Mean Field Equilibrium in Dynamic Games with Strategic Complementarities
- Creators
- Adlakha, Sachin
- Johari, Ramesh
Abstract
We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical distribution of the states of other players. Such games can be used to model a diverse set of applications, including network security models, recommender systems, and dynamic search in markets. Stochastic games are generally difficult to analyze, and these difficulties are only exacerbated when the number of players is large (as might be the case in the preceding examples). We consider an approximation methodology called mean field equilibrium to study these games. In such an equilibrium, each player reacts to only the long-run average state of other players. We find necessary conditions for the existence of a mean field equilibrium in such games. Furthermore, as a simple consequence of this existence theorem, we obtain several natural monotonicity properties. We show that there exist a "largest" and a "smallest" equilibrium among all those where the equilibrium strategy used by a player is nondecreasing, and we also show that players converge to each of these equilibria via natural myopic learning dynamics; as we argue, these dynamics are more reasonable than the standard best-response dynamics. We also provide sensitivity results, where we quantify how the equilibria of such games move in response to changes in parameters of the game (for example, the introduction of incentives to players).
Additional Information
© 2013 INFORMS. Received December 2010; revisions received May 2012, January 2013; accepted February 2013. An earlier version of this paper appeared in the IEEE Conference on Decision and Control, 2010. © 2010 IEEE. Reprinted with permission from Adlakha, S., Johari, R., "Mean field equilibrium in dynamic games with complementarities," 49th IEEE Conference on Decision and Control (CDC), 2010. The authors gratefully acknowledge helpful conversations with Rabah Amir, Stephen Boyd, Kevin Refett, and Gabriel Weintraub, as well as the comments of two anonymous referees and the editors. They also acknowledge financial support from the National Science Foundation, as well as the Defense Advanced Research Projects Agency under the ITMANET program. This work was supported by the National Science Foundation [Grants CMMI-0948434, CNS-0904609, CCF-0832820, and CNS-0644114].Attached Files
Published - 971.full.pdf
Submitted - 1011.5677v1.pdf
Supplemental Material - opre.2013.1192ec.pdf
Files
Additional details
- Eprint ID
- 41545
- Resolver ID
- CaltechAUTHORS:20130930-093204811
- NSF
- Defense Advanced Research Projects Agency ITMANET program
- CMMI- 0948434
- NSF
- CNS-0904609
- NSF
- CCF-0832820
- NSF
- CNS-0644114
- NSF
- Created
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2013-09-30Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field