With a little help from your friends: semi-cooperative games via Joker moves

TL;DR

This paper introduces Joker games, a new class of semi-cooperative concurrent games where players can assist each other using Joker moves, and develops strategies to minimize Joker usage for winning.

Contribution

It formalizes Joker games as cost games, analyzes their strategic properties, and applies the framework to improve test generation in model-based testing.

Findings

Cost-minimal Joker strategies differ from admissible strategies.

Randomization does not improve winning chances but reduces Joker usage.

Secondary objective minimizes Joker moves for more efficient strategies.

Abstract

This paper coins the notion of Joker games, a variant of concurrent games where the players are not strictly adversarial. Instead, Player 1 can get help from Player 2 by playing a Joker move. We formalize these games as cost games and develop strategies that minimize the use of Jokers - viewed as costs - to secure a win with the least possible help. Our investigation studies the theoretical underpinnings of these games and their associated Joker strategies. In particular, when comparing our cost-minimal strategies with admissible strategies, we find out that they differ. Moreover, while randomization can be beneficial in conventional concurrent games, it does not aid in winning Joker games, although it can help reduce the number of needed Jokers. We also enhance our framework by introducing a secondary objective, namely by minimizing the number of moves executed by a Joker strategy. Finally, we demonstrate the practical advantages of our approach by applying it to test generation in model-based testing.