A Nonspeculation Theorem with an Application to Committee Design

Various well known agreement theorems show that if players have common knowledge of actions and a “veto" action is available to every player, then they cannot agree to forgo a Pareto optimal outcome simply because of private information in settings with unique equilibrium. We establish a nonspeculation theorem which is more general than previous results and is applicable to political and economic situations that generate multiple equilibria. We demonstrate an application of our result to the problem of designing an independent committee free of private persuasion.

AGREEMENT THEOREMS FOR SELF-LOCATING BELIEF

In this paper, I first outline Aumann’s famous “no agreeing to disagree” theorem, and a second related theorem. These results show that if two or more agents, who have epistemic and credal states that are defined over algebras that do not include any self-locating propositions, have certain information about one another’s epistemic and credal states, then such agents must assign the same credence to certain propositions. I show, however, that both of these theorems fail when we consider agents who have epistemic and credal states that are defined over algebras that do include self-locating propositions. Importantly, these theorems fail for such agents even when we restrict our attention to the credences that such agents have in non-self-locating propositions. Having established this negative result, I then outline and prove three agreement theorems that hold for such agents.