Paul Weirich

To handle epistemic and pragmatic risks, Gärdenfors and Sahlin (1982, 1988) design a decision procedure for cases in which probabilities are indeterminate. Their procedure steps outside the traditional expected utility framework. Must it do this? Can the traditional framework handle risk? This paper argues that it can. The key is a comprehensive interpretation of an option's possible outcomes. Taking possible outcomes more broadly than Gärdenfors and Sahlin do, expected utility can give risk its due. In particular, Good's (1952) decision procedure adequately handles indeterminate probabilities and the risks they generate.

The conditional probability of h given e is commonly claimed to be equal to the probability that h would have if e were learned. Here I contend that this general claim about conditional probabilities is false. I present a counter-example that involves probabilities of probabilities, a second that involves probabilities of possible future actions, and a third that involves probabilities of indicative conditionals. In addition, I briefly defend these counter-examples against charges that the probabilities they involve are illegitimate

Standard principles of rational decision assume that an option's utility is both comprehensive and accessible. These features constrain interpretations of an option's utility. This essay presents a way of understanding utility and laws of utility. It explains the relation between an option's utility and its outcome's utility and argues that an option's utility is relative to a specification of the option. Utility's relativity explains how a decision problem's framing affects an option's utility and its rationality even for an agent who is cognitively perfect and lacks only empirical information. The essay rewrites standard laws of utility to accommodate relativization to propositions' specifications. The new laws are generalizations of the standard laws and yield them as special cases.

How do rational agents coordinate in a single-stage, noncooperative game? Common knowledge of the payoff matrix and of each player's utility maximization among his strategies does not suffice. This paper argues that utility maximization among intentions and then acts generates coordination yielding a payoff-dominant Nash equilibrium. ‡I thank the audience at my paper's presentation at the 2006 PSA meeting for many insightful points. †To contact the author, please write to: Philosophy Department, University of Missouri, Columbia, MO 65211; e-mail: [email protected].

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal normal-form games. In synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists.

Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where probabilities and utilities are indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory.

A computer simulation runs a model generating a phenomenon under investigation. For the simulation to be explanatory, the model has to be explanatory. The model must be isomorphic to the natural system that realizes the phenomenon. This paper elaborates the method of assessing a simulation's explanatory power. Then it illustrates the method by applying it to two simulations in game theory. The first is Brian Skyrms's (1990) simulation of interactive deliberations. It is intended to explain the emergence of a Nash equilibrium in a noncooperative game. The second is Skyrms's (2004) simulation of the evolution of cooperation. It is intended to explain cooperation in assurance games. The final section suggests ways of enhancing the explanatory power of these simulations.

Some decision theorists criticize expected utility decision analysis and propose mean-risk decision analysis as a replacement. They claim that expected utility decision analysis neglects attitudes toward risk whereas mean-risk decision analysis accords these attitudes their proper status. However mean-risk decision analysis and expected utility decision analysis are not incompatible, and it is advantageous for decision theory to develop each in a way that complements the other. Here I present a mean-risk rule that governs preferences among options and options given states. This mean-risk rule complements an expected utility rule that takes the utility of an option-state pair as the utility of the option given the state. I argue for the mean-risk rule using principles concerning basic intrinsic desires. The rule is comparative, but the last section offers some suggestions for its quantitative development.