English

A generalisation of Nash's theorem with higher-order functionals

Logic in Computer Science 2015-06-12 v1 Computer Science and Game Theory

Abstract

The recent theory of sequential games and selection functions by Mar- tin Escardo and Paulo Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is generalised to games defined by selection functions. A normal form construction is given which generalises the game-theoretic normal form, and its soundness is proven. Minimax strategies also gener- alise to the new class of games and are computed by the Berardi-Bezem- Coquand functional, studied in proof theory as an interpretation of the axiom of countable choice.

Keywords

Cite

@article{arxiv.1301.4845,
  title  = {A generalisation of Nash's theorem with higher-order functionals},
  author = {Julian Hedges},
  journal= {arXiv preprint arXiv:1301.4845},
  year   = {2015}
}
R2 v1 2026-06-21T23:12:47.623Z