Non-Determinism and Nash Equilibria for Sequential Game over Partial Order

Abstract : In sequential games of traditional game theory, backward induction guarantees existence of Nash equilibrium by yielding a sub-game perfect equilibrium. But if payoffs range over a partially ordered set instead of the reals, then the backward induction predicate does no longer imply the Nash equilibrium predicate. Non-determinism is a solution: a suitable non-deterministic backward induction function returns a non-deterministic strategy profile which is a non-deterministic Nash equilibrium. The main notions and results in this article are constructive, conceptually simple and formalised in the proof assistant Coq.
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David, René and Gardy, Danièle and Lescanne, Pierre and Zaionc, Marek. Computational Logic and Applications, CLA '05, 2005, Chambéry, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AF, Computational Logic and Applications (CLA '05), pp.77-86, 2005, DMTCS Proceedings
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Stéphane Le Roux. Non-Determinism and Nash Equilibria for Sequential Game over Partial Order. David, René and Gardy, Danièle and Lescanne, Pierre and Zaionc, Marek. Computational Logic and Applications, CLA '05, 2005, Chambéry, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AF, Computational Logic and Applications (CLA '05), pp.77-86, 2005, DMTCS Proceedings. 〈hal-01183332〉

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