The core of a strategic game

Abstract

AbstractIn this paper, I introduce and study the $\gamma$-core of a general strategic game. I first show that the $\gamma$-core of an arbitrary strategic game is smaller than the conventional $\alpha$- and $\beta$- cores. I then consider the partition function form of a general strategic game and show that a prominent class of partition function games admit nonempty $\gamma$-cores. Finally, I show that each $\gamma$-core payoff vector (a cooperative solution) can be supported as an equilibrium outcome of an intuitive non-cooperative game and the grand coalition is the unique equilibrium outcome if and only if the $\gamma$-core is non-empty.