Analysing the compatibility of Nash stability and information diffusion in hedonic games

Abstract

Hedonic games are mathematical models in which a group of agents is divided into appropriate subgroups, and have been studied as a field of cooperative games. Cooperative games with permission structures, on the other hand, are models in which an agent’s participation in a game is by permission of another agent. In this paper, we introduce a permission structure into SASHG, a type of hedonic game, and consider solutions to hedonic games in which information diffusion, i.e., the incentive to issue as many permissions as possible, holds. Specifically, we first show that Nash stable solutions and information diffusion are incompatible. Given this impossibility, we propose an algorithm with incentives for information diffusion and show the approximate rate of social surplus that can be achieved. As a result, we show the incompatibility theorem of social surplus maximization and Nash stability with incentives for information diffusion, and furthermore, we show that the achievable approximation rate is 0.