The Good, The Bad and The Cautious: Safety Level Cooperative Games

We study safety level coalitions in competitive games. Given a normal form game, we define a corresponding cooperative game with transferable utility, where the value of each coalition is determined by the safety level payoff it derives in the original—non-cooperative—game. We thus capture several key features of agents’ behavior: (i) the possible monetary transfer among the coalition members; (ii) the solidarity of the outsiders against the collaborators; (iii) the need for the coalition to optimize its actions against the worst possible behavior of those outside the coalition. We examine the concept of safety level cooperation in congestion games, and focus on computing the value of coalitions, the core and the Shapley value in the resulting safety level cooperative games. We provide tractable algorithms for anonymous cooperative games and for safety level cooperative games that correspond to symmetric congestion games with singleton strategies. However, we show hardness of several problems such as computing values in games with multi-resource strategies or asymmetric strategy spaces.