A Case Study on Pareto Optimality for Collaborative Stochastic Games

Dr Renyuan XU (University of Oxford)

Abstract

Pareto Optimality (PO) is an important concept in game theory to measure global efficiency when players collaborate. In this talk, we start with the PO for a class of continuous-time stochastic games when the number of players is finite.

The derivation of PO strategies is based on the formulation and analysis of an auxiliary N-dimensional central controller’s stochastic control problem, including its regularity property of the value function and the existence of the solution to the associated Skorokhod problem.

This PO strategy is then compared with the set of (non-unique) NEs strategies under the notion of Price of Anarchy (PoA). The upper bond of PoA is derived explicitly in terms of model parameters.

Finally, we characterize analytically the precise difference between the PO and the associated McKean-Vlasov control problem with an infinite number of players, in terms of the covariance structure between the optimally controlled dynamics of players and characteristics of the no-action region for the game. This is based on joint work with Xin Guo (UC Berkeley).

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