We present an axiomatic approach for a class of finite, extensive form ganies of perfect information that makes use of notions like "rationality at a node" and "knowledge at a node." We show that, in general, a theory that is sufEcient to infer an equilibrium must be modular: for each subgame G' of a game G the theory of game G must contain just enough inforniation about the subgame G' to infer an equilibrium for G'. This means, in general, that (...) the level of knowledge relative to any subgame of G must not be the same as the level of knowledge relative to tlie original game G. We show that whenever the theory of the game is the same at each node, a deviation from equilibrium play 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 cause any revision of the theory of the game. (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)
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.
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)
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)
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)
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)
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.
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 votersâ control over their elected representatives. We argue that both events were the consequence of citizensâ 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)
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.
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)
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)
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)
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)
In recent years 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 unique volume brings together the work of some of the preeminent 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)
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)
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)
