Nash定理的高阶泛函推广
A generalisation of Nash's theorem with higher-order functionals
摘要：
最近由马丁·埃斯卡多和保罗·奥利瓦提出的序贯博弈和选择函数理论被推广到参与者同时行动的博弈中。有限对策的混合策略均衡的纳什存在定理被推广到由选择函数定义的对策。给出了一个推广博弈论范式的范式构造，并证明了它的可靠性。极大极小策略也适用于一类新的博弈，并通过Berardi-Bezem- Coquand泛函计算，在证明论中作为可数选择公理的解释进行研究。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
