Strongly Robust Equilibrium and Incentive Compatibility in Common Agency
This paper studies the notion of strongly robust equilibrium (SRE) in common agency with multiple principals that is not only independent of the nature of competition embedded in any ad hoc common agency game but also free from a hierarchy of principals' beliefs on the continuation equilibrium off the equilibrium path following any principal's deviation to any complex mechanism. It shows that an equilibrium relative to any set of mechanisms is strongly robust if and only if it survives in every pure-strategy continuation equilibrium. Furthermore, the set of SRE allocations relative to any arbitrary set of complex mechanisms is equal to the set of SRE allocations relative to the set of menus. As for applications, this paper shows that each principal can infer a best continuation equilibrium for him as a continuation equilibrium in which the agent tells the truth only to him in a class of direct mechanisms with an endogenous incentive compatibility. Subsequently, the existence of SRE can be examined by checking whether the truth-telling continuation equilibria, one for each principal, induce a fixed point of a decision profile only on the equilibrium path given principals' direct mechanisms.
Strongly Robust Equilibrium, Common Agency, Multiple Principals
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