Participation Security and Elementary Mechanisms

A mechanism is participation secure if each agent has an action that guarantees them a payoff better than their outside option, no matter how other agents behave and no matter how uncertainty about preferences is resolved. Participation security implies that every agent’s interim payoff exceeds their outside option, in every information structure and equilibrium. The converse is true if the mechanism is elementary: Every action is the unique best response for some type in some information structure and equilibrium. Elementary mechanisms are shown to be a suffcient class for maximizing the welfare guarantee. Hence, for maximizing the guarantee, participation security is equivalent to interim participation in all information structures and equilibria.