A direct reduction of PPAD Lemke-verified linear complementarity problems to bimatrix games

@article{Adler2013ADR,
  title={A direct reduction of PPAD Lemke-verified linear complementarity problems to bimatrix games},
  author={Ilan Adler and Sushil Verma},
  journal={CoRR},
  year={2013},
  volume={abs/1302.0067}
}
The linear complementarity problem, LCP (q,M), is defined as follows. For given M ∈ R , q ∈ Rm, find z such that q + Mz ≥ 0, z ≥ 0, z(q + Mz) = 0, or certify that there is no such z. It is well known that the problem of finding a Nash equilibrium for a bimatrix game (2-NASH) can be formulated as a linear complementarity problem (LCP). In addition, 2NASH is known to be complete in the complexity class PPAD (Polynomial-time Parity Argument Directed). However, the ingeniously constructed reduction… CONTINUE READING

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