Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also common (...) knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (shrink)

In certain finite extensive games with perfect information, Cristina Bicchieri (1989) derives a logical contradiction from the assumptions that players are rational and that they have common knowledge of the theory of the game. She argues that this may account for play outside the Nash equilibrium. She also claims that no inconsistency arises if the players have the minimal beliefs necessary to perform backward induction. We here show that another contradiction can be derived even with minimal beliefs, so there is (...) no paradox of common knowledge specifically. These inconsistencies do not make play outside Nash equilibrium plausible, but rather indicate that the epistemic specification must incorporate a system for belief revision. Whether rationality is common knowledge is not the issue. (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)

Two justifications of backward induction (BI) in generic perfect information games are formulated using Bonanno's (1992; Theory and Decision 33, 153) belief systems. The first justification concerns the BI strategy profile and is based on selecting a set of rational belief systems from which players have to choose their belief functions. The second justification concerns the BI path of play and is based on a sequential deletion of nodes that are inconsistent with the choice of rational belief functions.

This commentary focuses on the parts of psychological game theory dealing with preference, as illustrated by team reasoning, and supports the conclusion that these theoretical notions do not contribute above and beyond existing theory in understanding social interaction. In particular, psychology and games are already bridged by a comprehensive, formal, and inherently psychological theory, interdependence theory (Kelley & Thibaut 1978; Kelley et al. 2003), which has been demonstrated to account for a wide variety of social interaction phenomena.

Subjunctive conditionals are fundamental to rational decision both in single agent and multiple agent decision problems. They need explicit analysis only when they cause problems, as they do in recent discussions of rationality in extensive form games. This paper examines subjunctive conditionals in the theory of games using a strict revealed preference interpretation of utility. Two very different models of games are investigated, the classical model and the limits of reality model. In the classical model the logic of backward induction (...) is valid, but it does not use subjunctive conditionals; the relevant subjunctive conditionals do not even make sense. In the limits of reality model the subjunctive conditionals do make sense but backward induction is valid only under special assumptions. (shrink)