Distributed constrained search by selfish agents for efficient equilibria

Search for stable solutions in games is a hard problem that includes two families of constraints. The global stability constraint and multiple soft constraints that express preferences for socially, or otherwise, preferred solutions. To find stable solutions (e.g., pure Nash equilibria - PNEs) of high efficiency, the multiple agents of the game perform a distributed search on an asymmetric distributed constraints optimization problem (ADCOP). Approximate (local) distributed search on ADCOPs does not necessarily guarantee convergence to an outcome that satisfies the stability constraints, as well as optimizes the soft constraints. The present paper proposes a distributed search algorithm that uses transfer of funds among selfish agents. The final outcome of the algorithm can be stabilized by transfer of funds among the agents, where the transfer function is contracted among the agents during search. It is shown that the proposed algorithm - Iterative Nash Efficiency enhancement Algorithm (INEA) - guarantees improved efficiency for any initial outcome. The proposed distributed search algorithm can be looked at as an extension to best response dynamics, that uses transfer functions to guarantee convergence and enforce stability in games. The best-response-like nature of INEA establishes its correct behavior for selfish agents in a multi-agents game environment. Most important, unlike best response, the proposed INEA converges to efficient and stable outcomes even in games that are not potential games.