SUPELEC,
3 rue JoliotCurie 91192 GIF SUR YVETTE CEDEX FRANCE
tembine(at)ieee.org
News:
Best paper award for Learning in UserCentric IPTV Services Selection in Heterogeneous Wireless Networks at Infocom workshop, 2011. (jointly with M. A. Khan and S. Marx)
Best paper finalist award for Random Matrix Games in Wireless Networks at IEEE Global High Tech Congress 2012 (jointly with M. A. Khan).
RESEARCH INTERESTS AND ACTIVITIES

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

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, noninvadable strategy, unbeatable state, stochastically stable state, continuously stable state, global evolutionarily stable state (GESS, the analogue of ESS for multiple population games), robust and riskdominant strategy or payoff, replicator dynamics, Brownvon NeumannNash dynamics, fictitious play, adaptive dynamics, imitate the better dynamics, best response dynamics, logit dynamics, Smith dynamics, projection dynamics, gradient methods, Gfunction 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


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 nonregular nonlinear differential equations or differential inclusions with time delays. We use the theory of delayed differential equation (DDE) to study stability, convergence and nonconvergence 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.
 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. 17511759, Autonomic and SelfOrganising Systems, July 2009

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 usercentric 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.
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 socalled 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 longrun 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 longrun 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 timeconsistent and dynamical coalitional solution concepts (an example could be the 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 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 largescale
systems and has methodological implications in many complex systems arising in engineering and socioeconomic areas, ecology and evolutionary biology.
 Energy management in wireless networks
 Intergenerational energy control
 Resourceconstrained competition in heterogeneous network
 Renewable energies in broadband wireless networks

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, FixedPoint Analysis, Decoupling Assumption
 BellmanShapley mean field optimality
 Spatial nonreciprocal interactions and their asymptotics
 Random number of interacting players, nonconvergent dynamics and nonequilibrium 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 socalled mean field games with additional individual state processes. Keywords: neutrally stable set, multigenerational equilibria, extension of HamiltonJacobiBellman equations (first and second types), Issacs conditions, double limit, Birkoff center, nonanticipative strategies with and without delays, open loop, closedloop 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 multiclass of players, the dynamics
describe both the intrapopulation interaction and interpopulation
interaction. The stochastic mean field game dynamics are in general
nonlinear (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 integrodifferential equations (SIDPE) etc.


Spatial mean field game dynamics for hybrid networks

Mobilitybased dynamics, multicomponent dynamics for nonpairwise interaction

Nonconvergent dynamics and limit cycle in communication systems

Introduction to Engineering Games. Applications in computer networks, wireless communications
Game theory and learning in wireless networks, coauthored with Samson Lasaulce, AP 2011.
Distributed strategic learning for wireless engineers, CRC Press, Taylor & Francis, 2012
Published by CRC Press, Taylor & Francis, Inc.
 Foreword by Tamer Basar, UIUC, US
 Preface by Eitan Altman, INRIA, France
 NEW: Tutorial course "Distributed strategic learning for engineers", 2012.

Teaching Activities

 Mean field stochastic games, Supelec, 2010.
 Distributed strategic learning for wireless engineers Winter 2010, Supelec. (previous titles: Learning and Dynamics in Networked Games or Distributed strategic learning in dynamic robust games).
 Wireless local area and adhoc networks, Master Program "Advanced wireless communications systems", SUPELEC, 2010.
 Signal processing and systems  Supelec, 2010
 RASS, Supelec, 2010
 SL, Supelec, 2010
 Advanced stochastic networks, Supelec, 2010
 20062009:

 Game Theory for Networks , Fall 2008
 Evolutionary Networking Games , Winter 2009
 Quality of Service (QoS) : Performance Evaluation (Graduate, IUPGMI), Prof. Yezekael Hayel, 20062009.
 Networks administration (Graduate, IUPGMI), Prof. Thomas Guthmann and Prof. Stephane Igounet, 20062009.
 Certification Computers & Internet (Undergraduate, Avignon University), Prof. Fabrice Lefevre and Prof. Thierry Valet, 20062009.




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