Rise and Decline of Social Capital Excess Co-operation in the One-Shot Prisoner's Dilemma Game

Abstract: In order to explain excess co-operation in the one-shot prisoner's dilemma game, we first question the standard assumption of stable and selfish preferences by introducing the concept of social capital. This analysis leads to a model that explains excess co-operation through an accumulation of social capital. We allow preferences and norms to change over time and hence endogenise them. Our results depend on individuals being able to acquire enough information to allow them to ascertain the social norm that fellow individuals subscribe to. However, our results do not depend on any assumptions about group size and no ostracism is required to generate co-operation. Our model gives three hypotheses about the emergence and stability of social capital and co-operation in society. First, neither unconditional cooperation nor universal defection is stable; second, for co-operation to be stable some individuals must be reciprocal in nature; third, we identify a 'rise and decline of social capital' which gives a cyclical pattern of co-operation in society. These findings may form the basis for future theoretical and empirical research. JEL classification: A12, C71, D23, D60, D70, Z13. Keywords: Social capital, co-operation, selfishness, reciprocity, altruism, preference dynamic, Prisoner's Dilemma. 1: INTRODUCTION 1 Contact address: Department of Economics, the Aarhus School of Business, Prismet, Silkeborgvej 2, DK-8000 Aarhus C, Denmark. E-mails: gts@asb.dk, and aup@asb.dk. We acknowledge financial assistance from the Danish Social Science Research Foundation and helpful comments from our colleagues. Special thanks to Martin Paldam, Christian Bjørnskov and the late Mancur Olson. 2 Why does excess co-operation occur in the one-shot prisoner's dilemma game? Economists have long wondered why people tend to co-operate more than they should according to standard economic theory. In several experiments, one-half of the first-mover in anonymous sequential Prisoner's dilemma games chose to trust their partners. Moreover, three-quarters of second-movers reciprocated this trust, thus co-operating rather than defecting, even though the latter would have maximized their money earnings. Thus, experimental and everyday observations indicate that people tend to co-operate and follow a set of social norms, even though, in terms of short-run monetary gains, it would be rational for the individual to defect, see We deal with the above-mentioned gap in the literature by developing a model giving us three main hypotheses about how social capital and co-operation can be generated in a single large group (indeed the entire society), even when there is no repeated interaction and no possibility of explicit punishment (say ostracism). Overall they suggest that a society will, at any point in time, find itself in one of several possible situations, or phases. These are: Universal and robust co-operation, universal but increasingly fragile co-operation, increasing defection and, finally, increasing co-operation. Indeed, we will observe a cyclical pattern, in the sense that society will move through each of these phases, and then start over again. The length of time that society will spend in the 'good' situation, where co-operation is universal, will depend on the extent to which society, through its institutions and education of its young, can maintain a social norm of reciprocity and prevent one of altruism from spreading. 3 Research on social capital has been classified into four groups: The anthropological, the sociological, the economic and the political science approach. 2 Our approach, is interdisciplinary and combines, we believe, the strongest features of some of these groups. In our view individuals can be fruitfully regarded and modeled as rational, or utility-maximizing, as in the economic approach, but their preferences should not be viewed as stable, or given, and these preferences are not necessarily selfish. People may be reciprocal or altruistic (or even spiteful and competitive). 3 We believe that this approach is able to deal both with the criticism that economics makes man too "under-socialized" and the criticism that sociological approaches make him "over-socialized" (see the discussion in Fershtman and Weiss (1998) explore the role of social status in bringing about cooperation in the PD game. In their model, individuals get status from being more cooperative than the average and individuals care to a differing extent about status relative to money payoffs. They show that for cooperation to establish itself, the concern for social status must be sufficiently strong (such that socially minded people can co-ordinate on the cooperative outcome), but not too strong (then socially minded individuals act like altruists who can be exploited by asocial people). However, it is, as above, relevant to point out that Fershtman and Weiss only allow for two preference types. Indeed, in their model the set of feasible types is either a 'Selfish' or a 'Reciprocal' type, or a 'Selfish' and 'Altruist' type. 2 See, for example, OECD (2001). 3 See Fehr and Fischbacher (2002), for a taxonomy of 'social preferences'. 4 Early contributions are 4 The rest of the article is organized as follows. In Section 2 we first question the standard assumption of stable and selfish preferences. Section 3 then introduces the concept of social capital. Section 4 sets up a model that analyses the interaction between social norms, social capital and the emergence of co-operation. All the formal result are given in the Appendix. 2: THE STANDARD VIEW OF PREFERENCES The standard view in economics is that preferences are stable (or given) and selfish. Individuals are concerned only with their own monetary payoff (see, for example, Becker and Stigler Do you want to understand why government officials behave the ways they do? All you need to know is that they are trying to maximize the budgets of their agencies. Do you want to understand what drives politicians? All you need to know is that they want to be re-elected. Do you want to understand legislation? Just see it as a sale of the coercive power of government to the highest bidder, like a cattle auction (ibid., p. 81). Kelman says that this account of the political process is a caricature of reality because it '…ignores the ability of ideas to defeat interests and the role that public spirit plays in motivating participants…' and that '…a norm of public spiritedness in political action -a view that people should not simply be selfish in their political behaviour -is crucial. The public choice school is part of the assault on that norm' (ibid.). Crucial to any ability to maintain public spirit is the continuing existence of a social norm that declares it appropriate for people to try to do the right thing in public behaviour, and inappropriate for them simply to seek to advance their personal interests. If the norm of public spirit dies, our society would look bleaker and our lives as individuals would be impoverished. The Robinson Crusoe idea that people are best conceived of as isolated units because is inadequate 5 And, in the market place motivations like reciprocity and fairness also play an important role. See, for example Kahneman, In the same vein, Cram (1998, p. 77) notes that in everyday life, 'people don't stop at every choice they make in their life and think about what will maximize my self-interest' Rather, they mostly follow socially defined rules which may not necessarily be in their own shortrun material self-interest. These views are overall consistent with the political science literature that depicts preferences as endogenous, i.e., that preferences develop within the institutional setting. In contrast, the overall economic literature perceives preferences as exogenous, i.e., given and independent of institutional set-ups. This point is the main political science objection against economics, namely that preferences are non-stable and not necessarily selfish We will seek to address these limitations of the standard view on preferences by introducing the concept of social norms and social capital in the following section. 3: SOCIAL CAPITAL People differ in the perceptions, motives and social norms that they 'carry' with them in society. The social norm that a person adheres to is expressed through the person's willingness to cooperate or defect in games like the Prisoner's Dilemma game. We will say that a social norm creates social capital when it allows the individuals carrying the social norm to rationally co-operate in the one-shot Prisoner's Dilemma. This is in line with the definition of social capital, given in e.g. In the presence of social capital and trust, fewer will commit crime, free-ride or ignore the rules in a contract. This is in stark contrast to the traditional political economy approach, which tends to ignore social norms and social capital when dealing with human nature. Here, if the risk of detection (and the cost associated with punishment) is lower than the benefits from committing a crime, a person will commit the crime. Anyone will rob an old lady in the street if it pays. In the absence of police and court systems, anarchy will occur Hobbes is the first to offer the classical solution to discipline human nature, which is that of third-party enforcement and the establishment of strong formal institutions. Because the 6 weakest member in society is capable of killing the strongest, a social contract is needed. individuals to trust that that other individuals will act co-operatively. This will happen even in the absence of a 'Leviathan'. Such trust assures an individual that he will not be taken advantage of by another individual, even if the latter might get an economic net benefit from doing it. Even if it pays economically to commit a crime, free-ride or ignore the rules in a contract, fewer will do it in the presence of trust because social norms tell them not to do so. Another key idea in the social capital approach is that the community members' preferences can be affected and shaped, due to social norms and social pressures (see When social capital in this way reduces the need for a Leviathan, i.e. third-party monitoring and enforcement of contracts, more transactions can take place at a lower cost. In this way, trust 'lubricates' society. For example, it may be argued that a firm lowers transaction costs by having numerous informal transactions taking place that are not formally sanctioned (see Coase, 1937). In this way, a society with members that trust each other may be capable of accomplishing more economic growth than a similar society without trust. Consequently, social capital could be a new production factor, which must be added to the conventional concepts of human and physical capital. In relation to macroeconomic policies, it follows that if people hold a high level of social capital, they will trust each other and elected decision-makers as well. By that, the build-up and maintenance of social capital will ease policy-making and make it more effective since less monitoring is necessary when a high 7 level of social capital is present. This point is illustrated by a new survey on shadow economy activities by Schneider and Enste (2002). Here, one could argue that less monitoring of shadow economy activity and tax evasion was needed in countries with high levels of social capital because people generally cheat less. Given all these observations, our key aim in the following section is to explore the question: To what extent will a social norm that allows individuals who have internalized this norm in their preferences to rationally co-operate, even in a one-shot situation and in a large community without neither formal nor informal enforcement (such as ostracism)? 4: A SIMPLE MODEL OF EMERGENCE AND VIABILITY OF SOCIAL CAPITAL In this section we study a simple formal model, in order to shed some light on how social capital is created and the extent to which it can be maintained. The basic set-up We imagine a large city, where people occasionally meet each other randomly on the central square. They meet in pairs, and then play the one-shot PD game, where they simultaneously choose between Cooperate (C) and Defect (D). The matrix below gives the money payoffs for the Prisoner's Dilemma (PD) game. In our model, social norms, embedded in individuals' preferences, may induce them to behave in a way that differs from the one normally assumed. We will consider the following three social norms: 1) The Reciprocal social norm (R): Reciprocate what the other opponent does, or is expected to do: If the opponent is going to, or is thought to play C, then an individual adhering to the Reciprocal norm will play C, too. Similarly, if the opponent is going to, or is suspected to play D, a Reciprocal individual will play D, too. Our interpretation of such behavior is that the individual has internalized a norm of reciprocity: If your opponent is (or is thought to be) kind, then be kind, too; and is the opponent is (thought to be) unkind, be unkind, too. We note that a Reciprocal person does not always maximize her monetary earnings: If the opponent plays C, she plays C, too, whereas a choice of D would have given her more. Reciprocity has ancient roots. The following quote [from Fehr and Gächter "A man ought to be a friend to his friend and repay gift with gift. People should meet smiles with smiles and lies with treachery." Reciprocity is a vigilant and attentive social norm: Behavior is conditioned on the opponent's identity. 2) The Selfish social norm (S): A person adhering to this norm always plays Defect. Our interpretation is that she obeys an (a)social norm of always seeking to maximize her monetary return. She is the 'standard' type of individual assumed in most of economics and game theory. In the style of the Edda, the Selfish type would subscribe to the following maxim: "Don't rely on anyone! Receive, but never give gifts. Never smile and lie whenever it helps you." 6 For good surveys of reciprocity and other 'social preferences', we refer the reader to cooperate. An interpretation is a norm of altruism: Always seek to maximize total (or just the opponent's) money surplus. The Altruist type could be interpreted as a certain variant of Kant's Categorical Imperative: Treat other's as you want them to treat you. The Altruistic type is a form of unconditional altruism. Inspired by the verse from the Edda quoted above, we could write: "Be good to everybody! A man ought to be a friend to everybody, and to give gifts. He should smile and never lie." The Reciprocal type distinguishes between opponents, on the basis of their preferences (i.e., social norms): If the opponent is thought to be 'kind' (play C), she plays C, too; otherwise she acts in an unkind manner (plays D). We may say that the Reciprocal type is conditionally kind. The Altruist type, on the other hand, is unconditionally kind: She plays C against all opponents. This is, as we shall se below, a crucial distinction, and it may affect the robustness of cooperation in a, perhaps at first sight, unintuitive way. We will assume that when two individuals meet income, skin color, area of residence, and so on, and that these are correlated with the social norms followed . We leave for future research the task of incorporating such, and other, realistic features into models of social norms and social capital. 7 Whatever the specific mechanism, we assume individuals on average correctly deduce their opponents' internalized social norms. 7 For a formal model, see 10 We can now consider what happens when individuals with different social norms or preferences meet and play the one-shot PD game given above. Let us focus on an encounter between two R-types. Here there are two possible outcomes: One where both are 'kind, i.e., choose C, and another where both are 'unkind', i.e., choose D. Precisely, both the (C,C) outcome and the (D,D) outcome are Nash equilibria. 8 We will assume that two Reciprocators can establish the cooperative (C,C) outcome. Our interpretation is that each Rindividual trusts that the R-opponent will play C, and hence the individual plays C. How does this trust arise? When two R-types meet, they see that they subscribe to the same social norm, one of reciprocity. This is not in itself enough to get co-operation, since (D,D) is also a Nash equilibrium. However, the (C,C) outcome is better in monetary terms for both individuals than the (D,D) outcome. We assume that this persuades each individual that the opponent will indeed co-operate. It follows that each R-type earns a monetary payoff of unity. The money payoffs arising from other encounters are quite straightforward to derive. 9 We thus obtain the matrix below, which contains the money payoff earned by a type in encounters with the other types. Cell (i,j) gives the money payoff earned by type i when meeting an opponent of type j, where i,j=A, R, S. 8 To see that (D,D) is a Nash equilibrium, note that an R-individual prefers D if the opponent plays D. It follows that if two R-types play D, each individual has no incentive to deviate. The same argument shows that (C,C) is a Nash equilibrium. There is, in addition to these two equilibria, also a mixed Nash equilibrium, where each R-type mixes between C and D, but we will ignore this possibility here. 9 A-A: Here both persons cooperate. Thus each gets a money payoff of unity. A-R: The A-type plays C; the Rtype does the same, since the R-type observes that the opponent will play C and hence her best reply is to do the same. We see that an altruist person performs well against other altruists and well against reciprocal individuals (they all co-operate), but is exploited by a Selfish person. The Reciprocator performs well against other reciprocal and altruist individuals, like the altruist, but is not exploited to the same extent as the altruist when meeting a selfish individual. Finally, the selfish person earns a lot of money when meeting an altruist and otherwise mediocre. We wish to endogenously determine how many people will internalize what kinds of social norms in their preferences. To do so, we postulate a dynamic process through which individuals' preferences may change over time. Our key assumption will be that those social norms or preferences who give their 'users' higher-than-average money payoffs tend to be internalized by more individuals over time. 10 An interpretation is that, in order to survive in the economic system, a social norm needs to give its followers a sufficiently high level of material welfare. This assumption, that 'only money matters', does not however a priori bias the analysis towards the survival of materialistic preferences: Any sort of social norm or preference that leads individuals to a materially superior, or just reasonable, behavior will prosper. Thus, if individuals with, say, Reciprocal, preferences earn more money than those with materialistic preferences, the population frequency of the former will tend to increase at the expense of the latter. Formally, let x i , where i=A, R, S, indicate the population proportion of individuals of type i