INTRODUCTION

One of the questions often asked of subjective Bayesian game theorists is where the prior (on opponents' moves) “comes from.” That is, how can such a probability distribution be elicited. This chapter addresses that question and shows that elicitation for games is exactly the same as elicitation for decision problems that involve uncertainty arising from other sources than the behavior of an opposing player. We review the elicitation of a single uncertain event, many events, dependence between action and state, and sequential decision problems. Each of these are shown to have application to game-theoretic contexts. The subjective Bayesian approach to game theory is thus shown to be operational.

We take standard Bayesian utility theory in the sense of Ramsey, Savage, and DeGroot as a standard of rational behavior. While we have studied various relaxations of these principles in other work, such as finite additivity: (Levi 1980, §§5.7, 5.9, 5.11,12.16; Schervish, Seidenfeld, and Kadane 1984), state-dependent utility (Seidenfeld, Schervish, and Kadane 1990), and ordering (Levi 1974, 1980, 1986; Schervish, Seidenfeld, and Kadane 1990), the only relaxation of importance for this paper is possible dependence between act and state. To those principles we would add other principles or accept constraints on these principles only reluctantly. A general review of the consequences of this stance for game theory is given in Kadane and Larkey (1982, 1983) (see also Harsanyi 1982). The issue we address here is how to find the prior opinions, with the intent of being operational.