Game theory and rational decision (original) (raw)

Satisficing equilibria: A non-classical theory of games and decisions

2002

Satisficing, or being "good enough," is the fundamental obligation of rational decision makers. We cannot rationally choose an option, even when we do not know of anything better, unless we know it is good enough. Unfortunately, we are not often in the position of knowing that there could be no better option, and hence that the option must be good enough. A complete search through all logical possibilities is often impractical, particularly in multi-agent contexts, due to excessive computational difficulty, modeling complexity, and uncertainty. It can be equally impractical, if it is even possible, to determine the cost of the additional required search to find an option that is good enough. In a departure from the traditional notion of satisficing as a species of bounded rationality, satisficing is here redefined in terms of a notion of intrinsic rationality. Epistemic utility theory serves as the philosophical foundation of a new praxeological decision-making paradigm of satisficing equilibria that is applicable to both single-and multiple-agent scenarios. All interagent relationships are modeled by an interdependence function that explicitly accommodates both self and group interest, from which multilateral and unilateral selectability and rejectability mass functions can be derived and compared via the praxeic likelihood ratio test.

Game Theory in Philosophy

Topoi, 2005

Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals with games in which all players have preference orderings over the possible outcomes of the game. This paper gives an informal introduction to the theory and a survey of applications in diverse branches of philosophy. No criticism is reviewed. Game theory is shown at work in discussions about epistemological dependence (prisoner's dilemma), liberalism and efficiency (Nash equilibrium), Hume's concept of convention (correlated equilibrium), morality and rationality (bargaining games), and distributive justice and egalitarianism (evolutionary game theory). A guide to the literature provides hints at applications in collective intentionality, epistemology, ethics, history of philosophy, logic, philosophy of language, and political philosophy.

EPISTEMIC FOUNDATIONS OF SOLUTION CONCEPTS IN GAME THEORY: AN INTRODUCTION

1997

We give an introduction to the literature on the epistemic foundations of solution concepts in game theory. Only normal-form games are considered. The solution concepts analyzed are rationalizability, strong rationalizability, correlated equilibrium and Nash equilibrium. The analysis is carried out locally in terms of properties of the belief hierarchies. Several examples are used throughout to illustrate definitions and concepts.

TR-2013007: On Definitive Solutions of Strategic Games

2013

In his dissertation of 1950, Nash based his concept of the solution to a game on the assumption that “a rational prediction should be unique, that the players should be able to deduce and make use of it.” We study when such definitive solutions exist for strategic games with ordinal payoffs. We offer a new, syntactic approach: instead of reasoning about the specific model of a game, we deduce properties of interest directly from the description of the game itself. This captures Nash’s deductive assumptions and helps to bridge a well-known gap between syntactic game descriptions and specific models which could require unwarranted additional epistemic assumptions, e.g., common knowledge of a model. We show that games without Nash equilibria do not have definitive solutions under any notion of rationality, but each Nash equilibrium can be a definitive solution for an appropriate refinement of Aumann rationality. With respect to Aumann rationality itself, games with multiple Nash equili...

Logic and the foundations of the theory of games and decisions: introduction

Research in Economics, 2003

Logic and the foundations of the theory of games and decisions: introduction This special issue of Research in Economics contains a selection of papers presented at the fifth conference on "Logic and the Foundations of the Theory of Games and Decisions" (LOFT5), which took place in Torino at the International Center for Economics Research (ICER) in June 2002. 1 The LOFT conferences have been a regular biannual event since 1994. With the exception of the first conference, which was hosted by the Centre International de Recherches Mathematiques in Marseille, the LOFT events have taken place at ICER and would not have been possible without ICER's generous support and hospitality. The LOFT conferences are interdisciplinary events that bring together researchers from a variety of fields: computer science, economics, game theory, logic, mathematical psychology, philosophy and statistics. There is substantial overlap between the LOFT community and the community of researchers who are active in another regular, biannual event, namely the conferences on Theoretical Aspects of Rationality and Knowledge (TARK), which have a longer history than the LOFT conferences. 2 In its original conception, LOFT had as its central theme the application of logic, in particular modal epistemic logic, to foundational issues in the theory of games and individual decision-making. Epistemic considerations have been central to game theory for a long time. For example, work has been done on the role of beliefs in refinements of Nash equilibrium since the 1970s and much has been written on common knowledge and common belief since Aumann's seminal paper during that time. The expression interactive epistemology has been used in the game-theory literature to refer to the analysis of what individuals involved in a strategic interaction know about facts concerning the external world as well as facts concerning each other's knowledge and beliefs. What is relatively new is the realization that the tools and methodology that were used in game theory are

Beyond rationality: Rigor without mortis in game theory

Behavioral and Brain Sciences, 2003

Psychological game theory encompasses formal theories designed to remedy game-theoretic indeterminacy and to predict strategic interaction more accurately. Its theoretical plurality entails second-order indeterminacy, but this seems unavoidable. Orthodox game theory cannot solve payoff-dominance problems, and remedies based on interval-valued beliefs or payoff transformations are inadequate. Evolutionary game theory applies only to repeated interactions, and behavioral ecology is powerless to explain cooperation between genetically unrelated strangers in isolated interactions. Punishment of defectors elucidates cooperation in social dilemmas but leaves punishing behavior unexplained. Team reasoning solves problems of coordination and cooperation, but aggregation of individual preferences is problematic.