Equilibria in social belief removal

Abstract

In studies of multi-agent interaction, especially in game theory, the notion of equilibrium often plays a prominent role. A typical scenario for the belief merging problem is one in which several agents pool their beliefs together to form a consistent “group” picture of the world. The aim of this paper is to define and study new notions of equilibria in belief merging. To do so, the authors assume the agents arrive at consistency via the use of a social belief removal function, in which each agent, using his own individual removal function, removes some belief from his stock of beliefs. The authors examine several notions of equilibria in this setting, assuming a general framework for individual belief removal due to Booth et al. The authors look at their inter-relations as well as prove their existence or otherwise. They also show how their equilibria can be seen as a generalisation of the idea of taking maximal consistent subsets of agents.