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Non-Determinism and Nash Equilibria for Sequential Game over Partial Order
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AF, Computational Logic and Applications (CLA '05), DMTCS Proceedings vol. AF, Computational Logic and Applications (CLA '05) (2005).

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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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     title = {Non-Determinism and {Nash} {Equilibria} for {Sequential} {Game} over {Partial} {Order}},
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Le Roux, Stéphane. Non-Determinism and Nash Equilibria for Sequential Game over Partial Order. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AF, Computational Logic and Applications (CLA '05), DMTCS Proceedings vol. AF, Computational Logic and Applications (CLA '05) (2005). doi : 10.46298/dmtcs.3468. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3468/

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