# Admissibility in Concurrent Games

## TL;DR

This paper investigates the concept of admissibility for randomized strategies in concurrent games, proving their existence, characterizing them, and developing methods for assume-admissible synthesis in omega-regular objectives.

## Contribution

It introduces the notion of admissibility in concurrent games, proves their existence, characterizes them, and provides a synthesis method for omega-regular objectives.

## Key findings

- Admissible strategies always exist in concurrent games.
- A precise characterization of admissible strategies is provided.
- Method for assume-admissible synthesis in omega-regular objectives is developed.

## Abstract

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates it, i.e., that wins (almost surely) against a super set of adversarial strategies. We prove that admissible strategies always exist in concurrent games, and we characterise them precisely. Then, when the objectives of the players are omega-regular, we show how to perform assume-admissible synthesis, i.e., how to compute admissible strategies that win (almost surely) under the hypothesis that the other players play admissible