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Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations
Version 1
: Received: 3 September 2018 / Approved: 5 September 2018 / Online: 5 September 2018 (04:59:41 CEST)
A peer-reviewed article of this Preprint also exists.
Aurell, A. Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations. Games 2018, 9, 88. Aurell, A. Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations. Games 2018, 9, 88.
Abstract
In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.
Keywords
mean-field type game; non-zero-sum differential game; cooperative game; backward stochastic differential equations; linear-quadratic stochastic control; social cost; price of anarchy
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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