# On Relevant Equilibria in Reachability Games

## TL;DR

This paper investigates the concept of relevant equilibria in multiplayer reachability games, focusing on Pareto optimality and social welfare, and provides complexity results for related decision problems.

## Contribution

It introduces notions of relevant equilibria in reachability games and analyzes their computational complexity.

## Key findings

- Existence of Nash and subgame perfect equilibria in reachability games.
- Identification of complexity results for decision problems related to relevant equilibria.
- Analysis of Pareto optimal and high social welfare equilibria in these games.

## Abstract

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those reachability games, it is known that there always exists a Nash equilibrium (NE) and a subgame perfect equilibrium (SPE). But sometimes several equilibria may coexist such that in one equilibrium no player reaches his target set whereas in another one several players reach it. It is thus very natural to identify "relevant" equilibria. In this paper, we consider different notions of relevant equilibria including Pareto optimal equilibria and equilibria with high social welfare. We provide complexity results for various related decision problems.