In a generic finite normal form game with 2(α) + 1 Nash equilibria, at least alpha of the equilibria are nondegenerate mixed strategy equilibria (that is, they involve randomization by some players).
Keywords: Normal form, mixed strategy, game theory
It seems reasonable to suppose that in repeated games in which communications is possible, play is determined through a process of negotiation and renegotiation as events unfold. In the absence of a satisfying theory of players’ bargaining power, it is unclear how to model this process. Symmetric repeated games are an important class in which the problem is less troublesome. Whatever its source, bargaining power is presumably the same for all players in a symmetric game. We take equal bargaining power to mean that a player can mount a credible objection to a continuation equilibrium in which he receives a particular expected present discounted value, if there are other self enforcing agreements that never give any player such a low continuation value after any history. This is formalized in a solution concept called consistent bargaining equilibrium.
Traditional agency theory assumes that the principal has no more information about the agent’s actions than the enforcement authorities have. This is unrealistic in many settings, and in repeated models, additional information possessed by the principal changes the nature of the problem. Such information can be used in implicit, self-enforcing contracts between principal and agent, that supplement the usual explicit contracts. This paper studies the way in which the two kinds of contracts are combined in constrained efficient equilibria of the agency supergame. The agent’s compensation is comprised of both guaranteed payments and voluntary bonuses from the principal. We give a simple characterization of the composition of remuneration in the optimal dynamic scheme.
This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The approach emphasizes the equilibrium value set and the static optimization problems embedded in external equilibria. We characterize these equilibria, and provide computational and comparative statics results. The “self-generation” and “bang-bang” propositions which were at the core of our analysis of optimal cartel equilibria [2], are generalized to asymmetric games and infinite action spaces. New results on optimal implicit reward functions include the necessity (as opposed to sufficiency) of bang-bang functions, and the nature of optimal punishment regions.
JEL Classification: 026
Keywords: Pure strategy sequential equilibria, Repeated games, Imperfect monitoring
There exist optimal symmetric equilibria in the Green-Porter model [5, 8] having an elementary intertemporal structure. Such an equilibrium is described entirely by two subsets of price space and two quantities, the only production levels used by firms in any contingency. The central technique employed in the analysis is the reduction of the repeated game to a family of static games.