In The Grammar of Society, first published in 2006, Cristina Bicchieri examines social norms, such as fairness, cooperation, and reciprocity, in an effort to understand their nature and dynamics, the expectations that they generate, and how they evolve and change. Drawing on several intellectual traditions and methods, including those of social psychology, experimental economics and evolutionary game theory, Bicchieri provides an integrated account of how social norms emerge, why and when we follow them, and the situations where we are most (...) likely to focus on relevant norms. Examining the existence and survival of inefficient norms, she demonstrates how norms evolve in ways that depend upon the psychological dispositions of the individual and how such dispositions may impair social efficiency. By contrast, she also shows how certain psychological propensities may naturally lead individuals to evolve fairness norms that closely resemble those we follow in most modern societies. (shrink)

What is considered to be fair depends on context-dependent expectations. Using a modified version of the Ultimatum Game, we demonstrate that both fair behavior and perceptions of fairness depend upon beliefs about what one ought to do in a situation—that is, upon normative expectations. We manipulate such expectations by creating informational asymmetries about the offer choices available to the Proposer, and find that behavior varies accordingly. Proposers and Responders show a remarkable degree of agreement in their beliefs about which choices (...) are considered fair. We discuss how these results fit into a theory of social norms. (shrink)

In the social sciences norms are sometimes taken to play a key explanatory role. Yet norms differ from group to group, from society to society, and from species to species. How are norms formed and how do they change? This 'state-of-the-art' collection of essays presents some of the best contemporary research into the dynamic processes underlying the formation, maintenance, metamorphosis and dissolution of norms. The volume combines formal modelling with more traditional analysis, and considers biological and cultural evolution, individual learning, (...) and rational deliberation. In filling a significant gap in the current literature this volume will be of particular interest to economists, political scientists and sociologists, in addition to philosophers of the social sciences. (shrink)

Often, when several norms are present and may be in conflict, individuals will display a self-serving bias, privileging the norm that best serves their interests. Xiao and Bicchieri (J Econ Psychol 31(3):456–470, 2010) tested the effects of inequality on reciprocating behavior in trust games and showed that—when inequality increases—reciprocity loses its appeal. They hypothesized that self-serving biases in choosing to privilege a particular social norm occur when the choice of that norm is publicly justifiable as reasonable, even if not optimal (...) for one of the parties. In line with the literature on motivated reasoning, this justification should find some degree of support among third parties. The results of our experimental survey of third parties support the hypothesis that biases are not always unilateral selfish assessments. Instead, they occur when the choice to favor a particular norm is supported by a shared sense that it is a reasonable and justifiable choice. (shrink)

This book explores how individual actions coordinate to produce unintended social consequences. In the past this phenomenon has been explained as the outcome of rational, self-interested individual behaviour. Professor Bicchieri shows that this is in no way a satisfying explanation. She discusses how much knowledge is needed by agents in order to coordinate successfully. If the answer is unbounded knowledge, then a whole variety of paradoxes arise. If the answer is very little knowledge, then there seems hardly any possibility of (...) attaining coordination. The solution to coordination and cooperation is for agents to learn about each other. The author concludes that rationality must be supplemented by models of learning and by an evolutionary account of how social order can persist. (shrink)

Subjects communicated prior to playing trust games; the richness of the communication media and the topics of conversation were manipulated. Communication richness failed to produce significant differences in first-mover investments. However, the topics of conversation made a significant difference: the amounts sent were considerably higher in the unrestricted communication conditions than in the restricted communication and no-communication conditions. Most importantly, we find that first-movers' expectations of second-movers' reciprocation are influenced by communication and strongly predict their levels of investment.

Using an economic bargaining game, we tested for the existence of two phenomena related to social norms, namely norm manipulation and norm evasion – the deliberate, private violation of a social norm. We found that the manipulation of a norm of fairness was characterized by a self-serving bias in beliefs about what constituted normatively acceptable behaviour, so that an individual who made an uneven bargaining offer not only genuinely believed it was fair, but also believed that recipients found it fair, (...) even though recipients of the offer considered it to be unfair. In contrast, norm evasion operated as a highly explicit process. When they could do so without the recipient's knowledge, individuals made uneven offers despite knowing that their behaviour was unfair. (shrink)

University of Pennsylvania, USA, el322{at}nyu.edu ' + u + '@' + d + ' '//--> One of the most consistent findings in experimental studies of social dilemmas is the positive influence of face-to-face communication on cooperation. The face-to-face `communication effect' has been recently explained in terms of a `focus theory of norms': successful communication focuses agents on pro-social norms, and induces preferences and expectations conducive to cooperation. 1 Many of the studies that point to a communication effect, however, do not (...) further explore whether and to what extent the communication medium affects cooperative behavior. In this article, we ask if pro-social behavior can emerge and survive in computer-mediated environments. We show that, like face-to-face communication, computer-mediated communication also positively affects cooperation in social dilemmas, but cooperation is more difficult to establish and maintain. We argue that the discrepancy between the computer-mediated and the face-to-face communication effects is a consequence of the distinct capabilities of different media to focus agents on pro-social norms and to allow them to develop mutual expectations about future behavior. Key Words: social dilemmas • laboratory experiments • communication • social norms • cooperation • computer-mediated communication. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

Using an economic bargaining game, we tested for the existence of two phenomena related to social norms, namely norm manipulation – the selection of an interpretation of the norm that best suits an individual – and norm evasion – the deliberate, private violation of a social norm. We found that the manipulation of a norm of fairness was characterized by a self-serving bias in beliefs about what constituted normatively acceptable behaviour, so that an individual who made an uneven bargaining offer (...) not only genuinely believed it was fair, but also believed that recipients found it fair, even though recipients of the offer considered it to be unfair. In contrast, norm evasion operated as a highly explicit process. When they could do so without the recipient's knowledge, individuals made uneven offers despite knowing that their behaviour was unfair. (shrink)

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

Experimental results in Ultimatum, Trust and Social Dilemma games have been interpreted as showing that individuals are, by and large, not driven by selfish motives. But we do not need experiments to know that. In our view, what the experiments show is that the typical economic auxiliary hypothesis of non-tuism should not be generalized to other contexts. Indeed, we know that when the experimental situation is framed as a market interaction, participants will be more inclined to keep more money, share (...) less, and disregard other participants’ welfare [Hoffman et al., 1994]. When the same game is framed as a fair division one, participants overall show a much greater concern for the other parties’ interests. The data thus indicate that the context of an interaction is of paramount importance in eliciting different motives. The challenge then is to model utility functions that are general enough to subsume a variety of motives and specific enough to allow for meaningful, interesting predictions to be made. For the sake of simplicity (and brevity), in what follows we will concentrate upon the results of experiments that show what appears to be individuals’ disposition to behave in a fair manner in a variety of circumstances [Camerer, 2003]., though what we are saying can be easily applied to other research areas. Such experimental results have been variously interpreted, each interpretation being accompanied by a specific utility function. We shall consider three such functions and the underlying interpretations that support them, and assess each one on the basis of what they claim to be able to explain and predict. (shrink)

The paper presents results of recent laboratory experiments that study if and how computer-mediated communication affects cooperation and trust. It is argued that communication medium does not matter much for trust-building and maintenance, whereas relevant pre-play communication and group size can have a major influence. The implications of the findings for the design of sites that depend on trusting communities are discussed.

It is usually assumed in game theory that agents who interact strategically with each other are rational, know the strategies open to other agents as well as their payoffs and, moreover, have common knowledge of all the above. In some games, that much information is sufficient for the players to identify a "solution" and play it. The most commonly adopted solution concept is that of Nash equilibrium. A Nash equilibrium is defined a combination of strategies, one for each player, such (...) that no player can profit from a deviation from his strategy if the opponents stick to their strategies. Nash equilibrium is taken to have predictive power, in the sense that in order to predict how rational agents will in fact behave, it is enough to identify the equilibrium patterns of actions. Barring the case in which players have dominant strategies, to play her part in a Nash equilibrium a player must believe that the other players play their part, too. But an intelligent player must immediately realize that she has no ground for this belief. Take the case of a one-shot, simultaneous game. Here all undominated strategies are possible choices, and the beliefs supporting them are possible beliefs, even if this game has a.. (shrink)

There has been a great deal of interaction among game theorists, philosophers and logicians in certain foundational problems concerning rationality, the formalization of knowledge and practical reasoning, and models of learning and deliberation. This volume brings together the work of some of the pre-eminent figures in their respective disciplines, all of whom are engaged in research at the forefront of their fields. Together they offer a conspectus of the interaction of game theory, logic and epistemology in the formal models of (...) knowledge, belief, deliberation and learning, and in the relationship between Bayesian decision theory and game theory, as well as between bounded rationality and computational complexity. (shrink)

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, we (...) do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

Gian Aldo Antonelli and Cristina Bicchieri. Forward Induction.

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common (...) reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction. (shrink)

Bicchieri's topic is the modeling of interaction between decision makers in situations in which the outcome of the interaction depends on what the parties jointly do. Examples include chess, firms competing for business, politicians competing for votes, jury members deciding on a verdict, animals fighting over prey, bidders competing in auctions, threats and punishments in long-term relationships. Rationality assumptions are a basic ingredient of game theory, but though rational choice might be unproblematic in normative decision theory, it becomes problematic in (...) interactive contexts, where the outcome of one’s choice depends on the actions of other agents. Another basic ingredient is the idea of equilibrium play: roughly, an equilibrium is a combination of strategies, one for each player, such that each player’s strategy is a best reply to the other players’ choices. Thus it is individually rational for each agent to play her equilibrium strategy; but, notoriously, such individually rational play can lead to sub-optimal outcomes, as in the well-known prisoner’s dilemma. The relationship between rationality assumptions and equilibrium play is Bicchieri’s main focus. (shrink)

The isolation and professionalization of philosophy is detrimental to it. The most interesting philosophical activity is conducted at the interface of philosophy and other disciplines. Thus philosophy must continue to cross boundaries and avoid fretting about what is and is not philosophy proper.

A large class of games is that of non-cooperative, extensive form games of perfect information. When the length of these games is finite, the method used to reach a solution is that of a backward induction. Working from the terminal nodes, dominated strategies are successively deleted and what remains is a unique equilibrium. Game theorists have generally assumed that the informational requirement needed to solve these games is that the players have common knowledge of rationality. This assumption, however, has given (...) rise to several problems and paradoxes. Most notably, it has been shown that the common knowledge assumption makes the theory of the game inconsistent at some information set. The present paper shows that a) no common knowledge of rationality need be assumed for the backward induction solution to hold. Rather, it is sufficient that the players have a number of levels of knowledge proportional to the length of the game, and b) it is also necessary that the number of levels of knowledge is finite and proportional to the length of the game. For a higher number of levels of knowledge, inconsistencies arise. (shrink)

Social cooperation often relies on individuals’ spontaneous norm obedience when there is no punishment for violation or reward for compliance. However, people do not consistently follow pro-social norms. Previous studies have suggested that an individual’s tendency toward norm conformity is affected by empirical information (i.e., what others did or would do in a similar situation) as well as by normative information (i.e., what others think one ought to do). Yet little is known about whether people have an intrinsic desire to (...) obtain norm-revealing information. In this paper, we use a dictator game to investigate whether dictators actively seek norm-revealing information and, if so, whether they prefer to get empirical or normative information. Our data show that although the majority of dictators choose to view free information before making decisions, they are equally likely to choose empirical or normative information. However, a large majority (more than 80%) of dictators are not willing to incur even a very small cost for getting information. Our findings help to understand why norm compliance is context-dependent, and highlight the importance of making norm-revealing information salient in order to promote conformity. (shrink)

Edited by three leading figures in the field, this exciting volume presents cutting-edge work in decision theory by a distinguished international roster of contributors. These mostly unpublished papers address a host of crucial areas in the contemporary philosophical study of rationality and knowledge. Topics include causal versus evidential decision theory, game theory, backwards induction, bounded rationality, counterfactual reasoning in games and in general, analyses of the famous common knowledge assumptions in game theory, and evaluations of the normal versus extensive form (...) formulations of complex decision problems. (shrink)

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a su cient for them to play the backward induction solution in centipede games. To obtain this result, (...) we do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

There has been a great deal of interaction among game theorists, philosophers and logicians in certain foundational problems concerning rationality, the formalization of knowledge and practical reasoning, and models of learning and deliberation. This volume brings together the work of some of the pre-eminent figures in their respective disciplines, all of whom are engaged in research at the forefront of their fields. Together they offer a conspectus of the interaction of game theory, logic and epistemology in the formal models of (...) knowledge, belief, deliberation and learning, and in the relationship between Bayesian decision theory and game theory, as well as between bounded rationality and computational complexity. (shrink)

The paper presents a simulation of the dynamics of impersonal trust. It shows how a "trust and reciprocate" norm can emerge and stabilize in populations of conditional cooperators. The norm, or behavioral regularity, is not to be identified with a single strategy. It is instead supported by several conditional strategies that vary in the frequency and intensity of sanctions.

During the Nineties Italian politics underwent major changes. Following the uncovering of systemic corruption, the current political establishment was wiped out. The system of representation at both the national and local level underwent a significant transformation that improved voters’ control over their elected representatives. We argue that both events were the consequence of citizens’ demand for greater accountability of public officers. We model the relationship between voters and politicians as a repeated Trust game. In such game, cooperation can be attained (...) by means of external or internal controls. Whereas judicial investigation is an external monitoring mechanism, the electoral reform provides controls internal to the political system. We explain the Italian transition between these different modes of control and show under which conditions a cooperative equilibrium can be established in which voters trust their representatives who in turn act in the public interest. (shrink)

Not so long ago, many economists and philosophers felt that their disciplines had no use for experimental methods. An experimental study was, by its nature, ‘not economics’ or ‘not philosophy’ – psychology maybe. Opinion has changed dramatically. This issue of Economics and Philosophy represents a collection of recent contributions to experimental research that explicitly deal with empirical findings or methodological questions in the intersection of the two disciplines. To the best of our knowledge, it is the first such collection dedicated (...) to addressing these common interests. (shrink)

Much of the history of game theory has been dominated by the problem of indeterminacy. The very search for better versions of rationality, as well as the long list of attempts to refine Nash equilibrium, can be seen as answers to the indeterminacy that has accompanied game theory through its history. More recently, the experimental approach to game theory has attempted a more radical solution: by directly generating a stream of behavioral observations, one hopes that behavioral hypotheses will be sharper, (...) and predictions more accurate. This article looks at several attempts to address indeterminacy, including the shift to evolutionary models. However, because its goal is to establish whether rational choice models are inescapably doomed to produce indeterminate outcomes, it pays much more attention to the experimental turn in game theory, the difficulty it encounters, and the promising results obtained by more realistic models of rationality that include a social component. (shrink)

Gian Aldo Antonelli and Cristina Bicchieri. Backwards Forwards Induction.