Abstract
We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.
Highlights
The questions of coalition formation and cooperation are central to the theory of strategic behavior.When a subset of the agents forms a coalition, they often behave “cooperatively” in the sense that they choose and implement a joint course of action
It is assumed that coalitions are given, and each coalition, rather than maximizing its individual payoff, maximizes a group payoff function, which can range from a simple sum of individual payoff functions (Mallozzi and Tijs [1,2,3]) to a vector valued function choosing points on the Pareto frontier of the individual payoffs of the members of the coalition (Ray and Vohra [4], Ray [5])
Even though we focus on the partial cooperative Cournot-Nash equilibrium for the sake of exposition, a similar result can be obtained with the partial cooperative
Summary
The questions of coalition formation and cooperation are central to the theory of strategic behavior.When a subset of the agents forms a coalition, they often behave “cooperatively” in the sense that they choose and implement a joint course of action. We prove the existence of partial cooperative Cournot-Nash and Stackelberg equilibria in supermodular games. In case these games are not supermodular, we show that a partial cooperative Stackelberg equilibrium exists if the strategy sets are compact, payoff functions are continuous and there exists a Nash equilibrium at the second stage of the game.
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