A Belief-Based Characterization of Reduced-Form Auctions

Abstract

We study games of chance (e.g., pokers, dices, horse races) in the form of agents' first-order posterior beliefs about game outcomes. We ask for any profile of agents' posterior beliefs, is there a game that can generate these beliefs? We completely characterize all feasible joint posterior beliefs from these games. The characterization enables us to find a new variant of Border's inequalities (Border, 1991), which we call a belief-based characterization of Border's inequalities. It also leads to a generalization of Aumann's Agreement Theorem. We show that the characterization results are powerful in bounding the correlation of agents' joint posterior beliefs.

arXiv commentGames of Chance, Posterior Beliefs, Reduced Form Auctions, Aumann's Agreement Theorem, Bayesian Persuasion