Invitation games and the price of stability

Abstract

Given an arbitrary 2-player game G that we refer to as the basic game, we propose a notion of a multiplayer invitation game that proceeds for a fixed number of rounds, where in each round some player (whose identity is determined by a scheduler) gets to invite a player of his choice to play a match of the basic game. The question that we study is how does the price of stability of the invitation game compare to that of the basic game. For a wide range of schedulers we prove a dichotomy result, showing that there are only two types of basic games, those that we call invitation resistant in which the price of stability of the invitation version is equal to that of the basic game, and those that we call asymptotically efficient in which the price of stability tends to 0 as the number of rounds grows. 1 In particular, when the basic game is the prisoners dilemma the game is asymptotically efficient if and only if the payoff when both players defect is nonzero.