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arXiv · 2609.23879

Finding a Positive Index Nash Equilibrium is PPADS-Complete

Andreas Kontogiannis·Ioannis Panageas·Vasilis Pollatos·Jingming Yan
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Abstract

Every nondegenerate bimatrix game has a Nash equilibrium of Shapley index +1, since all equilibria are isolated, have index +1 or -1, and their indices sum to +1. We prove that the following promise search problem is PPADS-complete: given a rational bimatrix game promised to be nondegenerate, find an exact Nash equilibrium of index +1. To our knowledge, this is the first PPADS-complete equilibrium search problem whose instances are explicit rational normal form payoff matrices, rather than succinct circuits or Turing machines, and thereby addresses an open question posed by Daskalakis [Daskalakis, 2019].

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Andreas Kontogiannis, Ioannis Panageas, Vasilis Pollatos, Jingming Yan. 2026-09-20. Finding a Positive Index Nash Equilibrium is PPADS-Complete. https://arxiv.org/abs/2609.23879

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