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Mean-Field-Type Game Theory
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Mean-Field-Type Game Theory

A special issue of Games (ISSN 2073-4336).

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 29975

Special Issue Editor

Dr. Hamidou Tembine

E-Mail Website
Guest Editor
Learning & Game Theory Laboratory, New York University Abu Dhabi, 19 Washington Square North, New York, NY 10011, USA
Interests: delayed evolutionary game dynamics; population games; distributed self-x learning; engineering mean-field-type games; psychological games; partial altruism; empathy; compassion; spitefulness and self-destroying behavior; mean-field asymptotics; stochastic games; risk-sensitivity; quantile-based games; non-asymptotic mean-field games; combined imitative learning; mean-field learning; particle swarm learning

Special Issue Information

Dear Colleagues,

The term “mean-field" has been referred to as a physics concept that attempts to describe the effect of an infinite number of particles on the motion of a single particle. Researchers began to apply the concept to social sciences in the early 1960s to study how an infinite number of factors affect individual decisions. However, the key ingredient in a game-theoretic context is the influence of the distribution of states and or control actions into the payoffs of the decision-makers. There is no need to have large population of decision-makers. A mean-field-type game is a game in which the payoffs and/or the state dynamics coefficient functions involve not only the state and actions profiles but also the distributions of state-action process (or its marginal distributions).

This Special Issue is devoted to contributions that focus on mean-field-type game theory and applications. Applications can be widespread and may include insurance, predictive maintenance, smart energy systems, intelligent transportation systems, big data, deep learning on social networks, millimeter wave next generation wireless networks, economics, physical and cyber security of the internet-of-everything, to mention some examples.

Dr. Tembine Hamidou
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Games is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Mean-field-type games
  • Cooperative mean-field-type games
  • Quantile-based mean-field-type games
  • Time-delayed mean-field-type games
  • Risk-sensitive mean-field-type games
  • Fractional mean-field-type games
  • Psychological mean-field-type games
  • Shallow/deep learning in mean-field-type games

Published Papers (5 papers)

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Research

107 pages, 7396 KiB  
Article
COVID-19: Data-Driven Mean-Field-Type Game Perspective
by Hamidou Tembine
Games 2020, 11(4), 51; https://doi.org/10.3390/g11040051 - 03 Nov 2020
Cited by 17 | Viewed by 5488
Abstract
In this article, a class of mean-field-type games with discrete-continuous state spaces is considered. We establish Bellman systems which provide sufficiency conditions for mean-field-type equilibria in state-and-mean-field-type feedback form. We then derive unnormalized master adjoint systems (MASS). The methodology is shown to be [...] Read more.
In this article, a class of mean-field-type games with discrete-continuous state spaces is considered. We establish Bellman systems which provide sufficiency conditions for mean-field-type equilibria in state-and-mean-field-type feedback form. We then derive unnormalized master adjoint systems (MASS). The methodology is shown to be flexible enough to capture multi-class interaction in epidemic propagation in which multiple authorities are risk-aware atomic decision-makers and individuals are risk-aware non-atomic decision-makers. Based on MASS, we present a data-driven modelling and analytics for mitigating Coronavirus Disease 2019 (COVID-19). The model integrates untested cases, age-structure, decision-making, gender, pre-existing health conditions, location, testing capacity, hospital capacity, and a mobility map of local areas, including in-cities, inter-cities, and internationally. It is shown that the data-driven model can capture most of the reported data on COVID-19 on confirmed cases, deaths, recovered, number of testing and number of active cases in 66+ countries. The model also reports non-Gaussian and non-exponential properties in 15+ countries. Full article
(This article belongs to the Special Issue Mean-Field-Type Game Theory)
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26 pages, 845 KiB  
Article
Hierarchical Structures and Leadership Design in Mean-Field-Type Games with Polynomial Cost
by Zahrate El Oula Frihi, Julian Barreiro-Gomez, Salah Eddine Choutri and Hamidou Tembine
Games 2020, 11(3), 30; https://doi.org/10.3390/g11030030 - 06 Aug 2020
Cited by 3 | Viewed by 3159
Abstract
This article presents a class of hierarchical mean-field-type games with multiple layers and non-quadratic polynomial costs. The decision-makers act in sequential order with informational differences. We first examine the single-layer case where each decision-maker does not have the information about the other control [...] Read more.
This article presents a class of hierarchical mean-field-type games with multiple layers and non-quadratic polynomial costs. The decision-makers act in sequential order with informational differences. We first examine the single-layer case where each decision-maker does not have the information about the other control strategies. We derive the Nash mean-field-type equilibrium and cost in a linear state-and-mean-field feedback form by using a partial integro-differential system. Then, we examine the Stackelberg two-layer problem with multiple leaders and multiple followers. Numerical illustrations show that, in the symmetric case, having only one leader is not necessarily optimal for the total sum cost. Having too many leaders may also be suboptimal for the total sum cost. The methodology is extended to multi-level hierarchical systems. It is shown that the order of the play plays a key role in the total performance of the system. We also identify a specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play. In the heterogeneous case, it is shown that the total cost is significantly affected by the design of the hierarchical structure of the problem. Full article
(This article belongs to the Special Issue Mean-Field-Type Game Theory)
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26 pages, 618 KiB  
Article
Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations
by Alexander Aurell
Games 2018, 9(4), 88; https://doi.org/10.3390/g9040088 - 01 Nov 2018
Cited by 5 | Viewed by 6735
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Mean-Field-Type Game Theory)
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21 pages, 315 KiB  
Article
A Stochastic Maximum Principle for Markov Chains of Mean-Field Type
by Salah Eddine Choutri and Tembine Hamidou
Games 2018, 9(4), 84; https://doi.org/10.3390/g9040084 - 21 Oct 2018
Cited by 6 | Viewed by 6410
Abstract
We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as [...] Read more.
We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications. Full article
(This article belongs to the Special Issue Mean-Field-Type Game Theory)
18 pages, 330 KiB  
Article
Linear–Quadratic Mean-Field-Type Games: A Direct Method
by Tyrone E. Duncan and Hamidou Tembine
Games 2018, 9(1), 7; https://doi.org/10.3390/g9010007 - 12 Feb 2018
Cited by 39 | Viewed by 7244
Abstract
In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control [...] Read more.
In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form. Full article
(This article belongs to the Special Issue Mean-Field-Type Game Theory)
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