The NCE (Mean Field) Principle With Locality Dependent Cost Interactions

We study large population stochastic dynamic games where each agent assigns individually determined coupling strengths (with possible spatial interpretation) to the states of other agents in its performance function. The mean field methodology yields a set of decentralized controls which generates an -Nash equilibrium for the population of size . A key feature of the mean field approximation (here with localized interactions) is that the resulting th individual agent's control law depends on that agent's state and the precomputable weighted average trajectory of the collection of all agents each applying a decentralized control law.