Axiomatic characterizations of solutions for Bayesian games

Bayesian equilibria are characterized by means of consistency and one-person rationality in combination with non-emptiness or converse consistency. Moreover, strong and coalition-proof Bayesian equilibria of extended Bayesian games are introduced and it is seen that these notions can be characterized by means of consistency, one-person rationality, a version of Pareto optimality and a modification of converse consistency. It is shown that, in case of the strong Bayesian equilibrium correspondence, converse consistency can be replaced by non-emptiness. As examples we treat Bayesian potential games and Bayesian congestion games.     

Arbitrage,rationality, and equilibrium

No-arbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, no-arbitrage is synonymous with subjective expected utility maximization in personal decisions, competitive equilibria in capital markets and exchange economies, and correlated equilibria in noncooperative games. The arbitrage principle directly characterizes rationality at the market level; the appearance of deliberate optimization by individual agents is a consequence of their adaptation to the market. Concepts of equilibrium behavior in games and markets can thus be reconciled with the ideas that individual rationality is bounded, that agents use evolutionarily-shaped decision rules rather than numerical optimization algorithms, and that personal probabilities and utilities are inseparable and to some extent indeterminate. Risk-neutral probability distributions, interpretable as products of probabilities and marginal utilities, play a central role as observable quantities in economic systems.     

Games,goals, and bounded rationality

A generalization of the standard n-person game is presented, with flexible information requirements suitable for players constrained by certain types of bounded rationality. Strategies (complete contingency plans) are replaced by policies, i.e., endmean pairs of goals and controls (partial contingency plans), which results in naturally disconnected player choice sets. Well-known existence theorems for pure strategy Nash equilibrium and bargaining solutions are generalized to policy games by modifying connectedness (convexity) requirements.     

The chain-store paradox revisited

The rationality of predatory practices has been extensively debated among economists and lawyers. Selten (1978) considered a fictitious chain-store confronted with potential entrances of local competitors. In his formal analysis via an extensive game with complete and perfect information predatory behavior is precluded by the unique sequential (and perfect) equilibrium. Kreps and Wilson (1982b) and Milgrom and Roberts (1982) established in modified models with incomplete information that predation against early entrants may be rational since it creates a reputation to the effect that later potential entrants are deterred. The present paper offers a modification of Selten's model with complete but imperfect information which renders possible reputation and deterrence.     

Dutch books and agent rationality

According to the Dutch Book Argument (DBA), if an agent's subjective probabilities fail to satisfy the axioms of the probability calculus and so make the agent vulnerable to a Dutch Book, the agent's subjective probabilities are incoherent and the agent is therefore irrational. Critics of DBA have argued, however, that probabilistic incoherence is compatible with various kinds of rationality – logico-semantic, epistemic, instrumental and prudential. In this paper, I provide an interpretation of DBA on which it is true that probabilistic incoherence entails agent irrationality. Articulating this interpretation requires the specification of some of the connections among the varieties of rationality. Once this is done, it becomes possible to vindicate a modest version of DBA.     

Strategic behavior under partial cooperation

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return.     

The individual rationality of maintaining a sense of justice

Let us say that an individual possesses aprincipled preference if she prefers satisfying her preferences without violating the principles of justice governing her community to satisfying her preferences by violating these principles. Although living among possessors of principled preferences benefits individuals, maintaining such a preference is individually costly. Further, individuals can benefit from others possessing principled preferences without themselves possessing one. In this paper, I argue that occupying a choice situation which mirrors key aspects of our own situation, maximizing rationality requires individuals to develop and maintain principled preferences.To establish that maintaining a principled preference is individually rational for the occupants of such a choice situation, I define a range of individual strategies for them, model their choice of individual strategies as a game, and argue that this game involves an equilibrium in which all of its participants would choose to develop and maintain a principled preference.     

Doxastic Conditions for Backward Induction

The problem of finding sufficient doxastic conditions for backward induction in games of perfect information is analyzed in a syntactic framework with subjunctive conditionals. This allows to describe the structure of the game by a logical formula and consequently to treat beliefs about this structure in the same way as beliefs about rationality. A backward induction and a non-Nash equilibrium result based on higher level belief in rationality and the structure of the game are derived.     

Axiomatizing bounded rationality: the priority heuristic

This paper presents an axiomatic framework for the priority heuristic, a model of bounded rationality in Selten’s (in: Gigerenzer and Selten (eds.) Bounded rationality: the adaptive toolbox, 2001) spirit of using empirical evidence on heuristics. The priority heuristic predicts actual human choices between risky gambles well. It implies violations of expected utility theory such as common consequence effects, common ratio effects, the fourfold pattern of risk taking and the reflection effect. We present an axiomatization of a parameterized version of the heuristic which generalizes the heuristic in order to account for individual differences and inconsistencies. The axiomatization uses semiorders (Luce, Econometrica 24:178–191, 1956), which have an intransitive indifference part and a transitive strict preference component. The axiomatization suggests new testable predictions of the priority heuristic and makes it easier for theorists to study the relation between heuristics and other axiomatic theories such as cumulative prospect theory.     

Marx on ideology,power and force

As Marx matured as a thinker, he became more acutely aware of the obstinate hold which capitalism exercised upon society. Consequently, he was forced to complement his theory of revolution with a theory of social structures. In this paper, I aim to explore Marx's ideas on this point as they emerge in three of his more mature works, i.e.,Capital, Grundrisse, and theTheories of Surplus Value. My enterprise is guided by my convictions that (i) the notions of ideology, power and force are still central to debates in modern social theory, and (ii) Marx's development of these notions has the intrinsic merit of providing a useful and sophisticated contribution to such debates.     

Individual rationality and the concept of social welfare

This paper, written in October 1974, deals with some game aspects of the social choice problem. The question asked is whether there exists a social decision rule satisfying the conditions imposed by Arrow over all the preference profiles that may logically arise under it (in the sense of being compatible with individual rationality). This question is answered in the affirmative. The meaning of this result is that if Arrow's condition of unrestricted domain is modified so as to exclude any profile which contradicts individual rationality, then an Arrovian social welfare function can be shown to exist (subject to the assumption that whenever the social outcome is in doubt, individuals use the maximin criterion in order to choose their voting strategy).This research was written up in October 1974 at Northwestern University and was partially supported by the National Science Foundation.     

Cognitive rationality and alternative belief measures

In this article, we first examine the various criticisms of the probabilistic model. Then we introduce capacities in order to show that if a probability measure corresponds to anesthetizing the belief of the agent's knowledge, it is then possible to suggest another type of rationality—namely, being able to describe a wise and a rash behavior when facing risk—and therefore another model of belief under uncertainty. While trying to specify various alternative measures, possibility, necessity, and measures resulting from a triangular norm or from a triangular conorm, we finally try to define the field of application of the probabilistic model as well as a sign of the rationality choice: constraint of mass-unity for traditional rationality, and constraint of duality for the one we present.This article is a revised version of a paper presented during the FUR V Congress, Duke University, North Carolina, USA, June 10–13, 1990. I am indebted to Bertrand Munier, Alain Chateauneuf, Olivier Favereau, Jacques-François Thisse, Bernard Walliser, and Kip Viscusi for helpful comments on earlier versions of this article.     

Is the Disposition of Constrained Maximization Chosen Rationally?

One of the most important issues in moral philosophy is whether morality can be justified by rationality. The purpose of this study is to examine Gauthier’s moral theory, focusing on the disposition of constrained maximization, which is the main thrust of his project to justify morality rationally. First of all, I shall investigate Gauthier’s assumption and condition for the rationality of the disposition of constrained maximization so as to disclose that the disposition of constrained maximization is not necessarily chosen by rational agents. Then I shall explore his other arguments including ones for the reinterpretation of rationality and the self-critical reflection of rational beings, which can be considered as his further efforts to make the disposition of constrained maximization a rational choice. By exploring them, I shall attempt to indicate that those arguments are not valid so long as he clings to the maximizing conception of rationality and thereby this conception of rationality itself is not enough to provide morality with a basis.     

How robust is the rationality assumption in economics? A statistical test based on student grade distributions

This note re-addresses the question of the rationality of economic actors in a new setting. We examine the distribution of final course grades for a “Principles of Economics Class” in an effort to draw conclusions about rational student work effort. Based on the concepts of the opportunity cost of time, the relative reward for earning various grades (based on university codes for determining grade points) and the concept of rationality, we expect to find a greater percentage of grades at the lower end of the distribution for each grade level. We find statistical evidence that there are more students at the lower end of each grade interval than at the upper end. This result is consistent with what economists have long conjectured: students are rational in the allocation of study time.     

On the consistency of choice

Consistency of choice is a fundamental and recurring theme in decision theory, social choice theory, behavioral economics, and psychological sciences. The purpose of this paper is to study the consistency of choice independent of the particular decision model at hand. Consistency is viewed as an inherently logical concept that is fundamentally void of connotation and is thus disentangled from traditional rationality or consistency conditions imposed on decision models. The proposed formalization of consistency takes two forms: internal consistency, which refers to the property that a choice model does not generate contradictory statements; and semantic consistency, which refers to the idea that a theory’s predictions are valid with respect to some observed data. In addressing semantic consistency, the relationship between theory and data is analyzed in terms of so-called duality mappings, which allow a passage between the two universes in a way that consistency is preserved. The formalization of consistency concepts relies on adapting the revealed preference theory to the context-dependent setting. The paper concludes by discussing the implications of the proposed framework and how it relates to classical revealed preference theory and other formalizations of the relationship between the theory and reality of choice.     

Identification of a princess under incomplete information: an amarna story

This article presents four analyses of an interaction between the middle-Bronze Age Pharaoh Nibmuarea and the Babylonian king Kadashman-Enlil as described in the Amarna letters (Moran [1992] The Amarna Letters, The Johns Hopkins Universiy Press, Baltimore, Maryland). Intent on denying the Pharaoh his daughter in marriage, the Babylonian king was faced with the choice of sending messengers who could ('dignitaries') or could not identify ('non-dignitaries') his missing sister in the Pharaoh's court. Intent on marrying the king's daughter, the Pharaoh was faced with the choice of showing the sister or showing someone else. Based on the assumption of complete information (game 1), the analysis revealed a dominant-strategy equilibrium: Nibmuarea shows the sister and Kadashman-Enlil sends non-dignitaries. Based on the assumption of one-sided incomplete information (Pharaoh's misperception; game 2), the analysis revealed that the Pharaoh had a dominant strategy of showing the sister irrespective of whether the king is keen or reluctant to learn about his sister's fate. Based on the assumption of one-sided incomplete information (Kadashman-Enlil's misperception; game 3), the analysis revealed that if non-dignitaries are sent, the Pharaoh prefers showing someone other than his sister. Based on the assumption of two-sided incomplete information (game 4), the Pharaoh finds it more beneficial to present the sister irrespective of whether his intentions are genuine or feigned. With incomplete information, it is difficult to judge the other's intentions; the cost of being caught cheating by not showing the sister to knowledgeable messengers was quite high. These analyses highlight the strategic uncertainty that characterized this Bronze-Age interaction.     

Norms and rationality. Is moral behavior a form of rational action?

This article addresses major arguments in the controversy about the “rationality” of moral behavior: can moral behavior be explained by rational choice theory (RCT)? The two positions discussed are the incentives thesis (norms are incentives as any other costs and benefits) and the autonomy thesis claiming that moral behavior has nothing to do with utility. The article analyses arguments for the autonomy thesis by J. Elster, A. Etzioni, and J. G. March and J. P. Olsen. Finally, the general claim is discussed whether norm following and norm emergence are utility maximizing. The conclusion is that the autonomy thesis is not tenable if one applies a wide subjectivist, social psychological version of RCT that includes the assumption of “bounded rationality.” The autonomy thesis is only compatible with a narrow version of RCT that excludes internal outcomes and that refers to norms that do not have external outcomes. It is argued that such a narrow version is not capable of explaining many forms of behavior social scientists are interested in.     

Implementation without rationality assumptions

Hurwicz (Social Choice and public decision making. Essays in honor of Kenneth J. Arrow, Cambridge University Press, Cambridge, 1986) was the first to study an approach to implementation theory based on choice functions instead of preference relations. We argue that the solution concept used by him, the generalized Nash equilibrium, is not really compatible with the idea that individual behavior is describable by a choice function. A new solution concept that better fits the choice function framework is then introduced. Using this, we investigate what behavioral assumptions are needed for the full characterizations of Nash implementable social choice correspondences to still hold. We will show that a condition known as Property α is central.     

Who gains from information asymmetry?

This article considers an asymmetric contest with incomplete information. There are two types of players: informed and uninformed. Each player has a different ability to translate effort into performance in terms of the contest success function. While one player’s type is known to both players, the other is private information and known only to the player himself. We compare the Bayesian Nash equilibrium outcome of a one-sided private information contest to the Nash equilibrium with no private information, in which both players know the type of the other player. We show conditions under which uncertainty increases the investment of the uninformed player and the rent dissipation of the contest, while decreasing the expected net payoff of the informed player. In addition, we consider conditions under which the informed player—before knowing his own type—prefers that the uninformed player knows his type. Moreover, we show conditions for the existence/non-existence of equilibrium in a two-stage contest in which the informed player declares his type (or does not declare) in the first stage and in the second stage the two players play according to the information available to them.