Dominance and Optimality

About this event

This paper proposes a general theory of dominance among choices that encompasses strict and weak dominance among strategies in games, Blackwell dominance among experiments, and first or second order stochastic dominance among monetary lotteries. One choice dominates another if in a variety of situations the former choice yields higher expected utility than the latter. We then investigate whether, in a finite set of possible choices, all undominated choices are optimal in some situation. We present a formal framework in which the answer to this question is positive, and we show that within this framework the set of undominated choices is the smallest set to which the decision maker can restrict attention ex ante without running the risk of not having an optimal choice in the particular situation in which she finds herself. For this result it is crucial that the dominating alternatives are allowed to be convex combinations (in games: mixed strategies). A detailed analysis of dominance in game theory, Blackwell dominance, and first or second order stochastic dominance in one common framework also allows us to compare the properties of these concepts, and to obtain insights into why certain versions of our result apply only to some, but not all of these concepts.