A new formalization of a meta-game using the lambda calculus

This paper presents a new game system formalism. The system describes both strategies and a game master (who computes scores in a given game system) in terms of λ-calculus. This formalism revisits the prisoner's dilemma game, to discuss how meta-strategies emerge in this classical game, even without repetition. We have also examined the evolution of meta-strategies in λ formalism.