Individual Resource Games and Resource Redistributions

Research in multiagent systems is advancing and one can predict its future widespread implementation in real-world systems. One needs however to acknowledge that the agents evolving in the real world have limited access to resources. They have to seek after resource objectives and compete for those resources. We introduce a class of resource games where resources and preferences are described with the language of a resource-sensitive logic. We study three decision problems, the first of which is deciding whether an action profile is a Nash equilibrium. When dealing with resources, interesting questions arise as to whether some equilibria can be eliminated or constructed by a central authority by redistributing the available resources among the agents. In our economies, division of property in divorce law exemplifies how a central authority can redistribute the resources of individuals, and why they would desire to do so. We thus study two related decision problems: rational elimination and rational construction. We consider them in the contexts of dichotomous or parsimonious preferences, and of logics that admit or not the weakening rule. This permits us to offer a variety of algorithms and complexity results that are applicable to a large number of settings.