Individual Resource Games and Resource Redistributions
Nicolas Troquard

TL;DR
This paper introduces resource games based on resource-sensitive logic, analyzing decision problems related to Nash equilibria and resource redistribution, with complexity results varying from PSPACE-complete to PTIME depending on the logic fragment used.
Contribution
It formalizes resource games using linear logic, studies equilibrium and redistribution problems, and identifies a new logic fragment enabling polynomial-time decision procedures.
Findings
Deciding Nash equilibria is PSPACE-complete with expressive logic.
Resource redistribution can eliminate or create equilibria.
A new logic fragment, MULT, allows efficient equilibrium decision-making.
Abstract
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…
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