Abstract:Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixedpoint logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers,… Show more
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