Equilibrium refinements for the network formation game

Abstract

This paper examines a normal form game of network formation due to Myerson (Game theory: analysis of conflict, Harvard University Press, Cambridge, 1991). All players simultaneously announce the links they wish to form. A link is created if and only if there is mutual consent for its formation. The empty network is always a Nash equilibrium of this game. We define a refinement of Nash equilibria that we call trial perfect. We show that the set of networks which can be supported by a pure strategy trial perfect equilibrium coincides with the set of pairwise-Nash equilibrium networks, for games with link-responsive payoff functions.