individualistic competitive postures and an unbalancedpower ratio assumptions can be explained by the equilibrium strategies of aleader/follower type game, through the Stackelberg strategy, where the playerwith the stronger assumption takes on the role of leader and the player withthe weaker assumption assumes the role of follower.

Proposed games: limit-case situations in the SGMFor the four situations described by the four cells that make up the vertices of the SGM,we found no corresponding classical games to explain and describe these games; wewill call them limit-case situations.

Since these new limit-case situations can also occur in the business world, onesignificant contribution of this paper is to explain these games and formally describetheir main characteristics. Figure 3 shows the two games which we propose to explainthe four situations remaining on the SGM.

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Further developments derived from this study could include, for instance, searching forsolutions to these games, through the mathematical models developed for them, for avariety of typical situations, pointing out the respective equilibrium strategies.

Paternalistic-solidary type game. This type of limit-case game is characterized bytwo players in two opposing positions, in different situations in the SGM cells, both ofwhom take on cooperative postures, as follows.

Paternalistic strategic position. This type of limit-case is located in the upperright-hand cell of the SGM and takes place in games where stronger players, by theirown decision, model their actions – and those of the other weaker players in thegame – seeking to ensure the development of “their” business as a whole. Thisnecessarily involves the other, weaker, players. These games are similar to the posturetaken on by the father (or mother) in a family, who supposedly exerts full authorityover his or her children. They do everything they consider necessary to promote thedevelopment, growth, well-being and harmony in their families, through a typicallypaternalistic behavior.

One equilibrium solution for this type of player in the Paternalistic position can befound as follows. Let ai with i ¼ 1, . . . , N, be the relative importance weights attributedto the other players by the paternalistic player, Pi, with 0 # ai # 1, such thatPN

i¼1ai ¼ 1, and let z ¼PN

i¼1aiJ ið. . .Þ, that is, a multicriteria objective function, takinginto account the objective functions of all the N players, the new objective function tobe optimized.

An equilibrium point for this limit-case game can be found as the solution to aproblem of multicriteria optimization where the new objective function becomes, forexample, a linear combination of all the objective functions of all the players (Haimesand Li, 1988). It should be made clear, however, that when the relative weights for theother players are determined, the Paternalistic players must factor into their decision

Figure 3.The two limit-case

situation strategic gamesmapped on the SGM


Play

ers’

pow

er-r

atio

ass

umpt

ions


Associative

Wea

ker

Bal

ance

dSt

rong

er

Hegemonic

SolidaryMarginal

Paternalistic


proposal

147

the risk that some solidary players, as described below, will prefer rather anautonomous strategy – that is, they will leave the game and act on their own.

Solidary strategic position. The solidary position is the opposite of the paternalisticposition described above, and is mapped to the lower right-hand SGM cell. It representsthe situation of a game where a player has a weaker power ratio assumption, but withan associative competitive posture. Being unable to impose its interests on the otherplayer or to negotiate with it from a balanced position, it seeks to follow the rules setdown by the strongest player in an attempt to obtain at least a certain individualadvantage. If it do not obtain such an advantage, it may prefer to leave the game. Thisis, for instance, how members of a cooperative organization behave: they need only todecide whether they should become – or remain – members of the “group” and thusobtain some advantage, or leave the association and operate on their own, with therisks that it entails. An equilibrium solution for a player in a solidary position for thistype of limit-case game can be treated simply as a problem of a decision-tree with onlytwo branches, that represent the opposing decisions of either “joining the group” or“operating independently”:

P7. A game featuring associative competitive postures and unbalanced powerratio assumptions can be explained by the equilibrium strategies of apaternalistic/solidary-type game, where the player with stronger assumptiontakes on a paternalistic role and the player with the weaker assumptionassumes a solidary role.

Hegemonic-marginal games. This type of limit-case game is characterized as havingtwo players in antagonistic positions, located at opposite upper and lower left-and cellsof the SGM and both taking on rival postures, as follows.

Hegemonic strategic position (mapped to the upper left-hand SGM cell).Characterizes the position where a player has full strength and, if possible, hasevery intention to destroy their smaller competitors. Its attitude can be one ofintimidation, blackmail, price war, blockage of sources of raw materials, for example,to try to “break” the smaller player. It can also pressure its customers into not buyingfrom smaller companies. One equilibrium point for the player in the hegemonicposition, for this limit-case game, can be obtained through the solution of a problem ofmono-criterion optimization, where the player in the hegemonic position ignores all theobjective functions of its smaller and weaker opponents and simply optimizes its ownobjective function. It can treat any opposing actions of the smaller player as if theywere mere “random noise,” simple contingencies of its business.

Marginal strategic position. In contrast to the hegemonic position described above,the marginal strategic position is charted in the lower left-hand SGM cell. In thisposition, a weaker player with a rival (combative and courageous) posture doeseverything it feels is necessary to survive. As far as possible, it seeks to obtain someadvantage, such as trying to cause losses to the player in the hegemonic position. Inthese games, an equilibrium point for a marginal player can be obtained by solving aproblem of optimization where a player in the marginal position tries to weaken theresults of the objective function of its main competitor, the hegemonic player, in orderto cause it the greatest damage possible, even if it has no objective chance to succeed:

P8. A game featuring rival competitive posture and unbalanced power ratioassumptions can be explained by the equilibrium strategies of a

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hegemonic/marginal type game, where the stronger player takes on thehegemonic role and the weaker player takes on the marginal role.

Considering the proposals above, we may now formally introduce the followingdefinitions:

Definition 1. The SGM is defined as a 3 £ 3 matrix where, on the horizontaldimension, the three types of competitive posture (rival, individualistic, andassociative) are represented, while, on the vertical dimension, the three power ratioassumptions (weaker, balanced, and stronger) are represented.

Definition 2. The nine cells of the SGM (hegemonic, leader, paternalistic,retaliatory, competitive, cooperative, marginal, follower, and solidary) represent thenine positions referring to the six games mentioned in P3-P8 above:

RQ3. According to the concepts of classical game theory, which game shouldmanagers play in any given conflict of interests for each different situation ofbusiness they face?

The problem of deciding what game an executive or a decision maker should choose toplay in each situation, which we shall discuss below, has been addressed by a numberof different authors, including Brandenburger and Nalebuff (1995, 1996) andGhemawat (1999).

In strategic planning processes, certain anomalies often observed in the choice ofcooperative and/or competitive strategies can be avoided through better understandingand more appropriate use of the concepts of conflicts of interest modeling, through useof the SGM.

By identifying the poor performance and inconsistencies resulting from aninadequate choice of strategic positioning and, consequently, of the choice of the gameto be played, the SGM can be used to better clarify the analysis and interpretation ofsituations of real or potential risks of losses or business failures.

In fact, the concepts derived from the use of the SGM should be incorporated intothe methods for formulating competitive and cooperative strategies, among others, inmanager training and development programs.

Managers, executives, planners, and decision makers could thus be better preparedfor their jobs, adding the following specific competencies to their repertoires ofmanagerial tools, to be able to:

. recognize that each situation of conflict of interests can be seen as “unique,” andthat there is no “standard solution” to be applied equally to all of them;

. evaluate the particular situation of power ratios among the players in particular,and work on the basis of the most adequate power ratio assumptions in each case;

. examine the real situation in each case and decide whether they should firmlytrust the goodwill and loyalty of their opponents in each case, and then decidewhether they should cooperate or not; and

. identify, through use of the SGM, which game to play in each case and chooseand implement the most suitable strategy without resorting to guesswork,sentimentality, and “gut feelings.”


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A3. In a nutshell, one can find the right game to play for any given situation by:analyzing the postures taken by each player involved (whether rival, individualisticor associative), assessing the balance of forces among players (whether balanced orunbalanced); and finding the corresponding game on the SGM.

RQ4. What are the possible consequences of choosing the wrong game in a typicalconflict of interest situation?

Choosing the wrong game could result in serious losses to any player who does so, bothin results and in maintaining – or failing to maintain – the relationship between theparties (Fisher et al., 1995; Leritz, 1987; Lewicki et al., 1996; Thompson, 2001).

The decisions and basic actions in each confrontation of conflict of interests can beclassified into two broad categories, according to the:

(1) choice of the right game to play; and

(2) right way to play the game.

The key question that now arises is: in the long-run, which of these categories ofdecision is most important for the company? This section of the present paper seeks todiscuss this important issue. The combination of these two options leads us to the fourfollowing scenarios in a single 2 £ 2 matrix with four possible outcomes, if:

(1) choices (1) and (2) are both right, this is an indication of possible success in thebusiness undertaking;

(2) choice (1) is right but choice (1) is wrong, we have an indication of learning; thismeans that, even if the game is played incorrectly, with the use of partial andintermediate results and with correction in direction, the right way to play thegame can be learned and gradually lead to the success quadrant;

(3) choice (1) is wrong but (1) is right, this is an indication of frustration because playersmight conclude that they are playing the game correctly but results are nonethelessunsatisfactory, and players could not figure out why; and

(4) choices (1) and (2) are wrong, this will definitely be an indication of failure, withlittle or no possibility of recovery in that case.

We hope that this topic will show managers and decision makers that all efforts shouldbe concentrated on discussing and choosing the right game to play in each situation.The long-term consequences of choosing the wrong game are far worse than those ofmaking wrong decisions in how the game will be played, even if it is the right game,because, in the latter case, there can at least be the opportunity for new attempts andnew learning. Erroneously, many companies invest a great deal of time and resourcesto teach their employees how to play the game well instead of teaching them how todecide which game to play, and this is exactly the focus of this paper:

A4. In short, choosing the wrong game may have dire consequences for the playerwho does so, both in objective results and in the player’s relationships withthe other parties. Furthermore, the long-term consequences of choosing thewrong game are far worse than those of playing the right game in the wrongway, since, in the latter case, one may at least have a learning opportunity anda chance at a new attempt.

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Case analysisAn illustration: applying the SGM to the PC industryInspired by the concept of network-value (Brandenburger and Nalebuff, 1995), in thissection we will present an application of the SGM, as described above, in order toanalyze strategic games in a complex business environment in the personal computer(PC) industry. For this purpose, we will use the Intel Corporation case study (Collinsand Pisano, 1999) as transcribed in Ghemawat (1999).

The chosen case study encompasses a long period of time in the history of the IntelCorporation (1968-1997), but the present application is focused on the competitivebusiness strategies used by Intel and its counterparts from 1990 to 1997.

The business environment at the Intel Corporation during the studied periodinvolved several types of companies: PC manufacturers (Apple, IBM, Compaq, Toshibaand others), production equipment suppliers, producers and suppliers of software foroperational systems (such as Microsoft), Intel licensees that manufacturemicroprocessors with its technology, as well as main Intel competitors (such asAMD) and even manufacturers of “clones” of Intel microprocessors.

We began by carefully identifying the players involved in the various aspects of thePC industry, including their relationships, conflicts of interests, power ratioassumptions and objective functions. Taking the Intel Corporation as the centralfocus of the analysis, as shown in Figure 4, two classes of games are clearly characterized

Figure 4.SGM analysis of the IntelCorporation case strategic

gamesSuppliers

IntelCorporation

Microprocessorsand

boards

Suppliers of productionequipments

Licenseesmicroprocessorsmanufacturers

using Intel technology

Microsoft andother software

producers

AMDClones

manufacturers

Indications:

1 – Nash game

2 – Pareto game

3 – Minimax game

4 – Stackelberg game

5 – Paternalistic-solidary game

6 – Hegemonic-marginal game

PC user market

1

2

5

4

3

6

5

PC manufacturers:Apple, AST, Compaq,Dell, Fujitsu, Gateway,IBM, NEC, Toshiba, etc

Competitors

Complementors

Clients


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in this case: three games with balanced power ratio assumptions, shown in Figure 4 bynumbers 1, 2 and 3, and three types of games with unbalanced power ratio assumptions,indicated by numbers 4, 5 and 6.

The following games were identified as having balanced power ratio assumptions:

(1) The strategic games played among PC manufacturers were typical Nash games;the multiple manufacturers were fighting for share in the huge PC user market.In most cases, they were equally competitive with their products.

(2) The strategic game played between Intel and Microsoft was a typical Paretogame because the companies had to work in close cooperation to add moreperceived value to their final products, with hardware and software designed inan articulated and complementary way, in order to be compatible with oneanother and address final users’ needs in an optimal manner.

(3) The strategic game played between Intel and AMD was found to be a typicalMinimax game, because both manufacturers compete for market shares in amarket of a presumed limited size.

The following games were identified as having unbalanced power ratioassumptions for their case:

(4) The strategic game played between Intel (in a stronger situation) and variousequipment production suppliers (the weaker players in this relationship) wasbasically a Stackelberg game, where Intel acted as the leader and the suppliersas followers.

(5) The Intel case describes how Intel proposed that its clients – PC manufacturersand therefore buyers of Intel microprocessors – take part in a marketingcampaign called Intel Inside, to increase Intel’s visibility in the eyes of endbuyers; the strategic game played between Intel – which, in this case, was thestronger player – and PC manufacturers, in this case the weaker players, was atypical Paternalistic-Solidary game, especially in regard to the Intel Insidestrategy, where Intel played the paternalistic role and the manufacturers, whichassociated with one another, played the solidary role; some manufacturersimmediately accepted the Intel proposal; others, such as IBM, were quitereluctant at first, though they eventually accepted the idea.

(6) The strategic game played between Intel (again acting as the stronger player) andthe manufacturers of Intel-like microprocessor “clones” (the weaker players) wasa typical hegemonic-marginal game. Since Intel could not destroy thesemanufacturers completely, it used strategies such as lower prices and continuousadvances in technology in an attempt to curtail the size and reach of these smallcompetitors so that they could not threaten Intel’s dominance over the market.

This PC industry case shows that application of the SGM allowed integrated analysis,interpretation, clarification and formulation of the competitive and cooperative strategiesfor the rational treatment of conflicts of interests between the Intel Corporation and itsclients, partners, suppliers, licensees and competitors, of varying sizes.

It should be noted that, in this analysis, all six games of the SGM described in thispaper were present in a single business environment and for a single player, Intel itself.

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The concept of co-opetition, as proposed by Brandenburger and Nalebuff (1996), wasthus expanded, since these authors treated only competitive and cooperative games.

Future developmentsOther theoretical and practical research articles, some of which are still being prepared,will ascertain whether the assumptions presented here are statistically valid. They willalso apply this matrix model to other complex situations of different conflict of interestsituations among numerous types of stakeholders.

As future developments, we also propose formal mathematical solutions to the newgames proposed here.

Conclusions and remarksThe present study expanded on the co-opetition concept proposed by Brandenburgerand Nalebuff (1995) and addressed the research problem of how to know which is theright game to play. We were able to answer the four basic research questionsformulated in the introduction:

(1) The question “Are competition and cooperation the only two models of behaviorthat executives should consider before deciding what game to play?” wasanswered by showing that, besides cooperation and competition, there are atleast three important, distinct and mutually exclusive types that may be used todescribe the competitive postures any given player can assume toward theother players: rival, individualistic and associative.

(2) The question “Does the power ratio among players define different games toplay?” was answered by showing that there are at least two types ofassumptions of power ratios that players can assume in any given game:balanced and unbalanced power ratios, both of which serve to characterizedifferent types of games to be played.

(3) The question “According to the concepts of classical game theory, what gameshould managers play in any given situation of conflict of interests, for eachdifferent situation of business they face?” was answered extensively throughthe descriptive and prescriptive SGM conceptual model.

(4) The question “What are the possible consequences of choosing the wrong gamein a typical situation of conflict of interests among players?” was answered; inshort, a player that chooses the wrong game may incur massive damages, both toobjective results and to the relationship between involved parties. Furthermore,the consequences of choosing the wrong game are far worse in the long run thanare those of making wrong decisions while playing the right game.

We examined a broad range of situations of conflict of interests in the business worldand came to the conclusion that another dimension besides competition andcooperation should be considered, namely, the power ratio among the players, whenthe question comes up as to what is the right game to play. This paper expands on theoriginal idea of co-opetition by providing a broader perspective for choosing a game toplay. As a possible model for this choice, the SGM is described and applied in thispaper. It indicates what games are advisable for each specific situation represented inthe cells of the matrix. The SGM treats nine different situations resulting from the


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combination of three different degrees of competition/cooperation and three differentdegrees of power ratios among the players. From the nine different situations, wederived six new games to be treated. Four of these have already been treated andsolved using the classical games, as Minimax, Pareto, Nash and Stackelberg games.The other two situations characterize two new games yet to be well-defined and solved:the paternalistic-solidary and the hegemonic-marginal games. Although these last twogames have not yet been fully solved, they are characterized and mathematicallydescribed in this paper.

Finally, the “Intel Case,” was presented as an illustration of the use of the SGM in the PCindustry. It proved very useful for illustrating the applicability of the SGM to analysis,interpretation and formulation of cooperative, competitive, and other strategies incomplex, multiple-interacting situations among agents in the business world.

The SGM therefore met the research objective proposed for this paper: developing agame theory-based tool that may be used by scholars and managers alike to identifywhich games can be played in each conflict of interest situation faced by companies intheir operating environment. Constructed with concepts taken from classical gametheory and with elements of the business world, the SGM is an original descriptiveanalytic tool for interpreting, analyzing, clarifying and formulating business strategiesand for supporting strategic management.

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About the authorsEliezer Arantes da Costa was born in Monteiro Lobato, Brazil, 1937. He received his BSc degree inElectronic Engineering from the Aeronautical Institute of Technology (ITA), Brazil, in 1962 and hisMSc and PhD degree in Electrical Engineering, in 1979 and 2008, respectively, both from the Schoolof Electrical and Computer Engineering, State University of Campinas (UNICAMP), Sao Paulo,Brazil. He worked as the head of the operational research team at Cia. Vale do Rio Doce a Brazilianiron ore exporter company, (1963-1974), and as staff member and executive for Promon Engenharia,Sao Paulo, Brazil, an engineering and project consulting company, (1975-1994). Now, he is workingas business consultant in strategic planning and strategic management for several companies,and for some non-profit organizations. He has published a book in strategic management,his main area of interest, in Portuguese, now in its second edition. Eliezer Arantes da Costais the corresponding author and can be contacted at: [email protected]

Celso Pascoli Bottura was born in Catanduva, Brazil, 1938. He received the BSc degree inAeronautical Engineering from ITA, Brazil, in 1962, the MSc degree in Mechanical Engineeringfrom Purdue University, USA, in 1964, and the PhD degree in Electrical Engineering from theUNICAMP, Brazil, in 1973. From 1984 to 1985, he was a Fullbright Visiting Scholar with theDepartment of Economics, University of California, Los Angeles. He is currently a Full Professorand a Member of the Laboratory for Intelligent Systems and Control, School of Electrical andComputer Engineering, UNICAMP. His research interests are in the areas of modeling,estimation and control, intelligent systems and control, dynamic games and strategicmanagement. He is a former President of Sociedade Brasileira de Automatica, the BrazilianSociety of Automatic Control. He has already published three books in his area of interest, all ofthem in Portuguese.

Joao Maurıcio Gama Boaventura was born in Sao Paulo, Brazil, 1962. He received the BSc,MSc and PhD degrees in Business Administration from the School of Business, Economics andAccounting of the University of Sao Paulo (USP), Brazil, in 1987, 1998 and 2003, respectively,from the same school. He is currently a Professor and a Researcher of the Graduate Program inBusiness Administration of the Fundacao Instituto de Administracao – FIA, Brazil. His researchinterest is in the area of strategic management and future studies. He has experience, as aprofessor of strategic management, in different business schools in Brazil, such as FundacaoGetulio Vargas, FECAP, UNIP and Trevisan.

Adalberto Americo Fischmann was born in Sao Paulo, 1946. He received the BSc in BusinessAdministration from USP, as well the PhD in Management. He realized Post-doctoral studies atthe Manchester Business School, UK, 1973-1974. He was a Fulbright – Visiting Scholar atMissouri Southern State University for the academic year 2006-07. He is currently a FullProfessor and a Research Coordinator at the School of Business, Economics and Accounting(USP), Director of the FIA, and Editor of Revista de Administracao. His research interest is in thearea of strategic management and future studies.


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