Min_LQG games and collective discrete choice problems

Roland Malhame
École Polytechnique de Montréal

We introduce a novel class of finite horizon linear quadratic Gaussian games involving distinct potential finite destination states, interpreted as discrete choices under social pressure. The model provides stylized interpretations of opinion swings in elections, the dynamics of discrete societal choices, as well as a framework for achieving communication constrained group decision making in micro-robotic based exploration. Two distinct cases are considered: (i) The zero noise or “deterministic” case where agents are initially randomly distributed over their range space; (ii) The fully stochastic case. Under mild technical conditions, the existence of ?-Nash equilibria is established in both cases although these equilibria may in general be multiple. The corresponding agent control strategies are of a decentralized nature and are characterized in each case by the fixed points of a specific finite dimensional operator. Individual agent destination choices are fixed at the outset in case (i), while by contrast, their probability distribution evolves randomly along trajectories in case (ii), with a deterministic limit for the complete population as the latter grows to infinity. This is joint work with Rabih Salhab and Jérôme Le Ny.

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