Weihrauch degrees of finding equilibria in sequential games

TL;DR

This paper explores the computational complexity of finding winning strategies and Nash equilibria in infinite sequential games, showing how this complexity correlates with the complexity of the game's winning sets within the hierarchy.

Contribution

It establishes a relationship between the Weihrauch degrees of strategy construction and the hierarchy level of the winning sets in infinite sequential games.

Findings

Complexity of strategies increases with the complexity of winning sets.

Weihrauch degrees effectively measure non-computability in game solutions.

Hierarchy levels directly influence the computational difficulty of finding equilibria.

Abstract

We consider the degrees of non-computability (Weihrauch degrees) of finding winning strategies (or more generally, Nash equilibria) in infinite sequential games with certain winning sets (or more generally, outcome sets). In particular, we show that as the complexity of the winning sets increases in the difference hierarchy, the complexity of constructing winning strategies increases in the effective Borel hierarchy.