Competing mechanisms and folk theorems: Two examples

In competing-mechanism games under exclusivity, principals simultaneously post mechanisms, and agents then simultaneously participate and communicate with at most one principal. In this setting, we develop two complete-information examples that question the folk theorems established in the literature. In the first example, there exist equilibria in which some principal obtains less than her min-max payoff, computed over all players' actions. Thus folk theorems must involve bounds on principals' payoffs that depend on the messages available to the agents, and not only on the players' actions. The second example shows that even this nonintrinsic approach is misleading: there exist incentive-feasible allocations in which principals obtain more than their min-max payoffs, computed over arbitrary spaces of mechanisms, but which cannot be supported in equilibrium. Key to these results is the standard requirement that agents' participation and communication decisions are tied together.