Honor among Thieves: Cooperation as a Strategic Response to Functional Unpleasantness

William B. Heller and Katri K. Sieberg

Honor among Thieves: Cooperation as a Strategic Response to Functional Unpleasantness

William B. Heller

Department of Political Science Binghamton University

wbheller@post.harvard.edu

Katri K. Sieberg Erkko Chair of North American Studies

University of Tampere, Finland Katri.sieberg@uta.fi

Version 1.13 February 2008

Abstract Stuff

We thank Erik Sieberg and Teresa Heller for their patience. We happily note that they bear no resemblance to the subjects in this paper. Whenever possible, each of us takes full credit for everything good in this paper and blames the other for all errors and omissions.

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Cooperation is difficult. Even if people want to treat each other fairly, collective dilemmas abound. Standard rationales for cooperation, such as small-group dynamics (Olson 1965), repeat play (Axelrod 1984), reciprocity (Boyd et al. 2003), do not apply to the kind of everyday cooperation we see where people interact, generally without conflict, with others whom they do not know and have no reason to expect to see again. As long as some people are willing to deviate from whatever behaviors are perceived as cooperative—that is, to cheat—cooperation cannot survive absent some enforcement mechanism. Cheaters are not necessarily “bad and ever ready to display their vicious nature,” as Machiavelli (1940 [1531]) characterized people nearly 500 years ago, but they nonetheless take advantage of others who might prefer cooperation over competition and conflict. People can and clearly do cooperate, however; but how does cooperation survive in the face of pervasive self-interest and the concomitant ubiquity of collective dilemmas? One solution is government—centralized enforcement of generally understood rules (Levi 1989; Weber 1958; and cf. Bates 2001; Flack et al. 2005a; Flack et al. 2006; Flack et al. 2005b; North 1990; Sieberg 2005). An alternative solution for many types of collective-action problems is decentralized enforcement: if enough individuals are willing to punish cheaters, even at a cost to themselves, cooperation can endure.

That individuals should be willing to bear costs in order to punish cheating behavior is itself problematic. Evidence from economics experiments (see, e.g., Axelrod 1984; Bowles, and Gintis 2002; Boyd, and Richerson 1992; Ensminger 2001; Fehr, and Gächter 2002; Fehr, and Rockenbach 2003; Henrich, and Boyd 2001; Henrich et al. 2001) as well as observation suggest that such punishment occurs (at least when the stakes are low; Henrich 2000); the problem is, paying costs to punish is irrational when the benefits are dispersed throughout society. Typically, scholars assume that some actors value cooperation enough to punish noncooperators (see, e.g., Boyd et al. 2003; Boyd, and Richerson 1992; Fehr, and Fischbacher 2003; Fehr et al. 2002; Fehr, and Gachter 2002; Fehr, and Gächter 2000; Fehr, and Henrich 2003; Fehr, and Schmidt 1999; Fowler 2005; Henrich 2004; Ostrom et al. 1992). Alternatively, Heller and Sieberg (Forthcoming) show using evolutionary game theory that fair players who do not themselves punish cheaters can survive in a population of cheaters, as long as some cheaters also are punishers.

In Heller and Sieberg’s (Forthcoming) analysis, actors behave according to type—Fair, Cheating, or Unpleasant (who both cheat and punish other cheaters). Unpleasant players turn out to be functional for society by creating the conditions for the survival of cooperation, even though they do not themselves value cooperation. In this paper we add a new dimension to Heller and Sieberg’s argument by modifying their Unpleasant player to account for strategic behavior. This player, the Strategic Unpleasant (SU) player evinces Unpleasant behavior (i.e., punishes cheaters), but also behaves cooperatively if the probability of being punished for cheating (that is, of meeting up with another Unpleasant player, whether strategic or not) is sufficiently high. We show that the presence of these SU players also makes cooperation possible, even when no one in society wants to play Fair.

Lit Review Homo politicus and homo economicus are nothing if not opportunistic. Unlike other social animals, however, people seem to recognize and care whether others behave fairly. Rhesus macaques might cultivate friendships in the interests of forming support coalitions (Maestripieri 2007), suggesting that they can recognize and behave according to some norm of reciprocity,

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much as people are observed to do (Dawes et al. 2007; Fehr, and Schmidt 1999; Pulkkinen 2007). Rhesus monkeys behave cooperatively only when the cost-benefit calculation is in their favor. Humans, by contrast, as demonstrated in “ultimatum game” experiments seem willing to forego some personal gains—in effect, to pay a cost—in order to provide a relatively equitable distribution of resources to others (Camerer 2003).1 More to the point, people who do not behave “fairly” in experiments find themselves the object of punishment (see, e.g., Axelrod 1984; Bowles, and Gintis 2002; Boyd, and Richerson 1992; Ensminger 2001; Fehr, and Gächter 2002; Fehr, and Rockenbach 2003; Henrich, and Boyd 2001; Henrich et al. 2001), at least when the stakes are low (Henrich 2000), and researchers around the world have found that “about half” of all players in myriad plays of the game reject offers that yield them less than 20% of the initial sum (Nowak et al. 2000; cf. Fehr, and Gachter 2002; Güth, and Tietz 1990; Henrich, and Boyd 2001). Skyrms (2003) shows, using evolutionary game theory, that players in societal ultimatum games generally will settle with splits (the specifics of his model yield a 50-50 split). When chimpanzees play the same basic game (for grapes rather than money), however, they neither play fairly nor do they punish each other for choosing selfishly (Jensen et al. 2007). They are, to put it simply, rational.

Fair play—or at least the willingness to punish those who do not play fair—might be a uniquely human trait. By the same token, it is reasonable to suppose that those who play fair do so precisely because they are afraid of being punished. Fehr and Fischbacher (2003) show that people both expect others to cheat and are very good at recognizing cheating behavior. Given the right conditions, individuals who punish unfair behavior (which we shall generically term “cheating”) can ensure the survival of cooperation and, hence, of society. Given social norms that define what is fair (Fehr, and Rockenbach 2003; notions of fairness can vay across societies; Vogel 2004) and a credible willingness on the part of individuals or groups to punish violations of those norms (Flack et al. 2005a; Flack et al. 2006; Flack et al. 2005b; Levi 1989), cheating turns out to be unprofitable on average, opening the door to the evident human capacity to cooperate in “large groups of unrelated individuals” to build societies without the benefit of government (Wedekind 1998; see also, e.g., Bowles, and Gintis 2002; Fehr, and Fischbacher 2003; Fehr, and Gachter 2002; Henrich, and Boyd 2001; Rubin 2002).

A taste for reciprocity need not signal a concern for fairness. Does a willingness to punish, at personal cost, unfair behavior without a reasonable expectation of later benefits imply that people value fairness? It could, and many efforts to unravel the question of why people tend to treat strangers well begin with the assumption that at least some people care enough about fairness in and of itself to forego gains from cheating as long as others also play fair (see, e.g., Boyd, and Richerson 1992; Boyd et al. 2003; Camerer, and Fehr 2006; Fehr, and Fischbacher 2003; Fehr et al. 2002; Fehr, and Gächter 2000; Fehr, and Henrich 2003; Fehr, and Schmidt 1999; Fowler 2005; Hibbing, and Alford 2004; Henrich 2004; Ostrom et al. 1992; Sigmund, and Nowak 2000). Alternatively, playing fair and punishing others for cheating could amount to a strategic investment in personal reputation that reduces the chance of being cheated in the future (see, e.g., Fehr, and Fischbacher 2003; Fehr, and Henrich 2003). In a world that is divided into distinct competing groups, norms that encourage cooperation within a group, along with individuals willing to enforce them, might make it stronger vis-à-vis other groups (Sethi, and

1 In an ultimatum game, two players have to agree on a division of a sum of money, with one player proposing a division and the other accepting or rejecting. If the proposal is accepted, the money is divided according to the proposal; if the proposal is rejected, neither player gets anything.

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Somanathan 1996; and cf. Fowler 2005). Underpinning this latter approach is the notion that there are two levels of selection and payoffs: on one hand, competition among individuals means that individuals who punish free riders suffer reduced fitness; on the other hand, competition among groups favors those that include such punishers and thus are better equipped to engage in collective action to produce, employ, and consume collective goods (Fowler 2005; Henrich 2004; Sethi, and Somanathan 1996; and cf. Rubin 2002).

People do punish others, even at a cost to themselves, who behave in ways that they perceive to be unfair (Nowak et al. 2000; Herbert Gintis, cited in Vogel 2004). Experiments by Fehr and Fischbacher (2004) show that even people who observe but are unaffected by cheating behavior are willing to punish it, even at a cost to themselves, lending credence to the notion that cooperation survives precisely because people care about fairness. Of course, no one wants to cooperate if cheaters can ignore societal norms unimpeded (Sieberg 2005), because absent some kind of punishment it pays to cheat. A frequent explanation for the apparent irrationality of punishing cheaters is culture. Cultural familiarity can breed trust, creating repeat-play conditions that support opportunities for cooperation (but see Cook et al. 2005). Alesina and La Ferarra (2002) find that group heterogeneity increases the transaction costs of social experiences with members of other groups. Barr (1999) and Coleman (1990) argue that “familiarity breeds trust.” The cultural effect, however, relies on the assumptions that groups are small and homogeneous enough for players to have sufficient information to sanction one another for cheating (Saari-Sieberg 1998). It also relies on the assumptions that members value cooperation and that they care enough about other members in their group that they will both cooperate with them and will punish cheaters.

The cultural explanation finds mixed experimental support. In games that tested willingness to contribute to a group, Brandts, Saijo, and Schram (2004) found little evidence for cross-country differences in behavior in Japan, the Netherlands, and Spain. However, Ockenfels, and Weimann (1999), in comparisons of games between East and West Germans, found more selfish behavior in East Germans than in their West German counterparts. Ultimately, there are any number of possible origins of the drive to punish—it could be ingrained and emotional (Bowles, and Gintis 2002; Sanfey et al. 2003; and see Bewley 2003), strategic (Fehr and Fischbacher 2003; Fehr and Henrich 2003), or based on reciprocity built on an altruistic concern for fairness (Dawes et al. 2007; Fehr, and Schmidt 1999; Pulkkinen 2007). Heller and Sieberg (Forthcoming) take a different tack, abandoning the notion that people punish cheating because they value fairness. Rather, they posit a new breed of Unpleasant players, who cheat whenever they can but punish other cheaters, not because they care about fairness but because they are, in a word, unpleasant.

In Heller and Sieberg’s (Forthcoming) analysis, Unpleasant players, by penalizing cheating behavior, make it possible for Fair players to persist in society. In this paper we take the analysis a step further, by introducing the potential for some of the Unpleasant players to use strategic behavior—in the form of ‘acting fair’ in the hopes of avoiding punishments from other Unpleasant types. This type of player is not a true Fair player and will, in fact, cheat in any opportunity to do so with impunity. Instead, he/she represents the notion of “honor among thieves.” To explain, many analyses of criminal behavior (Becker 1968; Sieberg 2005) note that criminals frequently are strategic and that many will avoid committing certain crimes if they believe that it is likely that they will get caught. This avoidance on their part does not mean a change of heart; rather they simply choose to commit their crimes at a different time or location. Our Strategically Unpleasant player is similar. She wants to cheat and will do so when the

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circumstances are favorable, but will behave fairly if the risk of being punished is high enough. Interestingly, the presence of this type of player not only makes Fair behavior a possibility, but over time it also makes fair play the observed societal norm.

Building on the criminal analogy, several researchers (Sieberg 2005; Skaperdas 2001) have noted the ability of mafia groups to provide cooperation in a given area. Generally, these analyses protray this cooperation production in the form of protection or contract enforcement services. In a parallel to our argument, the mafia punishes those who fail to cooperate. These services are provided by the mafia in order to maximize revenues from the society in question. The ability to provide the services is largely derived from the power, size, and resources of the mafia. Thus players who are not themselves inclined to obey the law can bring about cooperative behavior. Our result, in contrast, does not rely on the factors of group size or power. Instead, we show that individual Unpleasant players who strategically play fair when they deem it necessary to avoid punishment can enter a group of Cheaters and Unpleasant players and eventually dominate it.

Modeling Strategic Cooperation Previous analyses of the survival of cooperation in human society begin with the assumption that at least some people are by nature Fair. We show that it is possible for cooperation to emerge even in a society where everyone prefers to cheat others, as long as two conditions hold. First, some Cheaters must also be Unpleasant players who cheat and punish other players who cheat; and second, some Unpleasant players must also want to avoid being punished for cheating and be capable of strategically cooperating—playing fair—when the probability of meeting another Unpleasant player is high. We thus begin with a population of three distinct types: pure Cheaters (C), pure Unpleasant players (U), and Strategic Unpleasant players (SU).

Consider the kind of everyday activities that require cooperation, but that do not amount to collective action except in a minimal sense. Such quotidian activities as driving on public roads, walking in crowded hallways, or buying tickets for a popular show would be chaotic at best if people did not evince at least some consideration for the effect of their behavior on others.2 When people do not cooperate, at least in the sense of trying not to get in each other’s way, problems arise. As long as each driver on a crowded but not jammed freeway in essence cooperates with all other drivers—by moving with the flow of traffic, maintaining a judicious distance from other vehicles, and changing lanes only when it is possible to do so without risking an accident or forcing others to swerve or brake—traffic moves safely and reasonably rapidly. We define the payoff in this situation, when everyone is playing fair, as [ )0,1α ∈ . A Cheater on the same road—someone who drives faster than others, passes on both left and right, cuts into lanes so close to other cars that their drivers have to slow or swerve, or both—moves at least as fast and probably faster than everybody else. We normalize the payoff to successful cheating as 1. If β is the cost of being cheated—e.g., the time lost from having to slow down, or even being involved in an accident occasioned by but not affecting a C player, then the payoffs when two C

2 The rules governing this class of day-to-day cooperation vary widely, as anyone who has driven in different cities or countries can attest. Cooperation exists even on the streets of Boston or Mexico City, however—people make it home for dinner and near misses far outnumber accidents—even though it might not be obvious to an outsider.

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players meet are 1 and 1 β− , as when a speeding driver is overtaken and cut off by a faster driver: a player can cheat or be cheated, but not both. If everyone cheats, then everyone’s net

payoff is 1 12

β+ − . We assume that Unpleasant players, unlike pure Cheaters, cannot be cheated.

Rather, like a driver who slows down in order to box in a car that was seeking to pass on the left, they pay a cost, φ , every time they punish another player, who consequently pays γ . (Table 1 summarizes our basic notation and the relative values of key parameters.)

Table 1. Basic Notation and Parameter Limits [ )0,1α ∈ Payoff to fair player meeting fair player (baseline)

β , β α< Cost of being cheated φ , φ γ< Cost of punishing γ , γ β> , 1 γ α− < Cost of being punished

[0,1]q∈ Probability that a SU player plays fair

When two pure U players meet, one pays a cost φ to punish the other, who in turn pays γ , the cost of being punished. In a population of pure U players, on average everyone punishes half the

time and receives punishment the rest of the time, so everyone’s expected payoff is 2

2 γφ −− , as

shown in Table 2. A C player in a population of U players does rather less well, with an expected

payoff of 2

2 βγ −− , while a U player invading a population of C players can expect 2

2 φ− . As

long as φ β< , i.e., the cost of punishing is less than the cost of being cheated—which makes punishing cheaters and thereby avoiding punishment reasonable—pure U always beats pure C (for a full discussion of interactions between C and U players—and including Fair players as well—see Heller, and Sieberg Forthcoming).

Table 2: Payoff Matrix with Three Player Types

Payoff to When meeting population of

C U SU

C 2

2 β− 2

2 βγ −− 2

2 ββγ q+−−

U 2

2 φ− 2

2 γφ −− 22

qγ φ φ− − +

SU 2

2q qφ α− + − ( )2 1

2qγ α γ φ− + − + + −

( )2 12

qφ γ φ α γ− − + − + +

Bringing SU players into the mix changes the dynamics. Like their pure-U counterparts, SU players always punish cheaters. Unlike pure-U players, however, SU players are increasingly likely to cooperate, neither cheating nor suffering the consequences of punishment, if the probability of meeting up with another U or SU player is sufficiently high. If for a given population mix q is the probability that an SU player will play fair, the payoffs to an SU player in

a population of C or pure-U players are 22

q qφ α− + − and [ ]2 12

qγ α γ φ− + − + + −, respectively

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(see Table 2). The respective payoffs to C and pure-U players in a population of SU players are

22 ββγ q+−− and ( )2

2qγ φ φ− − +

, while a SU player in the same population can expect a

payoff of [ ]2 12

qφ γ φ α γ− − + − + +.3

Of the three actor types we have defined—C, U, and SU—none would ”cooperate” and not cheat on their fellows if they could get away with cheating. Of the three types, only SU players even have the option of cooperating. Is it nonetheless reasonable to expect to observe fair behavior emerging and surviving as an evolutionarily stable strategy (ESS)?

Fair play, as a consequence of strategic cooperation by SU players, can emerge as an ESS if SU players do better among their own type than either pure-U or pure-C players. For this to be the case, the following two conditions must hold:

Condition 1: ( )2 1 22 2

q qφ γ φ α γ γ φ φ− − + − + + − − +>

Condition 2: ( )2 1 22 2

q qφ γ φ α γ γ β β− − + − + + − − +>

Condition 1 holds if ( ) 01 >−+γαq . This simplifies to γα −>1 , which is one of the given constraints on γ and implies that Condition 1 holds for any proportion q of SU players. The underlying intuition of Condition 1 is straightforward and reasonable: in order for strategically cooperative, punishing behavior to survive, it must yield a higher payoff than cheating and being punished.

Condition 2 reduces, with a little algebra, to ( 1 )q qβ α γ φ β φ+ − + + + > + , which obtains as long

as q is sufficiently large—specifically, 1

q φ βα γ φ β

−>

+ + − −. Whether or not Condition 2 holds

therefore depends on the relative values of the variables. If βφ > , for example, then numerator and denominator both are positive (since we know that 1 0α γ+ − > ), and the entire fraction is less than 1. If, as is eminently plausible if SU players are truly strategic, q increases with the probability of punishment for cheating, it should be quite high (essentially 1) in the all-SU population contemplated in Conditions 1 and 2 above. Condition 1 should hold, therefore, under reasonable conditions.

If φ β< , by contrast, the numerator is negative, but the denominator can be either negative (if 1φ β α γ− > + − ) or positive (if 1φ β α γ− < + − ). In the latter case, the right-hand side of the

inequality is negative, making fair play reasonable for any value of 0q > ; in the former case, the entire fraction remains positive, and q again must be relatively large. (Note that q cannot be greater than 1, which implies that if the entire fraction is positive then it must be the case that

1φ β φ γ α β− < + − + − . This condition holds nicely because 1α γ+ > by assumption, so it

3 Here we follow Heller and Sieberg (Forthcoming) in assuming that U players cannot be cheated. Half the time they recognize and punish cheaters (U or C), and half the time they have the opportunity to cheat (or to be punished). Heller and Sieberg (Forthcoming) provide an appendix with a more complicated model that allows U players to be cheated and to punish simultaneously.

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follows straightforwardly that 0 1γ α< + − .) It is therefore possible to see strategically fair behavior emerge despite the complete absence of dedicated (or, depending on one’s perspective, naïve) Fair players in the population.

Fair play can emerge in the form of a Strategic Unpleasant ESS. This potential is noteworthy, but not exceptional, given that in a pure SU population, the players are difficult to distinguish from Fair players who punish Cheaters. Literature on cooperation has long established the role that Fair Punishers play in establishing and maintaining cooperation (see, e.g., Boyd, and Richerson 1992; Boyd et al. 2003; Camerer, and Fehr 2006; Fehr, and Fischbacher 2003; Fehr et al. 2002; Fehr, and Gächter 2000; Fehr, and Henrich 2003; Fehr, and Schmidt 1999; Fowler 2005; Hibbing, and Alford 2004; Henrich 2004; Ostrom et al. 1992; Sigmund, and Nowak 2000). Thus, to distinguish our Strategically Unpleasant players from Fair players who punish cheating, we explore their behavior in groups of other player types. To this end, it could be that the pure Strategic Unpleasant ESS need not be the sole ESS possible. For our purposes, the more interesting question is whether SU players can contribute to an ESS that includes fair behavior in a population that includes C or pure-U players, who of course never cooperate. We begin by looking at the possibility of an ESS with a mix of SU and U or SU and C players. Intuitively, fair play should be less common in a population of C and SU players, and relatively more common in a population of pure-U and SU players.

To see if an ESS with a mix of C and SU players is possible, we calculate the population proportions of the two player types. Formally, if p is the population proportion of SU players and 1 p− is the proportion of C players, as shown in Table 3, then a C–SU mix can be an ESS if

( ) ( ) ( ) pqpqqpqp2

1212

22

212

2 γαφγφαφββγβ ++−+−−+−

−+−=

+−−+−

−

—that is, if ( )

(1 )qpq

α β φγ φ β− − +

→+ −

. This only works if the numerator is positive, since the

denominator always is (since by the definition given in Table 1 γ β> ), which in turn requires that 0q qφ α β− − − > . This cannot hold for the reasonable case where the cost of punishing is less than the cost of being cheated φ β< and will hold in the less-reasonable circumstance that φ β> only if q is sufficiently small relative to β . However, at the limit as 0q → , there is no solution; similarly, as 1q → the fraction is necessarily greater than unity, which suggests that no ESS is possible for a C–SU population mix.

Table 3: Population Proportions and Payoffs in a C–SU Mix 1-p p When meeting population of

Payoff to C SU

C 2

2 β− 2

2 ββγ q+−−

SU 2

2q qφ α− + − ( )2 1

2qφ γ φ α γ− − + − + +

A mix of C and SU players is not possible, but what about U and SU players? To check formally, there could be an ESS only if

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( )

( ) ( ) ( )

2 212 2

2 1 2 11

2 2

qp p

q qp p

φ γ γ φ φ

γ α γ φ φ γ φ α γ

− − − − +− +

− + − + + − − − + − + += − +

.

Solving for p, q q qpq qα γφ φ

− −→

− +, which simplifies to ( )

0q q α γ− + and implies that a stable

combination of Unpleasant and Strategic Unpleasant players is impossible.

Table 4 Population Proportions and Payoffs in a U–SU Mix 1-p p When meeting population of

Payoff to U SU

U 2

2 γφ −− 22

qγ φ φ− − +

SU ( )2 12

qγ α γ φ− + − + + − ( )2 1

2qφ γ φ α γ− − + − + +

Having solved the potential for mixed strategy equilibria, our attention turns to dynamics in the general population. In particular, we now address the potential for populations to be invaded by other players, in order to be able to use dynamic methods to determine whether or not our population may have an internal equilibrium—one not given by traditional evolutionary game theory methods. Table 3 and Table 4 show the payoffs to such sole invaders compared to the payoffs members of the respective populations. The payoff to a C player in a population of C

players, for example, is 2

2 β− , while the payoff to a sole SU player in the same population

is 22

q qφ α− + − . A SU player will thrive in a C population only if (1 )qφ α β+ − < , which

certainly will be the case if q is sufficiently small—again, a condition that is likely to obtain given that the likelihood that a sole SU player in an otherwise all-C population would be punished for cheating is nil. Recall that the SU player chooses a mixed strategy q of mimicking Fair Punishing behavior and 1 q− of behaving as an Unpleasant behavior based on the likelihood of meeting another SU or U player. In a solely C population, then, the SU player has no reason to evince Fairness, thus q will be 0. In this case, SU players can invade a Cheating population. It is important to note that they do so not by playing Fair, but rather by behaving as pure-U players who punish, but cheat when they can. This distinction highlights a key difference in behavior between our Strategic Unpleasant players and the Fair Punisher players that thrive in the literature. As for a pure-SU population (where SU players do look like Fair Punishers), we already have established that it is an ESS and hence is not vulnerable to invasion by Cheaters.

Figure 1 depicts the intuition behind the above discussion of Table 3. Consider a population of C and SU players, anchored at the extremes by homogeneous populations of only one type of player. The line in Figure 1 represents the range of all possible combinations of C and SU players, with a pure-SU population at the extreme left and a pure-C population at the extreme right. The arrows indicate which type fares best overall in interactions with other players, for the

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population proportions defined by the point in question. They point toward the SU vertex, indicating (as we have shown) that there is no stable population mix of SU and C player types.

Figure 1: Graphic Depiction of Population Proportions in a SU–C Mix

Another question of interest concerns the ability for either of U or SU player types to invade the other. As can be seen in Table 4, the payoffs to U and SU players in an otherwise pure-U

population are 2

2 γφ −− and ( )2 12

qγ α γ φ− + − + + −, respectively. A little algebraic

manipulation makes it clear that a small number of SU players can invade a population of U players, as 0q q qα γ+ − > . At the SU end of the line, C players can invade if

( )2 2 1q qγ φ φ φ γ φ α γ− − + > − − + − + + , a situation that cannot obtain for any 0q > because q q q q qφ φ α γ< + + − . If we were to draw a figure for the U–SU line analogous to Figure 1, both arrows would point in the same direction—toward the SU end.

Thus far, we have seen that it is no stable mixes of either C and SU or U and SU players are possible. Heller and Sieberg (Forthcoming) have shown that no mix is possible between C and U players (with the population collapsing to C, in the unlikely event that φ β> , or to U if β φ> . These three sets of dynamics between two player types are shown in Figure 2, where each leg of the triangle represents the range of possible population proportions of the types anchored at the vertices. Any point not at a vertex on one of the sides of the triangle represents a mix of the two player types. Any point inside the triangle represents a mix of all three types.

The dynamics of the above figure are not particularly exciting from a technical perspective, but they do illustrate our main point in this paper. All of the arrows eventually point to the SU vertex. Dynamically, this means that in a population characterized as we describe, Cheaters and pure Unpleasant players will be overcome by Strategic Unpleasant players. As the population becomes wholly populated by these types, all of them will behave fairly towards each other. Thus, the introduction of players who mimic Fair players for purely strategic, self serving reasons, despite their Unpleasant nature, can create a world dominated by Fair behavior.

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As noted, the above figure portrays a simple situation. We also explore if it is possible for more dynamics to exist in this population mixture. We first address the question using traditional evolutionary game theory, to determine if we can expect a mix of Cheaters, Unpleasant players, and Strategic Unpleasant players to form an ESS. A mix of all three population types can be an ESS if there is some combination of types in proportions such that the expected payoffs for Cheaters are the same as the expected payoffs for Unpleasant and Strategic Unpleasant types. To calculate players’ expected utilities, we begin by defining p1 as the fraction of SU players in the population and p2 as the fraction of Unpleasant players. That leaves Cheaters as the residual category, making up 1 21 p p− − of the population (Figure 2: Population Simplex for Cheating, Unpleasant, and Strategic Unpleasant Types

(a)

(b)

(h)

(d)

(i)

(f)

(e)

(g)

(c)

Table 5). If we find positive values for p1, p2 and 1 21 p p− − , then an ESS of all three player types is possible.

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Figure 2: Population Simplex for Cheating, Unpleasant, and Strategic Unpleasant Types

(a)

(b)

(h)

(d)

(i)

(f)

(e)

(g)

(c)

Table 5: Population Proportions and Payoffs for Three Player Types

1-p1-p2 p2 p1 Payoff to When meeting population of

C U SU

C 2

2 β− 2

2 βγ −− 2

2 ββγ q+−−

U 2

2 φ− 2

2 γφ −− 22

qγ φ φ− − +

SU 2

2q qφ α− + − ( )2 1

2qγ α γ φ− + − + + −

( )2 12

qφ γ φ α γ− − + − + +

In order for the payoffs to different player types in a three-player mixed population to be equal, it

must be the case that ( )1 2 2 12 2 21

2 2qp p p p

sβ γ β γ β β− − − − − +

− − + + =

12

( )1 2 2 12 2 21

2 2 2qp p p pφ φ γ γ φ φ− − − − − +

− − + + =

( ) ( ) ( )1 2 2 1

2 1 2 12 12 2 2

q qq q p p p pγ α γ φ φ γ φ α γφ α − + − + + − − − + − + +− + −

− − + + . Solving

for p1 yields either ( )1p

qβ φβ φ−

→−

, which is positive, but, because q is a proportion, not less

than unity; or 21

q q q ppq q qα β φ γβ γ φ

− + + − +→

− −. In this latter case, the denominator clearly is negative,

so p1 can be positive only if 21 pα β φ γ β γ φ<− + + − + − − . This translates to 21 pα γ γ− + < − , which is impossible by definition of γ . Hence, no polymorphic ESS including SU players is possible.

Is it possible that there could be an unstable—that is fluctuating, but nonetheless enduring—polymorphic mix, even though an ESS is ruled out? We check using Saari’s (2002) qualitative approach toward evolutionary game theory, as illustrated in Figure 2. To check whether an internal equilibrium can exist, we jointly evaluate local equilibria (on the sides and at the vertices of the triangle) and winding numbers (Milnor 1997).

To compute winding numbers for the population simplex in, begin at the point labeled “start” and move counterclockwise around the triangle, counting the number of full revolutions indicated by the arrows. Each counterclockwise revolution is worth 1, and each clockwise revolution is worth –1. Beginning at “start” in Figure 2 trace: (a) a 120° counterclockwise rotation; (b) a 60° clockwise rotation; (c) a 120° clockwise rotation; (d) another 60° clockwise rotation; (e) a second 120° counterclockwise rotation, erasing all gains in either direction; (f) a 60° counterclockwise rotation and (g) a third 120° counterclockwise rotation; (h) another 120° counterclockwise rotation, followed by (i) another 60° counterclockwise rotation. The winding number (the number of counterclockwise rotations minus the number of clockwise rotations) for the triangle in Figure 2 thus is 1.

The winding number must equal the sum of local equilibria indices, where an equilibrium index is the product of the signs of the two pairs of arrows at each equilibrium. Arrow pairs pointing toward the equilibrium take a negative sign, and arrow pairs pointing away from the equilibrium take a positive sign. The indices for the equilibria in Figure 2 thus are, beginning with the lower-right vertex of the triangle and moving counterclockwise, as follows: ( )1 1 1× = ; ( )1 1 1− × = − ;

( )1 1 1− ×− = . The sum of equilibrium indices for the simplex in Figure 2 is 1. Because the sum of equilibrium indices is equal to the figure’s winding number, we know that there is no internal equilibrium, hence no feasible polymorphic population mix.

Discussion Our finding that Strategic Unpleasant players will eventually dominate a society made up of Cheaters and non-strategic Unpleasant types is interesting for two reasons. First, the result flies in the face of arguments that what we might term “civilized” society can exist only if individuals themselves are sufficiently civilized (see in particular Almond, and Verba 1989). Indeed, we argue in essence that the veneer of cooperative behavior that underpins civil society could well be a consequence of widespread incivility, or at least a general willingness on the part of

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individuals to treat each other badly. In this regard, we do not disagree with others who model punishment of cheating behavior as an overt defense of fairness. In our model, however, as long as people are sophisticated enough to consider the consequences of their actions, fair play emerges not despite incivility, but rather because of it.

Second, the result hinges on two key assumptions. The first and perhaps more plausible assumption is that no Unpleasant actor will punish Cheaters if the cost of doing so is more than the cost of being cheated. As we have shown elsewhere (Heller, and Sieberg Forthcoming), where this assumption does not apply those who punish do not do well. The second assumption is that the probability q that a SU player plays fair rather than cheating is essentially equal to the probability of being punished for cheating—so that a SU player in a population of other U or SU players never cheats, but a lone SU player in a population of C players (or Fair players, though we do not analyze this case here) always cheats. It might in fact be more realistic to assume that q lies between zero and one, but never reaches either extreme. One reason to relax the close relationship between q and the probability of being punished is informational; another is that just as punishing malefactors appears to be an emotional response, not a reasoned one (Bewley 2003; Bowles, and Gintis 2002; Sanfey et al. 2003), so it might be that even the most strategic of cheaters might not be able to restrain himself from trying to gain advantage once in a while. The end result, whatever the rationale, is that SU players always play mixed strategies—that is, they never look like either pure–U players or the completely Fair Punishers of legend.

Constraining q to lie between 0 and 1 could change the dynamics of population interactions—and subsequent population mixes—in interesting ways. If the lowest values for q are sufficiently high (higher than some q*), for example, a pure C population would not be vulnerable to invasion by SU players, even as the pure SU ESS would remain, as illustrated in Figure 3. If the highest values for q are sufficiently low, a pure SU population would be vulnerable to invasion by C players, yielding four possibilities: 1) all arrows point toward the pure SU population, as in Figure 1; 2) all arrows point to the C vertex, with C as the ESS; 3) the arrows point away from each other toward the pure-C and pure-SU populations, indicating that each is an ESS and that there is an equilibrium (probably unstable) in which the populations mix; and 4) the arrows point away from the pure-C and pure-SU populations, indicating that neither is an ESS, but that a mix of the two is.

Figure 3: Population Proportions in a SU–C Mix If q∈(q*,1]

On the SU–U line, changing the constraints on q would change nothing, nor (obviously) would any changes in q affect the dynamics on the C–U line. For values of q yielding the unstable C–SU mix depicted in Figure 3, the full-population dynamics are much more interesting, and a global equilibrium mix of all three player types is possible, as shown in Figure 4. The winding number for this figure is –1 and the sum of local indices is –2, which indicates that there must be some internal equilibrium with a positive sign.4 We have depicted the predicted equilibrium in

4 It is possible that there are several equilibria whose indices sum to 1. The key point, however, is that there is at least one internal equilibrium.

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the figure as a repellor; an attractor is unlikely, given the logic of the dynamics illustrated in the figure.

Figure 4: Internal Dynamics When U Players Can Invade a C–SU ESS

(a)

(b)

(h)

(d)

(i)

(f)

(e)

(g)

(j)

(k)

(c)

Strategic Unpleasant players are very much like real people, just as observers from Macchiavelli to Madison to Przeworski (1991) have seen them. It is an attractive thought to suppose that the Good Society is achieved through the efforts of Good people, but in a world of Good people a Cheater can make a killing. If people were indeed Good, so that all valued fairness and cooperation, one might expect government to be a rather less conflictual exercise than it tends to be. People are not Good in that sense, however (though they might not be as bad as Macchiavelli apparently thought), and as Przeworski (1991) sees it, the whole point of democratic government is to manage the inevitable conflicts that arise among different interests. More to the point, managing conflict peacefully requires designing a government where officeholders of various sorts can in essence punish each other—by keeping them from getting what they want (cf. Heller 2001b;2001a;2002)—as James Madison did when he used his fear of faction as the foundation for a system of government in which “opposite and rival interests [would supply] the defect of better motives” (Madison 1778 [1947]). This kind of government can only work if those who hold office are able and credibly willing to behave badly toward each other.

Conclusion Two wrongs don’t make a right—or do they? Heller and Sieberg (Forthcoming) demonstrated that altruism is not necessary for cooperation (or Fair behavior) to emerge in a group. The

15

presence of an Unpleasant player—one who cheats and punishes others for cheating—is sufficient to create the grounds for Fair behavior to exist. This paper takes the issue a step further. Using traditional evolutionary game theory and a dynamic approach, we show that Fair behavior can emerge in a group entirely dominated by players who prefer to cheat. So long as it is in a player’s self-interest to mimic Fair behavior in order to avoid punishment from similarly Unpleasant players, then it is possible not only for Fair behavior to exist but to be dominant.

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References

Alesina, Alberto, and Elianna La Ferrara. 2002. "Who Trusts Others?" Journal of Public

Economics 85 (2):207-234. Almond, Gabriel A., and Sydney Verba. 1989. The Civic Culture. Newbury Park: Sage. Axelrod, Robert. 1984. The Evolution of Cooperation. New York: Basic Books. Barr, Abigail. 1999. "Familiarity and Trust: An Experimental Investigation." In Center for the

Study of African Economies Working Paper Series: Center for the Study of African Economies.

Bates, Robert H. 2001. Prosperity and Violence: The Political Economy of Development. New York and London: W.W. Norton.

Becker, Gary S. 1968. "Crime and Punishment: An Economic Approach." The Journal of Political Economy 76 (2):169-217.

Bewley, Truman. 2003. "Fair's fair." Nature 422:125-126. Bowles, Samuel, and Herbert Gintis. 2002. "Homo Reciprocans." Nature 415:125-128. Boyd, Robert, Herbert Gintis, Samuel Bowles, and Peter J. Richerson. 2003. "The Evolution of

Altruistic Punishment." Proceedings of the National Academy of Sciences 100 (6):3531-3535.

Boyd, Robert, and Peter J. Richerson. 1992. "Punishment Allows the Evolution of Cooperation (or Anything Else) in Sizable Groups." Ethology and Sociobiology 13 (3):171-195.

Brandts, Jordi, Takatoshi Saijo, and Arthur Schram. 2004. "How Universal is Behavior? A Four Country Comparison of Spite and Cooperation in Voluntary Contribution Mechanisms." Public Choice 119 (3-4):381-424.

Camerer, Colin F. 2003. Behavioral Game Theory: Experiments in Strategic Interaction. Princeton, NJ: Princeton University Press.

Camerer, Colin F., and Ernst Fehr. 2006. "When Does 'Economic Man' Dominate Social Behavior?" Science 311:47-52.

Coleman, James. 1990. Foundations of Social Theory. Cambridge, Mass.: Harvard University Press.

Cook, Karen S., Russell Hardin, and Margaret Levi. 2005. Cooperation without Trust? Edited by K. S. Cook, R. Hardin, and M. Levi. New York: Russell Sage Foundation.

Dawes, Christopher T., James H. Fowler, Tim Johnson, Richard McElreath, and Oleg Smirnov. 2007. "Egalitarian motives in humans." Nature 446 (7137):794-796.

Ensminger, Jean. 2001. "Market Integration and Fairness: Evidence from Ultimatum, Dictator, and Public Goods Experiments in East Africa." Pasadena, California: California Institute of Technology.

Fehr, Ernst, and Urs Fischbacher. 2003. "The nature of human altruism." Nature 425 (6960):785-791.

———. 2004. "Third-party punishment and Social Norms." Evolution and Human Behavior 25 (2):63-87.

Fehr, Ernst, Urs Fischbacher, and Simon Gächter. 2002. "Strong reciprocity, human cooperation, and the enforcement of social norms." Human Nature 13 (1):1-25.

Fehr, Ernst, and Simon Gachter. 2002. "Altruistic punishment in humans." Nature 415 (6868):137-140.

17

Fehr, Ernst, and Simon Gächter. 2000. "Cooperation and Punishment in Public Goods Experiments." American Economic Review 90 (4):980-994.

———. 2002. "Altruistic punishment in humans." Nature 415:137-140. Fehr, Ernst, and Joseph Henrich. 2003. "Is Strong Reciprocity a Maladaptation? On the

Evolutionary Foundations of Human Altruism." In Genetic and Cultural Evolution of Cooperation, ed. P. Hammerstein. Cambridge, Mass.: MIT Press.

Fehr, Ernst, and Bettina Rockenbach. 2003. "Detrimental effects of sanctions on human altruism." Nature 422:137-140.

Fehr, Ernst, and Klaus M. Schmidt. 1999. "A Theory of Fairness, Competition, and Cooperation." The Quarterly Journal of Economics 114 (3):817-868.

Flack, Jessica C., Frans B. M. de Waal, and David C. Krakauer. 2005a. "Social Structure, Robustness, and Policing Cost in a Cognitively Sophisticated Species." In The American Naturalist.

Flack, Jessica C., Michelle Girvan, Frans B. M. de Waal, and David C. Krakauer. 2006. "Policing stabilizes construction of social niches in primates." Nature 439:426-429.

Flack, Jessica C., David C. Krakauer, and Frans B. M. de Waal. 2005b. "Robustness mechanisms in primate societies: a perturbation study." Proceedings of the Royal Society B 272 (1568):1091-1099.

Fowler, James H. 2005. "Altruistic punishment and the origin of cooperation." Proceedings of the National Academy of Sciences 102 (19):7047-7049.

Güth, Werner, and Reinhard Tietz. 1990. "Ultimatum Bargaining Behavior: A Survey and Comparison of Experimental Results." Journal of Economic Psychology 11:417-449.

Heller, William B. 2001a. "Making Policy Stick: Why the Government Gets What It Wants in Multiparty Parliaments." American Journal of Political Science 45 (4):780-798.

———. 2001b. "Political Denials: The Policy Effect of Intercameral Partisan Differences in Bicameral Parliamentary Systems." Journal of Law, Economics, and Organization 17 (1):34-61.

———. 2002. "Regional Parties and National Politics in Europe: Spain's estado de las autonomías, 1993 to 2000." Comparative Political Studies 35 (6):657-685.

Heller, William B., and Katri K. Sieberg. Forthcoming. "Functional Unpleasantness: The Evolutionary Logic of Righteous Resentment." Public Choice.

Henrich, Joseph. 2000. "Does Culture Matter in Economic Behavior? Ultimatum Game Bargaining among the Machiguenga of the Peruvian Amazon." The American Economic Review 90 (4):973-979.

———. 2004. "Cultural group selection, coevolutionary processes and large-scale cooperation." Journal of Economic Behavior & Organization 53 (1):3-35.

Henrich, Joseph, and Robert Boyd. 2001. "Why People Punish Defectors: Weak Conformist Transmission Can Stabilize Costly Enforcement of Norms in Cooperative Dilemmas." Journal of Theoretical Biology 208 (1):79-89.

Henrich, Joseph, Robert Boyd, Samuel Bowles, Colin Camerer, Ernst Fehr, et al. 2001. "In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies." The American Economic Review 91 (2):73-78.

Hibbing, John R., and John R. Alford. 2004. "Accepting Authoritative Decisions: Humans as Wary Cooperators." American Journal of Political Science 48 (1):62-76.

Jensen, Keith, Josep Call, and Michael Tomasello. 2007. "Chimpanzees Are Rational Maximizers in an Ultimatum Game." Science 318:107-109.

18

Levi, Margaret. 1989. Of Rule and Revenue. Berkeley: University of California Press. Machiavelli, Niccolò. 1940 [1531]. "Discourses on the First Ten Books of Titus Livius." In The

Prince and The Discourses, ed. M. Lerner. New York: The Modern Library. Madison, James. 1778 [1947]. "The Federalist. No. 51." In The Federalist: A Commentary on the

Constitution of the United States, ed. E. G. Bourne. New York: Tudor Publishing. Maestripieri, Dario. 2007. Macachiavellian Intelligence: How Rhesus Macaques and Humans

Have Conquered the World. Chicago: University of Chicago Press. Milnor, John W. 1997. Topology from a Differentiable Viewpoint. Revised ed. Princeton:

Princeton University Press. North, Douglass C. 1990. Institutions, Institutional Change and Economic Performance. Edited

by J. E. Alt, and D. C. North. Cambridge: Cambridge University Press. Nowak, Martin A., Karen M. Page, and Karl Sigmund. 2000. "Fairness versus Reason in the

Ultimatum Game." Science 289:1773-1775. Ockenfels, Axel, and Joachim Weimann. 1999. "Types and patterns: an experimental East-West-

German comparison of cooperation and solidarity." Journal of Public Economics 71 (2):275-287.

Olson, Mancur. 1965. The Logic of Collective Action: Public Goods and the Theory of Groups. Cambridge, Mass.: Harvard University Press.

Ostrom, Elinor, James Walker, and Roy Gardner. 1992. "Covenants With and Without a Sword: Self-Governance is Possible." The American Political Science Review 86 (2):404-417.

Przeworski, Adam. 1991. Democracy and the Market : Political and Economic Reforms in Eastern Europe and Latin America. Edited by J. Elster, and G. Hernes. Cambridge: Cambridge University Press.

Pulkkinen, Otto. 2007. "Emergence of Cooperation and Systems Intelligence." In Systems Intelligence in Leadership and Everyday Life, ed. R. P. Hämäläinen, and E. Saarinen. Espoo, Finland: Systems Analysis Laboratory, Helsinki University of Technology.

Rubin, Paul H. 2002. Darwinian Politics: The Evolutionary Origin of Freedom. New Brunswick, N.J., and London: Rutgers University Press.

Saari-Sieberg, Katri. 1998. "Rational Violence: An Analysis of Corruption." New York: Department of Political Science, New York University.

Saari, Donald G. 2006. "Mathematical Social Sciences;" An Oxymoron? Pacific Institute for Mathematical Sciences 2002 [cited 13 March 2006]. Available from http://www.pims.math.ca/science/2002/distchair/saari/.

Sanfey, Alan G., James K. Rilling, Jessica A. Aronson, Leigh E. Nystrom, and Jonathan D. Cohen. 2003. "The Neural Basis of Economic Decision-Making in the Ultimatum Game." Science 300:1755-1758.

Sethi, Rajiv, and E. Somanathan. 1996. "The Evolution of Social Norms in Common Property Resource Use." The American Economic Review 86 (4):766-788.

Sieberg, Katri K. 2005. Criminal Dilemmas: Understanding and Preventing Crime. 2nd ed. Berlin and Heidelberg: Springer.

Sigmund, Karl, and Martin A. Nowak. 2000. "Evolution and Social Science: Enhanced: A Tale of Two Selves." Science 290 (5493):949-950.

Skaperdas, Stergios. 2001. "The Political Economy of Organized Crime: Providing Protection when the State Does not." Economics of Governance 2 (3):173-202.

Skyrms, Brian. 2003. The Stag Hunt and the Evolution of Social Structure. Cambridge: Cambridge University Press.

19

Vogel, Gretchen. 2004. "The Evolution of the Golden Rule." Science 303:1128-1131. Weber, Max. 1958. "Politics as a Vocation." In From Max Weber : Essays in Sociology, ed. H.

H. Gerth, and C. W. Mills. New York: Oxford University Press. Wedekind, Claus. 1998. "Game Theory: Give and Ye Shall Be Recognized." Science 280

(5372):2070-2071.