Mean-field type games between two players driven by backward stochastic differential equations
type: Item
instance of: scholarly article
title: Mean-field type games between two players driven by backward stochastic differential equations
zbMATH Open document ID: 1419.91062
author: Alexander Aurell
published in: Games
publication date: 2019-01-21T00:00:00Z
review text: Summary: 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, noncooperating, 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 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.
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 7003981
zbMATH Keywords: mean-field type game
zbMATH Keywords: non-zero-sum differential game
zbMATH Keywords: cooperative game
zbMATH Keywords: backward stochastic differential equations
zbMATH Keywords: linear-quadratic stochastic control
zbMATH Keywords: social cost
zbMATH Keywords: price of anarchy
MaRDI profile type: Publication
full work available at URL: g9040088
OpenAlex ID: W2889866947
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Wikidata QID: Q129074029
DOI: 10.3390/G9040088
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