Abstract
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.
Highlights
∗ SRI - Center for Uncertainty Quantification in Computational Science & Engineering CEMSE, KAUST (e-mail: tembine@ieee.org)
From a game-theoretic point of view, the distinguishing feature of distributed systems is that they give rise to nonlinear interaction problems that involve mean-field term
The objective of this tutorial will be to present a thorough overview of these mean field techniques and their applications
Summary
∗ SRI - Center for Uncertainty Quantification in Computational Science & Engineering CEMSE, KAUST (e-mail: tembine@ieee.org). Key social networking needs in growth areas such as smart cities, social networks, risk management of nuclear waste, corrosion failure detection, pollution control, cloud-based auction mechanism have motivated extensive research on learning, analysis and optimization of complex distributed systems across all science and engineering disciplines. From a game-theoretic point of view, the distinguishing feature of distributed systems is that they give rise to nonlinear interaction problems that involve mean-field term.
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