Strategical languages of infinite words

TL;DR

This paper explores strategical languages of infinite words generated by nondeterministic strategies, providing a minimal strategy, topological characterization, and a Nash equilibrium concept with illustrative examples.

Contribution

It introduces the concept of minimal strategies for strategical languages and characterizes these languages as closed sets in the topological space of infinite words.

Findings

Existence of a minimal strategy with explicit expression

Strategical languages are characterized as closed sets topologically

Definition and illustration of Nash equilibrium in this context

Abstract

We deal in this paper with strategical languages of infinite words, that is those generated by a nondeterministic strategy in the sense of game theory. We first show the existence of a minimal strategy for such languages, for which we give an explicit expression. Then we characterize the family of strategical languages as that of closed ones, in the topological space of infinite words. Finally, we give a definition of a Nash equilibrium for such languages, that we illustrate with a famous example.