Problem
Research questions and friction points this paper is trying to address.
Nash Equilibrium
Shapley Index
PPADS-Complete
Finding a Positive Index Nash Equilibrium is PPADS-Complete
🤖 AI Summary
本文解决了非退化双矩阵博弈中寻找Shapley指数+1的纳什均衡问题，证明了该问题是PPADS-完全的，填补了Daskalakis提出的一个开放性问题。
📝 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].
Innovation
Methods, ideas, or system contributions that make the work stand out.
PPADS-complete
Nash equilibrium
bimatrix game
Shapley index
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