Paul Weirich

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.

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.

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.

Weirich examines three competing views entertained by economic theory about the instrumental rationality of decisions: the first says to maximize self-interest, the second to maximize utility, and the third to satisfice, that is, to adopt a satisfactory option. Critics argue that the first view is too narrow, that the second overlooks the benefits of teamwork and planning, and that the third, when carefully formulated, reduces to the second. Weirich defends a refined version of the principle to maximize utility. A broad conception of utility makes it responsive to the motives and benefits critics allege it overlooks. He discusses generalizations of utility theory to extend it to nonquantitative cases and other cases with nonstandard features.

When a trustee makes a decision for a client, a standard objective is to decide as the client would if he had the trustee's information. How can this objective be attained when, given the trustee's information, there is still uncertainty about the consequences of alternative courses of action? A promising approach is to apply the rule to maximize expected utility using the client's utilities for consequences and the trustee's probabilities for states. But taking utilities and probabilities from different sources causes a problem that has to be resolved. Briefly, the problem is that the client's utilities for consequences involve assessments of risks that are uninformed because he does not have informed probabilities. And the resolution of the problem is to reconstruct his utilities for consequences using a component due to risk that the trustee supplies for the client, and a component due to other consequences that the client supplies for himself.

In a decision problem with a dynamic setting there is at least one option whose realization would change the expected utilities of options by changing the probability or utility function with respect to which the expected utilities of options are computed. A familiar example is Newcomb's problem. William Harper proposes a generalization of causal decision theory intended to cover all decision problems with dynamic settings, not just Newcomb's problem. His generalization uses Richard Jeffrey's ideas on ratifiability, and material from game theory on mixed strategies. Harper's proposal has two drawbacks, however. One concerns the mechanism for choosing among ratifiable options. The other concerns the proposal's reliance upon mixed strategies. Here I make another proposal that eliminates these two drawbacks.