1 research outputs found
Equilibria in Quantitative Concurrent Games
Synthesis of finite-state controllers from high-level specifications in
multi-agent systems can be reduced to solving multi-player concurrent games
over finite graphs. The complexity of solving such games with qualitative
objectives for agents, such as reaching a target set, is well understood
resulting in tools with applications in robotics. In this paper, we introduce
quantitative concurrent graph games, where transitions have separate costs for
different agents, and each agent attempts to reach its target set while
minimizing its own cost along the path. In this model, a solution to the game
corresponds to a set of strategies, one per agent, that forms a Nash
equilibrium. We study the problem of computing the set of all Pareto-optimal
Nash equilibria, and give a comprehensive analysis of its complexity and
related problems such as the price of stability and the price of anarchy. In
particular, while checking the existence of a Nash equilibrium is NP-complete
in general, with multiple parameters contributing to the computational hardness
separately, two-player games with bounded costs on individual transitions admit
a polynomial-time solution