tembine hamidou

SUPELEC,
3 rue Joliot-Curie 91192 GIF SUR YVETTE CEDEX FRANCE
tembine(at)ieee.org

NEW: Tutorial course "Distributed strategic learning for engineers", Supelec, February 23-24, 2012.

RESEARCH INTERESTS AND ACTIVITIES

My research interests are in the general area of game theory and applications

Evolutionary games

Evolutionary game theory studies the evolution of populations of players (agents, users, nodes, individuals etc) interacting strategically. Applications were originally in biology and social sciences. Examples of situations that evolutionary game theory helps to understand include animal conflicts (Hawk & Dove games). The interactions may be with individuals from the same population (a mobile with other mobiles, males fighting other males), or with individuals from other populations (males interacting with females or buyers with traders). The individuals are typically animals in biology, firms in economics and mobiles or nodes in networks. The point of departure for an evolutionary model is to belief that the players (mobiles or animals) are not always rational. In the place of Nash equilibrium (NE) in classical game theory, evolutionary game theory use the the concept of evolutionary stability and refined notions of equilibria: unbeatable state, evolutionarily stable state (ESS), globally stable state etc and the interactions are random. Evolutionary games are well adapted to describe competition situations between large populations but also local coalition among the players.

Keywords: evolutionarily stable state, neutrally stable state, non-invadable strategy, unbeatable state, stochastically stable state, continuously stable state, global evolutionarily stable state (GESS, the analogue of ESS for multiple population games), robust and risk-dominant strategy or payoff, replicator dynamics, Brown-von Neumann-Nash dynamics, fictitious play, adaptive dynamics, imitate the better dynamics, best response dynamics, logit dynamics, Smith dynamics, projection dynamics, gradient methods, G-function based dynamics, evolutionary game dynamics with diffusion, evolutionary game dynamics with migration, spatial evolutionary game dynamics with migration and time delays etc.

Applications in Biology
Applications in Networking
Applications in Economics

Selected journal papers
M. Khan, H. Tembine, A. Vasilakos, Game Dynamics and Cost of Learning in Heterogeneous 4G Networks, IEEE Journal on Selected Areas in Communications, 2012. A draft is available here. The idea of cost of learning in user-centric QoE in IPTV services received the best paper award at INFOCOM Workshop, 2011.

H. Tembine, Dynamic robust games in MIMO systems, IEEE Transactions on Systems, Man, Cybernetics Part B, 99, Volume: 41 Issue:4, pp. 990 - 1002, August 2011. A draft is available here.

Delayed evolutionary game dynamics

Consider large populations of players with finite, infinite or Borel set of actions for each member of each population. An action taken today will have its effect some time delay later. The delays can be symmetric or not, functional or not. We get delayed payoff (or fitness) functions. The evolution of the system leads to delayed evolutionary game dynamics. Delayed evolutionary game dynamics are in general system of first order non-regular nonlinear differential equations or differential inclusions with time delays. We use the theory of delayed differential equation (DDE) to study stability, convergence and non-convergence of the system under time delays. Some challenging open problems are (i) characterization of the stability region (as a function of the time delays or delay functions), (ii) threshold between speed of convergence, stability and limit cycle, (iii) unstable ESS.

Information dissemination with delayed feedback

Propagation of diseases/viruses in large systems

Evolution of transport protocols

Selected journal papers:

H. Tembine, E. Altman, R. ElAzouzi, Y. Hayel, Evolutionary Games in Wireless Networks, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, issue 3, pp. 634 - 646, 2010.

H. Tembine, E. Altman, R. ElAzouzi, Y. Hayel, Bio-inspired Delayed Evolutionary Game Dynamics with Networking Applications, Telecommunication Systems Journal, 2011, DOI: 10.1007/s11235-010-9307-1.

E. Altman, R. ElAzouzi, Y. Hayel, H. Tembine, The Evolution of Transport Protocols: An Evolutionary Game Perspective, Elsevier Computer Networks Journal, Vol. 53, Issue 10, pp. 1751-1759, Autonomic and Self-Organising Systems, July 2009.

Dissertations:

Population games with networking applications, PhD thesis, University of Avignon, September 2009
(with hghest honors): ''mention tres honorable avec les felicitations du Jury a l'unanimite''.

Population games in large-scale networks: time delays, mean field dynamics and applications, LAP ISBN 978-3-8383-6392-9, 2009.

Repeated games with unknown horizon, horizon controlled by a single player

Repeated games with complete information are known to have several equilibria and equilibrium payoffs. A well known result in that field is the so-called Folk Theorem which characterize the set of equilibrium payoffs: under rational players and perfect monitoring, every feasible and individually rational payoff (at least the minmax point) can be obtained by an equilibrium in the repeated game. Our objective is to characterize equilibrium payoff (or refinement of equilibrum payoff) in more general model of repeated games including stochastic games with perfect/imperfect monitoring (public or private signal), and finite, infinite or unknown horizon or horizon controlled by a specific player (jammer...).

Evolutionary Coalitional games

Evolutionary coalitional game theory can be used to model a form of confederation, alliance or network community formation over long-run interactions. In current networked systems, decision makers may decide locally to pool their resources if they all benefit from the coalition. We have introduced a learning framework to explain the formation of coalitions over long-run interactions. In evolutionary coalition games, a player try to join a new coalition or to be alone depending the results of its past experiences. Inside each coalition, one needs to a time-consistent and dynamical coalitional solution concepts (an example could be dynamical Shapley value). Our goal is to understand how new coalitions will be formed. The work aims to characterize the space and properties of allocations such that immunity to coalition formation is guaranteed using heterogenous and hybrid learning among the players per coalitions.

Stochastic population games with additional individual states

Consider large populations of agents. Each agent has its own state. In each state, there is a set of actions (discrete or continous). The transition probabilities between individual states depend on the past and current states and actions of the agent but also on the action of the others agents via the population profile. At each time, some random number of agents are selected for an interaction. The game has many local interactions at the same time and the opponents can be different from one slot to another slot. In addition, the subpopulations are subjected to coupled constraints, and the global state of the environment is considered. Some challenging open problems are (a) existence of equilibria (even in the atomic case, the existence of equilibria in stationary strategies is still an open problem), (b) sufficient conditions for existence of constrained equilibria, (c) computation of constrained equilibria, (d) evolutionary game dynamics for stochastic population games with individual states. (e) connection with differential population games. This research is of importance for dealing with complexity in stochastic dynamic optimization of large-scale systems and has methodological implications in many complex systems arising in engineering and socio-economic areas, ecology and evolutionary biology.

Energy management in wireless networks

Intergenerational energy control

Resource-constrained competition in heterogeneous networks

Renewable energies in broadband wireless networks

Journal papers
Y. Hayel, H. Tembine, E. Altman, R. El-Azouzi, Markov Decision Evolutionary Games with Individual Energy Management, in Annals of the International Society of Dynamic Games,Advances in Dynamic Games: Theory, Applications, and Numerical Methods, Editors: Michele Breton,Krzysztof Szajowski, pages 313-335, 2010.

E. Altman, Y. Hayel, H. Tembine, and R. El-Azouzi, Markov Decision Evolutionary Games with Expected Average Fitness., Evolutionary Ecology Research Journal, Special issue in honour of Thomas Vincent (Joel S. Brown & Tania L. S. Vincent, Eds), May 2009.

Mean field stochastic games

We introduce evolving stochastic games with finite number players, in which each player in the population interacts with other randomly selected players (the number of players in interaction evolves in time). The states and actions of each player in an interaction together determine the instantaneous payoff for all involved players. They also determine the transition probabilities to move to the next state. Each individual wishes to maximize the total expected payoff over an infinite horizon. Under restricted class of strategies, the random process consisting of one specific player and the remaining population converges weakly to a jump process driven by the solution of a system of differential equations. We characterize the solutions to the team and to the game problems at the limit of infinite population. We prove that the large population asymptotic of the microscopic model is equivalent to a (macroscopic) stochastic evolutionary game in which a local interaction is described by a single player against a population profile. A new class of differential games called differential population games is obtained. In these games, an individual optimizes its expected fitness during its sojourn time in the system under population dynamics.

[audio: Mean field stochastic games, around 48mn] The slides are here.

Validity domain of Replica methods, Propagation of Chaos, Fixed-Point Analysis, Decoupling Assumption
Bellman-Shapley mean field optimality
Spatial non-reciprocal interactions and their asymptotics
Random number of interacting players, non-convergent dynamics and non-equilibrium behaviors

Differential population games

We introduce a class of games called differential population games. In these games, there are large populations of players and many local resources. Each player has its own type, internal state and make a occasionally a decision based on its experience, local resource state, internal state. The population profile evolves according to deterministic or stochastic differential equations or inclusions and the state process is a jump and drift process. In the case of continuum of players, this class is related to the so-called mean field games with additional individual state processes. Keywords: neutrally stable set, multigenerational equilibria, extension of Hamilton-Jacobi-Bellman equations (first and second types), Issacs conditions, double limit, Birkoff center, non-anticipative strategies with and without delays, open loop, closed-loop equilibria etc.

Mean field game dynamics

We introduce a class of game dynamics obtained from asymptotic of dynamic games with variable number of interacting players. These dynamics cover the standard dynamics known in evolutionary games and population games. In the case of multi-class of players, the dynamics describe both the intra-population interaction and inter-population interaction. The stochastic mean field game dynamics are in general non-linear (partial or not) differential equations or inclusions. This last class occurs when the mean process converges weakly to another process described by a drift plus a noise. Keywords: Ito's formula, Kolmogoroff backward/forward equations, partial differential equations (PDE) or inclusions (PDI), stochastic integro-differential equations (SIDPE) etc.

Spatial mean field game dynamics for hybrid networks

Mobility-based dynamics, multicomponent dynamics for non-pairwise interaction

Non-convergent dynamics and limit cycle in communication systems

Introduction to Engineering Games. Applications in computer networks, wireless communications

Game theory and Learning in Wireless Networks, co-authored with Samson Lasaulce

Recent Talks

New: forthcoming lecture notes, Distributed strategic learning for engineers.
Reading Group: Distributed strategic learning for engineers, Tutorial course, see also the previous tutorial here

Tutorial course on mean field stochastic games.

Recent/next meetings:

Invited talks: Paris 7 (January 2012), GDR (february 2012, pdf), UCLA (February 2012), UC Berkeley (April 2012).
Worskshop co-chair at Gamenets 2012. Call for proposals.
Co-organizer of the Track on "Mean Field Control, Games and Applications" at Valuetools, 2012. Call for contribution.
Co-organizer of the session "Mean Field Games" at NetGcoop 2011
Co-organizer of the session "Games, Auctions, and Mean Field Limits" at Allerton 2011
Session chair at ACC'2011

Recent talks

CSMA networks: a mean field approach, University of California at Berkeley Cory, Room 258, UCB, April 13, 2012.
Mean field stochastic games, University of California at Berkeley, Trust center, 337, UCB, April 6, 2012.
Combined learning in random matrix games, University of California at Berkeley, Cory, Room 258, UCB, April 6, 2012.
Mean field stochastic games, University of California at Los Angeles , February 29, 2012
Combined learning: an overview, University of California at Los Angeles, February 27, 2012.
Distributed strategic learning for engineers, Supelec, February 23-24, 2012.
Mean field stochastic games, GdR Telecoms ParisTech, February 2, 2012.