Steering the Distribution of Agents in Mean-Field Games System

Yongxin Chen (), Tryphon T. Georgiou () and Michele Pavon ()
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Yongxin Chen: Iowa State University
Tryphon T. Georgiou: University of California
Michele Pavon: Università di Padova

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 1, No 16, 332-357

Abstract: Abstract The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. This is formulated as a mean-field game problem, and is discussed in both non-cooperative games and cooperative games settings. In the non-cooperative games setting, a terminal cost is used to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. In the cooperative games setting, the goal is to find a common optimal control that would drive the distribution of the agents to a targeted one. We focus on the cases when the underlying dynamics is linear and the running cost is quadratic. Our approach relies on and extends the theory of optimal mass transport and its generalizations.

Keywords: Mean-field games; Linear stochastic systems; Weakly interacting particle system; McKean–Vlasov dynamics; Optimal control; 91A13; 60J60; 49J20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1365-7

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