1 research outputs found
Individual Resource Games and Resource Redistributions
We introduce a class of resource games where resources and preferences are
specified with the language of a resource-sensitive logic. The agents are
endowed with a bag of resources and try to achieve a resource objective. For
each agent, an action consists in making available a part of their endowed
resources. All the resources made available can be used towards the agents'
objectives. We study three decision problems, the first of which is deciding
whether an action profile is a Nash equilibrium: when all the agents have
chosen an action, it is a Nash Equilibrium if no agent has an incentive to
change their action unilaterally. 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: (i)
rational elimination: given an action profile's outcome, can the endowed
resources be redistributed so that it is not the outcome of a Nash equilibrium?
(ii) Rational construction: given an action profile's outcome, can the endowed
resources be redistributed so that it is the outcome of a Nash equilibrium?
Among other results, we prove that all three problems are PSPACE-complete when
the resources are described in the very expressive language of the
propositional multiplicative and additive linear logic. We also identify a new
modest fragment of linear logic that we call MULT, suitable to represent
multisets and reason about the inclusion and equality of bags of resources. We
show that when the resources are described in MULT, the problem of deciding
whether a profile is a Nash equilibrium is in PTIME.Comment: To appear in Journal of Logic and Computation. A preliminary version
of this paper was published in the proceedings of IJCAI2016, with the title
"Nash Equilibria and Their Elimination in Resource Games