Consequentialism and Bayesian Rationality in Normal Form Games

In single-person decision theory, Bayesian rationality requires the agent first to attach subjective probabilities to each uncertain event, and then to maximize the expected value of a von Neumann–Morgenstern utility function (or NMUF) that is unique up to a cardinal equivalence class. When the agent receives new information, it also requires subjective probabilities to be revised according to Bayes’ rule. In social choice theory and ethics, Harsanyi (1953, 1955, 1975a, 1975b, 1976, 1978) has consistently advocated Bayesian rationality as a normative standard, despite frequent criticism and suggestions for alternatives. In game theory, however, Bayesian rationality is almost universally accepted, not only as a normative standard, but also in models intended to describe players’ actual behaviour. Here too Harsanyi (1966, 1967–8, 1977a, b, 1980, 1982a, b, 1983a, b) has been a consistent advocate. In particular, his work on games of incomplete information suggests that one should introduce extra states of nature in order to accommodate other players’ types, especially their payoff functions and beliefs. Later work by Bernheim (1984), Pearce (1984), Tan and Werlang (1988), and others emphasizes how subjective probabilities may be applied fruitfully to other players’ strategic behaviour as well. In the past I have tried to meet the social choice theorists’ understandable criticisms of the Bayesian rationality hypothesis. To do so, I have found it helpful to consider normative standards of behaviour in single-person decision trees. In particular, it has been useful to formulate a surprisingly powerful “consequentialist” hypothesis. This requires the set of possible consequences of behaviour in any single-person decision tree to depend only on the feasible set of consequences in that tree. In other words, behaviour must reveal a consequence choice function mapping feasible sets into choice subsets.