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Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2018 (English)In: Games, ISSN 2073-4336, E-ISSN 2073-4336, Vol. 9, no 5Article in journal (Refereed) Published
Abstract [en]

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, non-cooperating, differential games where the players’ state dynamics solve backward stochastic differential equations (BSDE) 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 playercosts, 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.

Place, publisher, year, edition, pages
2018. Vol. 9, no 5
Keywords [en]
Backward stochastic differential equations; Cooperative game; Linear-quadratic stochastic control; Mean-field type game; Non-zero-sum differential game; Price of anarchy; Social cost
National Category
Probability Theory and Statistics Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-248531DOI: 10.3390/g9040088Scopus ID: 2-s2.0-85056271574OAI: oai:DiVA.org:kth-248531DiVA, id: diva2:1303364
Note

QC 20190514

Available from: 2019-04-09 Created: 2019-04-09 Last updated: 2019-05-20Bibliographically approved

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Aurell, Alexander

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