Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/219209
Authors: 
Aurell, Alexander
Year of Publication: 
2018
Citation: 
[Journal:] Games [ISSN:] 2073-4336 [Volume:] 9 [Year:] 2018 [Issue:] 4 [Pages:] 1-26
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, 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 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.
Subjects: 
mean-field type game
non-zero-sum differential game
cooperative game
backward stochastic differential equations
linear-quadratic stochastic control
social cost
price of anarchy
Persistent Identifier of the first edition: 
Creative Commons License: 
https://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
Appears in Collections:

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.