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AIMS Mathematics

2017, Volume 2, Issue 4: 706-735. doi: 10.3934/Math.2017.4.706
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Research article

Mean-field-type games

  • Learning and Game Theory Laboratory, New York University Abu Dhabi
  • Received: 13 August 2017 Accepted: 06 December 2017 Published: 20 December 2017

  • MSC : 91A15, 91A25, 49L20, 49L25

  • This article examines games in which the payoffs and the state dynamics depend not only on the state-action profile of the decision-makers but also on a measure of the state-action pair. These game situations, also referred to as mean-field-type games, involve novel equilibrium systems to be solved. Three solution approaches are presented: (ⅰ) dynamic programming principle, (ⅱ) stochastic maximum principle, (ⅲ) Wiener chaos expansion. Relationship between dynamic programming and stochastic maximum principle are established using sub/super weak differentials. In the non-convex control action spaces, connections between the second order weaker differentials of the dual function and second order adjoint processes are provided. Multi-index Wiener chaos expansions are used to transform the non-standard game problems into standard ones with ordinary differential equations. Aggregative and moment-based mean-field-type games are discussed.

    Citation: Hamidou Tembine. Mean-field-type games[J]. AIMS Mathematics, 2017, 2(4): 706-735. doi: 10.3934/Math.2017.4.706

    Related Papers:

  • This article examines games in which the payoffs and the state dynamics depend not only on the state-action profile of the decision-makers but also on a measure of the state-action pair. These game situations, also referred to as mean-field-type games, involve novel equilibrium systems to be solved. Three solution approaches are presented: (ⅰ) dynamic programming principle, (ⅱ) stochastic maximum principle, (ⅲ) Wiener chaos expansion. Relationship between dynamic programming and stochastic maximum principle are established using sub/super weak differentials. In the non-convex control action spaces, connections between the second order weaker differentials of the dual function and second order adjoint processes are provided. Multi-index Wiener chaos expansions are used to transform the non-standard game problems into standard ones with ordinary differential equations. Aggregative and moment-based mean-field-type games are discussed.


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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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