APPLICATIONS OF GAME THEORY IN A SYSTEMS DESIGN …

25th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES

APPLICATIONS OF GAME THEORY IN A SYSTEMS DESIGNAPPROACH TO STRATEGIC ENGINE SELECTION

Simon I. Briceno, Dimitri N. MavrisAerospace Systems Design Laboratory, Georgia Institute of Technology

Keywords: Systems Design, Decision Making, Game Theory, Engine Design

Abstract

Engine development programs present difficultand complex problems for manufacturers. Thetechnical requirements have historically beenaddressed through performance analyses using"physics-based" codes. To assess economic vi-ability of the engine programs, firms typicallycarry out extensive market and financial analyses.However, these analyses typically fail to considercompetitive market uncertainties due to limitedinformation about the competitor and the market.The use of game theory is explored in this pa-per as a method to assist the selection process ofcommercial engine architectures in the presenceof competitive uncertainties. A strategic simula-tion model is developed that represents the deci-sion analysis for a particular engine company. In-formation is continuously fed back from the mar-ket (and competitors) in order to allow the de-signer to identify the most profitable and compet-itive engines. Game theory-enabled analysis in-tegrated into this simulation within the strategicdecision model provides a basis for a systematicexploration of both engineering and business de-cisions. The analysis employs game theories toenumerate the decisions, moves, available and toformulate a process by which a winning decisioncan be achieved.

1 Introduction

The most important design choices an enginecompany makes are those strategic decisions thatdetermine the final engine core architecture and

size. The reasoning behind this is primarilydriven by the exceedingly high cost of core ar-chitecture development and the fact that these ar-chitectures must be capable of meeting require-ments as they emerge over time. The risk in de-signing these engines has meant that engine pro-gram launch decisions are becoming more andmore dependent on non engineering-related de-sign factors. A company cannot afford to base itsdecisions on information that does not accountfor the uncertainty associated with engineeringassumptions and customer requirements as wellas financial and competitive factors that are criti-cal to decision-making.

Understanding the changing requirementsand design uncertainty is only half the problem.Some type of analysis is needed early to con-sider the broader perspective of design for growthwithin a product family and how to strategicallyposition the family to maximize its return oninvestment in today’s and tomorrow’s markets.Furthermore, if one were to assume a rational,capitalistic society, then as a decision maker aglobal design objective would be to dominate therequirements space and maximize profitability.For these reasons technical and non-technical de-sign issues have to be addressed simultaneouslyearly in design in order to answer questions suchas: "how much design margin (for robustnessagainst uncontrollable design factors) is neces-sary?", "how much growth potential should bebuilt into the product?", "when is a strategic al-liance the optimal business strategy?"

Although it may be difficult to answer thesestrategic questions analytically, this challenge

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SIMON I. BRICENO, DIMITRI N. MAVRIS

Fig. 1 Players in Commercial Aircraft Engine Design

can be overcome with a framework that gives de-signers a means to use decision-critical knowl-edge to model, structure and negotiate solutionswithin the context of risk and uncertainty andultimately provide a foundation for exploringstrategic moves.

This paper proposes the development of astrategic decision-making simulation environ-ment that is capable of modeling a commer-cial engine selection process. The environmentutilizes business, engineering, and probabilis-tic tools to address the competitive nature ofthe problem and to provide mitigation strategiesfor uncertain solutions. In addition, formula-tions based on the well-established field of gametheory are employed to facilitate the decision-making process through a rapid and transparentpayoff simulation. The more complicated andcompetitive a given market is, the more there is aneed for quantitative methods for analyzing busi-ness strategies and the influence of engineeringdecisions on a strategy. It is therefore suitableto borrow some of these algorithms, couple themwith the physics of the problem and use them toguide the decision-making process.

2 Engine Design Programmatics

In today’s world where affordability precedesperformance in design, emphasis is placed onmaking the right decisions in the early phases of

design [1]. The margins on regulations, environ-mental awareness and life-cycle cost now havemore influence on the success of a program thanat any other time in the past. Decisions at themanagerial or higher level typically determinethe design path and are often made by those withlimited information or engineering knowledge ofthe product. The notion of strategic business de-cision making as part of the traditional designprocess was not thought of until recently. Com-mercial aircraft engine design is a typical exam-ple of business decision making in which enginemanufacturers are competing against one anotherin a global market in order to capture the largestmarket share possible. A complex relationshipexists between the engine manufacturers and theairframe companies and the airlines, as illustratedin Fig.1.

New design methods and computation ca-pabilities have allowed engine manufacturers toproduce highly complex and reliable engineswith substantially decreased operating costs.Modern designs however, continue to be morecomplicated and more expensive to manufacture.Risk is not only a function of the probability offailure but also the cost associated with failing.One approach suggested by Roth is to examinethis risk is to identify the main factors that drivethe likelihood and cost of failure [2]. The fourmain areas that have to be examined early in en-

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Applications of Game Theory in a Systems Design Approach to Strategic Engine Selection

Fig. 2 A Notional Engine Design Space

gine conceptual design are the uncertainty, com-plexity, technology and business environment.

2.1 Engine Design Uncertainty

There are several probabilistic methods that dealwith design uncertainty, requirements uncer-tainty, economic uncertainty, etc. Whether it isaircraft mission changes or changes in emissionsand noise regulations, there are emerging designmethods that allow decision makers to select themost robust or flexible design to all these uncon-trollable effects of the future. Probabilistic meth-ods are commonly employed to understand un-certain effects in design. Fig.2 illustrates someuncertain characteristics associated with enginedesign.

The points illustrated in this figure repre-sent specific engines and their associated thrustranges. The two notional architectures repre-sent two engine "cores" to which changes can bemade to create derivative engines. Although theengine design space occupies many dimensions,for visualization purposes two dimensions havebeen selected and shown here. Two types of en-gine sizing trends are shown. The first growthtrend is physics-driven, by which an engine canbe made to produce more thrust at the expenseof increased weight. The other growth trend istechnology-driven. The exact position of an en-gine in the space can be described as a probabil-ity distribution depicted as solid density contours

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0 10000 20000 30000 40000 50000 60000 70000

THRUST (LBS)

SF

C (

1/hr

)

GEAE Engines

PW Engines

IAE Engines

BMW-ROLLS

Fig. 3 Product Positioning of North AmericanCommercial Aircraft Engines [4]

centered around the nominal engine design point.The likelihood of a particular engine meeting theairframe design requirements can be determinedby the intersection of two joint probability dis-tributions. One that describes the airframe re-quirements uncertainty and the other that repre-sents the engine design uncertainty. Mavris andBriceno demonstrate a measure of design "suc-cess" that can be obtained by these probabilityintersections [3].

The analysis of uncertainty in engine design,discussed in the preceding section, does not ac-count for future engine design considerations. It

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considers only the impact of uncertainty on a sin-gle requirement point without considering the as-sociated uncertainty of evolving requirements. Inorder to take maximum advantage of emergingmarkets, designers must be prepared to strategi-cally position their core design relative to theircompetition and design along the lines of a prod-uct family instead of a single application. To bet-ter understand this broader perspective and howit interacts with the joint probabilistic require-ments/design space previously described, con-sider Fig.3 which is a representation of the air-craft engine industry as it stands today [4]. Notethat families of engines built around commoncores largely fall along a line of points, just aswas the case for Fig.2. Each point on the plot isan existing engine that represents a single "move"by an engine manufacturer to fulfill an engine re-quirement.

2.2 Engine Design Complexity

Engine complexity can be viewed as a degreeof balance between several competing aspects ofdesign including thermodynamic performance,cost, weight, maintainability, efficiency, etc. Tra-ditionally, the design of propulsion systems wasdriven mainly by performance and weight withvery little emphasis on efficiency and cost. Butwith the rising cost of fuel and a competitiveglobal market a new design paradigm is neededto address these issues [2].

2.3 Engine Technology Integration

Another trend visible in Fig.2 is technology in-tegration. In this type of growth, thrust maybe added to the engine at a constant weight, oreven with a weight savings, by the use of newtechnologies and the expense of increased enginecost. It is possible to see that none of the sixexisting engines in the two architectures shownin this figure satisfy the requirements; thus, anewly developed engine design will be required.However, infusing new technologies is inherentlymore risky and their performance in a produc-tion product can never be precisely known a pri-ori. With new technologies the core design space

must be described probabilistically due to un-known effects resulting from technology infu-sion.

In addition to probabilistic methods for tech-nology uncertainty evaluation there are well es-tablished techniques that focus on rapid identi-fication and evaluation of technology concepts,provide a risk/reward ranking of technology de-velopment options and provide a compromise be-tween analysis accuracy and time/cost to conductpreliminary-level technology assessments[5].

If technologies do not successfully improve adesign, the process might then involve the modi-fication of an existing engine or the creation of anew engine. The question of which path is bestnow arises and represents the engineering viewof the engine market problem.

2.4 Engine Design Business Environment

In conceptual design there is often a disconnectbetween decision makers that are at the engineer-ing design level and those managers at higher lev-els. This often results in failed promises to cus-tomers and the accumulation of financial penal-ties. A strategic business environment is an in-tegral part of the decision making process inthese phases, particularly in a competitive mar-ket where marginal improvements can be the dif-ference between a multimillion dollar profit or amultimillion dollar failure. Such risks can be mit-igated by introducing system thinkers to supportengineering scientists as they continue to be pres-sured by demands in increased productivity andefficiency. McMasters in Fig.4 affirms that "engi-neering is not done for its own sake, it’s practicedin context" to which he concludes that "in thefuture, the role played by the configurator mustnow be assumed by an increasing number of the"deep generalists" acting as system architects andintegrators." [6] The next sections describe how astrategic business environment can be employedas a simulation platform for engine design.

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Fig. 4 The Design Onion [6]

3 Strategic Decision Making Framework

The creation of a strategic decision-making en-vironment represents a major research challengeto engine designers. The modeling and analy-sis of uncertainty in requirements can alone posesignificant problems. But the added complexityof uncertainty associated with the larger strate-gic business environment can make the design ofengines a truly formidable challenge. These hur-dles are quickly being overcome with the aid ofemerging techniques found in fields such as gametheory, probability and decision theories, and in-novative systems design methods. These promis-ing new advanced analysis methods can be in-corporated into a strategic framework as shownin Fig.5. The central element of this vision isa global "plug-and-play" design and decision-making environment. As described earlier, thereare four areas of interest in the design of complexsystems: Uncertainty, Technology, Complexityand Business. Analyses within these areas aresupported by a visualization environment. Thistool facilitates the many trade-offs that are anal-ogous with this highly multi-objective space andenables the successful selection of a competitiveengine core. The process by which some of thesedesign methods may be employed is described inthe following sections.

A key requirement of this model is to linkthe basic engine design parameters with the over-all business metrics and encompass other mar-

ket variables such as competitor position, main-tenance effects, customer value, etc., that im-pact the return on investment. Creation of sucha model that accurately simulates the businessenvironment requires a substantial amount ofresources and expert knowledge. The genera-tion of these independent models are thereforenot within the scope of this research. Instead,the proposed strategic framework is supportedby a simulation environment that uses severalindustry-generated models and tools as a meansto validate the advanced design methods dis-cussed here.

An effective decision-making technique re-lies on the ability of the engine manufacturer toquantify the uncertainty associated with a givenset of requirements and determine an optimumstrategy which mitigates the implied risk. Thepossible management options must be clarified.Since engine design is a process, the develop-ment of a new engine is rarely characterized assimply a ’go’ or ’no-go’ decision. Alternatives tosuch oversimplification would include deferringa decision, continuing with initial developmentand then reassessing the project, and other mixedmanagement options. To construct the strategicframework, certain methods need to be createdthat will support the decision maker in the evalu-ation of these management options. These meth-ods may be characterized as essential "enablers"for this proposed decision framework. These en-ablers, critical for the development of the deci-sion making environment, include:

1. The creation of an integrated, physics-based environment for engine design.

2. Game Theory methods to address the pres-ence of competition, provide strategic solu-tions and to enable designers to efficientlysearch for such solutions through multi-objective optimization.

3.1 Engine Modeling and Simulation Envi-ronment

The modeling and simulation environment con-sists of a suite of analysis modules/tools that

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Fig. 5 Strategic Decision Framework

Strategic Decision Module

Engine Cycle and Flowpath Analysis

Aircraft Performance

Analysis

Engine Maintenance Module

Customer Value Analysis

Manufacturer Financial Analysis

Emissions

Noise

Competitor Engine

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4 5

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Fig. 6 Engine Modeling and Simulation Process

represent the different aspects of engine designand selection process. The different modulesare: Engine Cycle and Flowpath Analysis, En-gine Maintenance Model, Aircraft Sizing Model,Customer Value Model, Engine Financial Modeland Strategic Decision Model. Each module con-sists of an analysis method which can be either aphysics-based analysis code or analysis method.A schematic of this type of simulation environ-ment is illustrated in Fig.6.

The five main analysis modules that describe

the core engine design process are labeled 2through 6. Module 1 is a strategic decision modelthat allows the decision maker to switch strate-gies and monitor the overall progress of the sim-ulation. This is done through a graphical user in-terface, shown in Fig.7, which is coupled with themodeling and simulation process. The interfaceis also functions as a customer value model thatenables designers to incorporate the characteris-tics of airline operations into the engine selectionprocess.

The simulation process Fig.6 does not repre-sent any specific engine design program. It wascreated to characterize the interaction betweenthe different fields that influence the design pro-cess of a typical engine program. It is commonfor engine companies to design engines for dif-ferent airframe configurations they anticipate theairframer and market may introduce in the future.This simulation environment provides the enginemanufacturer with a testbed for new emergingtechnologies. The process outlined in Fig.6 hasthe capability of modeling various airframes inorder to test competing engines on multiple air-frames and over different mission scenarios.

A particular aircraft will typically have a va-riety of missions requirements throughout its lifewith an airline. These missions are often not sim-ilar in range and payload. For instance, airlinesoften operate the Boeing 777-200ER over a va-

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Fig. 7 Customer Value Interface Model

riety of different missions and payloads, rangingfrom 1000 nm to 6000 nm and with payloads of40,000 to 120000 lbs. Any combination thereofis feasible, provided that fuel volume and takeoffweight limits are met. Mission mixes potentiallyhave a large impact on engine design since theyare expected to perform optimally during everymission scenario.

3.2 Game Theory Implementation Process

To successfully create the efficient decision mak-ing environment described above, a generalmethodology for engine selection needs to be for-mulated that will require the application of ad-vanced methods to find the best set of strategiespossible. One potential technique is game the-ory. A comment in an article from a prominentmanagement consulting firm says that "The ap-plication of game theory is not going to give youa single answer. The best you can hope for is thatit forces you to categorize what you know, whatyou don’t know and what the drivers are." [7] Thefollowing sections discuss how game theory canbe applied to an engine selection problem.

3.2.1 Introduction to Game Theory

Many advances have been made over the past fewyears in the field of decision-making and new

innovative approaches and algorithms have beenproposed in the field of game theory. Game the-ory presents a logical and mathematically basedmeans of approaching problems involving com-petitors and decision making. A game is a modelof a competitive situation, and game theory is aset of mathematical methods for analyzing thesemodels and selecting optimal strategies. Gametheoretic methods also provide a basis for enu-merating decisions available, evaluating optionsor "moves", ruling out "moves" that do not makestrategic sense, determining the viability of part-nerships, and conducting "what-if" analyses forvarious scenarios. These techniques can be ap-plied to solve most decision making problems bycreating games where the following "rules" areestablished[8]:

• There are two or more autonomous deci-sion makers called players;

• Each player has a choice of two or moreactions;

• A player’s information set is his/her stateof information at the time he or she takesan action.

• A strategy is a rule to tell the player whichof the available actions to choose, subjectto available information, each time he/shemakes an action.

• The payoff of a game for each of its play-ers can be be defined in either of two ways:a) as the utility received at the end of thegame, or b) as the expected utility obtainedas a function of the strategy space of aplayer.

The more complicated and competitive agiven market is, the more there is a need for quan-titative methods for analyzing business strategiesand the influence of engineering decisions on astrategy. It is therefore suitable to borrow some ofthese algorithms, couple them with the physics ofthe problem and use them to guide the decision-making process.

The game model itself can contain sophis-ticated company analysis codes and simplifieddescriptions of competitors. Game theory may

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involve the application of simple optimizationsof combinatorial problems, including for in-stance, the application of "competing" genetic al-gorithms as players in a game model.

The use of game theory in this paper is dis-cussed as a method for assisting the process ofselecting commercial engine architectures in thepresence of competitive uncertainties. A gametheoretic optimization scheme is then coupledwith the selection process to evaluate the multi-objective problem that is common in engine de-sign.

3.2.2 Technique Review

There are several types of games and a descrip-tion of their mathematical implementation in [9].Game theory has taken a supporting role in de-cision making for large complex design prob-lems. One approach to engineering design is the"Game-Based Design" method that describes themathematic principles of rational behavior for de-cision makers in design scenarios [9]. It com-bines game theory, decision theory, utility theory,and Bayesian probability theory to assist withthe non-subjective rational decision making pro-cess. Further research in multidisciplinary de-sign problems has been conducted by employ-ing game theory techniques. An approach tothis problem has been to study the interactions inmultidisciplinary design as a sequence of gamesamong a set of players, which are embodied bythe design teams and their computer-based tools[10].

Game theory is not only prevalent as a de-cision making tool but also as a multi-objectiveoptimization method. It has been demonstratedhow game theory as a design tool applies be-yond scalar optimization to the multi-criteria op-timization problem. The multi-criteria optimiza-tion task is examined not only from the perspec-tive of a single designer but from that perspectiveof team design as well [11, 12]. The aspect ofoptimality may be used when a multi-objectivedesign problem has been assigned to several de-signers or design teams with each designer be-ing responsible for one or more design objectives.

- Core Size Selection - Architecture Selection - Cycle Selection

Do Nothing

Engine Company Response to Emergence of Engine Requirement

Compete Exit Market

Upgrade Existing Core Design New Centerline

Tech 1

Tech 2

etc... Tech 1

Tech 2

etc...

(Introduce New Techs)

Strategic Alliance (?)

Fig. 8 Notional Engine Tree Decision Game

Decentralizing responsibility in such a way is anatural choice in the design of large-scale sys-tems integration such as aircraft-engine match-ing. With several designers each with his ownobjectives, the nature of the optimization processcan take several paths and the total design maynot be optimal in the sense that a single designertheoretically could do better. Game theory ap-plied to this type of situation provides a methodfor understanding and perhaps guiding the opti-mization process. As such, it provides an impor-tant management tool for use in decentralized de-sign. The following section outlines an approachfor strategic design for an engine design problem.

3.2.3 Game Process for Engine Design

A notional competitive scenario between enginemanufacturers can be translated into a gameboard wherein each competitor has certain strate-gies that can be carried out. Fig.8 shows a sim-ple example in decision-tree format of the avail-able strategies that a typical engine manufacturermight have. In reality, many more sub-decisions,like resource allocation, will have to be made un-der each of these. However, this provides a goodstart to enumerating decisions that must be madeinitially at the start of an engine program.

The game process as shown in Fig.9 begins

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with a clear list of design actions available to eachengine manufacturer, player, as stated above. Thesimulation begins with the emergence of a newrequirement. This could be in the form of a newairframe or an airframe variant. All pertinent in-formation related to the problem, including anyknowledge about the competitor and their posi-tion in the market is collected. A comparisonis made between the players’ engine capabilitieson multiple dimensions like thrust, SFC, engineweight, etc., as depicted in Fig.3. Each playermust then assess their strategic options and ca-pabilities with respect to these requirements andtheir competitors’ strategic options. This can bedone by generating scenarios that are representa-tive of potential strategy combinations.

A new technique called "Competitive Adap-tation" uses the natural adaptation mechanismsfound in nature as a model for "artificial adap-tation" of complex scenarios[13]. In particular,certain optimization techniques such as geneticalgorithms and evolutionary game theory[14, 15]can be implemented to create a pool of game sce-narios as shown in the middle box of Fig.9.

Once the game board is mapped out and thegame scenarios are outlined, they are run throughsimulation model shown in the bottom box ofFig.9. This primarily consists of the modelingand simulation environments described earlier inFig.6. The pool of scenarios are modeled throughthis environment for the purpose of assessingwhich engine designs are more robust to mar-ket and competitive uncertainties. Each playerhas the ability to individually change the set-tings/characteristics of their simulation to max-imize their market share. The market assump-tions are dictated by representative airlines thateach have differing operating structures and pref-erences on the engines. The market share is de-termined based on how well the engines matchthe needs of the airlines. For each scenario simu-lated, the overall market share will be determinedbased on the airline preferences dialed into the in-terface tool in Fig.7.

As part of the simulation process, an opti-mization scheme is implemented by each playerso as to search for potential designs that would

Design Options

Strategic "Moves"

A - Throttle Push B - Bill of Materials C - New LP System D - New HP System

A

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ABCD

Throttle Push (if requirements are within throttle push margin)

Throttle Push + Bill of Matl's (if reqt's within throttle push and matl's margin)

Fixed Core Derivative (if reqt's are within core power margin)

Fixed Centerline Derivative (if reqt's are within centerline power margin)

New Cycle (for any cycle, core power margin, throttle push margin)

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Game 1

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Move "chromosomes" for B

1 Game Scenario

Pool of n Game Scenarios

Engine Market Model

Player C

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Modeling and Simulation

Environments

A Engine Value

B Engine Value

C Engine Value

A Market Share

B Market Share

C Market Share

Simulation Model

A Payoff

B Payoff

C Payoff

Move "chromosomes" for A

Move "chromosomes" for C



Aircraft Performance Analysis




Emissions

Noise

Competitor Engine

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Emissions

Noise

Competitor Engine

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Emissions

Noise

Competitor Engine

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Fig. 9 Game Simulation Process

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be more competitive and thus more successful inthe game. This optimization process is in mostcases multi-objective with a large number of sig-nificant variables. This multi-objective enginedesign problem may be envisioned as a game inwhich the objective functions are market shareand net present value function. The variablesare each player’s strategy choices and they com-pete to optimize their position in a system subjectto constraints. Economists, in studying competi-tive systems, have developed theories for gameswhich are readily applicable to engineering de-sign. Two theories have been used to describe theinteraction of players: the noncooperative theory,based on the concept of Nash Equilibrium[16],and cooperative game theory, based on the con-cept of Pareto minimum solution [17].

The fundamental assumption in noncooper-ative theory of games is that players are onlyconcerned about their own interests. Players se-lect strategies to optimize their position or payoffwith no concern of how their choice will affecttheir opponents or their objectives. In repeatedgames, players may have the option to bargainor negotiate in order to improve their situation.At the end, there is typically an game equilib-rium that has been achieved. This solution isoften referred to as a Nash equilibrium. At thisequilibrium, no player may improve his objec-tive by unilaterally changing their strategies, aslong as the other players maintain their selectedstrategies. Multiple equilibrium points may ex-ist depending on the order and in which playerschoose strategies. Theories on first and secondmover advantage may demonstrate this effect. Fi-nally, although the Nash equilibrium is generallythe "safe" strategic combination for players, thereare solutions that exist where players may havebetter payoff values.

In cooperative game theory, each playerworks collectively as a group in which eachplayer is willing to compromise his own objec-tive to improve the group solution. A Pareto op-timal solution is then achieved select strategiesthat are as optimal as possible to all players. Un-like non-cooperative theory, each player must se-lect strategies that are beneficial to them but not

detrimental to another player. One method isto select strategies such that all players are asfar from their worst cases as possible. The bestknown method of optimizing several objectiveswhile leaving them independent of one anotheris the minimax method. This entails minimizingthe maximum deviation from the objective goals(desired values) with the constraint that the solu-tion be Pareto optimal. A Pareto optimal solutionis a solution to a multi-criteria problem in whichany decrease in one objective results in a simul-taneous increase in one or more of the other ob-jectives.

An advanced approach to cooperative mod-eling is through the construction of rational re-action sets (RRS) [10]. The RRS of a playercharacterizes how a player would react to anystrategies and variables that other players have.This method is most beneficial if approximatedthrough design of experiments and response sur-face methodology [18].

These techniques described above are intro-duced into the optimization phase of the mod-eling process where the engines undergo designchanges and technologies are implemented to im-prove on the competition. After a competitiveassessment is made with the new optimized en-gine, a decision is made to determine whetherfurther optimization is required or if new designrequirements should be introduced into the mod-eling process. The game simulation becomes aniterative process that allows the decision mak-ers to conduct "what-if" analyses for various sce-narios with his/her competitors. An organizedframework for decision making is therefore gen-erated by reducing the complexity of engine de-sign down to the critical decision criteria and ob-jectives.

4 Conclusions and Future Work

This paper introduced an approach to commercialengine selection that can benefit decision mak-ers under time constraints and with influentialsources of uncertainty. The method proposed as-sists decision-makers in answering global ques-tions regarding the basic architecture and core

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size/growth path decisions. A variety of gametheoretic techniques were discussed as a way tooptimize engine architectures in the presence ofcompetitive uncertainty and as potential means toquantify and evaluate the influence of present andfuture market competition on the decision mak-ing process.

Future simulation studies will involve explor-ing the probability and timeline of the intro-duction of derivative aircraft in order to assesslong-term competitiveness and assist in core sizeand architecture selection. Engine sizing strate-gies may differ significantly if an engine is de-signed for maximum performance as an entry-into-service engine versus one that performs wellover a spectrum of derivative aircraft. An exam-ple is demonstrated for the regional jet market in[19].

References

[1] Mattingly, J. D., Heiser, W. H., and Pratt, D. T.,Aircraft Engine Design. AIAA Education Se-ries, 2nd edition ed., 2002.

[2] Mavris, D. and Roth, B., “Commercial EngineArchitecture Selection in the Presence of Uncer-tainty and Evolving requirements,” ISOABE, IS-ABE - International Symposium on Air Breath-ing Engines, 2001.

[3] Mavris, D. N. and Briceno, S. I., “Imple-mentation of a Physics Based Decision Mak-ing Framework for Evaluation of the Multi-disciplinary Aircraft Uncertainty,” World Avia-tion Conference (WAC) SAE, no. 2003-01-3055,2003.

[4] “Aerospace Source Book,” Aviation Week &Space Technology, January 2001.

[5] Kirby, M. R., A Method for Technology Identifi-cation, Evaluation, and Selection in Conceptualand Preliminary Aircraft Design. PhD Thesis,Georgia Institute of Technology, 2001.

[6] McMasters, J., “From farther, faster, higherto leaner, meaner, greener - Future directionsin airplane design in the new century,” 41stAIAA Aerospace Sciences Meeting & Exhibit,no. 2003-0553, 2002.

[7] “Games or Serious Business?,” The FinancialTimes, March 2002.

[8] Hazelrigg, G. A., Systems Engineering: An Ap-proach to Information-Based Design. PrenticeHall, 1996.

[9] Marston, M. C., Game Based Design: A GameTheory Based Approach to Engineering Design.PhD Thesis, Georgia Institute of Technology,2001.

[10] Lewis, K. and Mistree, F., “Modeling interac-tions in multidisciplinary design - A game theo-retic approach,” AIAA- Symposium on Multidis-ciplinary Analysis and Optimization, 1996.

[11] Vincent, T. L., “Game Theory as a Design Tool,”Journal of Mechanisms, Transmissions, and Au-tomation in Design, vol. 105/165, 1983.

[12] Sen, P. and Yang, J.-B., Multiple Criteria Deci-sion Support in Engineering Design. Springer-Verlag London, 1998.

[13] Simon, H. A., The Sciences of the Artificial.MIT Press, 3rd edition ed., 1996.

[14] Vincent, T. L. and Brown, J. S., Evolution-ary Game Theory, Natural Selection, and Dar-winian Dynamics. Cambridge University Press,2005.

[15] Samuelson, L., Evolutionary Games and Equi-librium Selection. MIT Press Cambridge, Mas-sachusetts, 1997.

[16] Nash, J. F., “Equilibrium Points in N-personGames,” Proceedings of the National Academyof the USA, vol. 36(1), 1950.

[17] Rao, S. S. and Freiheit, T. I., “A Modified GameTheory Approach to Multi-Objective Optimiza-tion,” ASME Transactions, vol. Vol. 113, 286,1991.

[18] Myers, R. H. and Montgomery, D. C., ResponseSurface Methodology: Process and Product Op-timization Using Designed Experiments. Wiley,2002.

[19] Ramsay, B., “Trends in Regional A/C EngineDevelopment,” 2003 AIAA/ICAS InternationalAir and Space Symposium and Exposition: TheNext 100 Years, 2003.

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APPLICATIONS OF GAME THEORY IN A SYSTEMS DESIGN …