Section: New Results

Network engineering games

Participants : Eitan Altman, Konstantin Avrachenkov, Ilaria Brunetti, Richard Combes, Julien Gaillard, Majed Haddad, Manjesh Kumar Hanawal, Alexandre Reiffers.

Fairness

Anti-trust laws have been introduced by many countries in the last century. This is due to the perception that free competition is better for society. This motivated H. Kameda (Univ. Tsukuba, Japan), C. Touati and A. Legrand (Mescal , Inria - CNRS) in cooperation with E. Altman, to define in [28] a fairness concept related to the outcome of competition, which is the Nash equilibrium concept.

Association problem

In [70] , E. Altman and M. Haddad study in collaboration with C. Hasan and J.-M. Gorce (Socrate , Inria - INSA) games related to the association problem of mobiles to an access point. It consists of deciding to which access point to connect. Here the choice is between two access points or more, where the access decisions may depend on the number of mobiles connected to each one of the access points. New results were obtained using elementary tools in congestion and crowding games.

Association and placement

The location of a base station has an impact on the throughuput of arriving mobiles that decide to connect to it. Given a cooperative behavior among base stations, E. Altman derives in [54] in collaboration with A. Coluccia (Univ. Salento, Italy) the equilibrium association policy and maximizes its performance by a suitable cooperative positioning of the base stations. The non-cooperative related model was studied in [16] by E. Altman, in collaboration with A. Kumar, C. Singh and R. Sundaresan (all three from IISc, Bangalore, India).

Power control with energy state

In [42] and [64] , E. Altman, M. Haddad, J. Gaillard study with D. Fiems (Gent Univ., Belgium) a power control game over a collision channel. Each player has an energy state. When choosing a higher transmission power, the chance of a successful transmission (in the presence of other interference) increases at the cost of a larger decrease in the energy state of the battery. This dynamic game is studied when restricting to simple non-dynamic strategies that consist of choosing a given power level that is maintained during the lifetime of the battery. Surprising paradoxes were identified in the proposed Hawk and Dove game.

Routing games

In [65] , M. Haddad, E. Altman and J. Galliard study in collaboration with D. Fiems (Gent Univ., Belgium) a sequential dynamic routing game on a line, where the decision of a user is spatio-temporal control. Each user ships its demand over time on a shared resource. Explicit expressions of the equilibrium of such systems are presented and compared to the global optimum case. The basic idea is taken from a previous paper on this subject by M. K. Hanawal (also with Univ. Avignon/LIA) and E. Altman, in collaboration with R. El-Azouzi (Univ. Avignon/LIA) and B. Prabhu (CNRS - LAAS), who show in [67] that one may transform the time dimension into a spatial component and thus obtain an equivalent standard routing game (where time plays no role) with infinitely many nodes.

Bayesian games in networking

We have considered several problems in networks in which decision makers have asymmetrical information. One of these is how one agent may benefit from revealing part of his information? We considered two types of hierarchical scenarios. In the first, we assume that an agent signals some information to another agent who then chooses an action based on that signal. This action determines the utility of both agents. In the second scenario, a player takes an action (such as pricing) and then the second player reacts to it. Both players' utilities depend on the actions of the two players. The action of the first player may reveal to the second player some of his private information. We use the framework of signalling game to solve the first type of problem and that of Bayesian game to solve the second. Other problems include pricing access to the Internet with partial information [52] (by I. Brunetti (Univ. Bologna, Italy), M. Haddad (Univ. Avignon/LIA) and E. Altman). In [45] , M. Haddad and E. Altman, in collaboration with P. Wiecek (Wroclaw Univ. of Technology, Poland), apply Bayesian games for the association problem in which users have to decide to which access point to connect.

Jamming

We have been working on various models that capture different aspects of jamming (on purpose noise generation). Jamming with partial information is studied in [51] using Bayesian games, by M. Haddad (Univ. Avignon/LIA), E. Altman and S. Azad, as well as [62] and [63] by E. Altman in collaboration with A. Garnaev (St. Petersburg State Univ., Russia) and Y. Hayel (Univ. Avignon/LIA). With K. Avrachenkov, they further consider a dynamic jamming problem in [61] . In all these models the jammer creates interference to the data packets. In [29] V. Kavitha and R. El-Azouzi (Univ. Avignon/LIA), R. Sundaresan (IISc, Bangalore, India), and E. Altman study a different type of jamming game. The jammer attacks the signalling channel and not the data itself. A Bayesian game is formulated and solved there.

Network neutrality and collusions

Network neutrality is a key issue in the future Internet. It is related to the question of whether the access to Internet will remain a universal service or whether it would be regulated by market forces according to economic interests of those that control the Internet access. One form of network non-neutrality is when an ISP gives preferential treatment to one content provider over others. We call this “collusion” or “vertical monopoly”. In collaboration with T. Jimenez and Y. Hayel (Univ. Avignon/LIA), E. Altman studies this in [71] along with “horizontal monopolies” that may occur when several ISPs merge. They introduce a new concept of “price of collusion” and identify in [44] cases in which not only consumers loose from collusions but also the colliding agents, as also seen in a different model for network non-neutrality given in [69] by M. K. Hanawal (also with Univ. Avignon/LIA) and E. Altman in collaboration with R. Sundaresan (IISc, Bangalore, India). This is related to a special kind of Braess type paradox.

Competition over popularity in social networks

We focus on competition of video contents for popularity. We analyze the impact of sharing, embedding, advertisement and other actions by the users for increasing the popularity and visibility. This then allowed E. Altman in [80] , [38] and [95] to propose stochastic game models and to fully determine the equilibrium policy. He further proposes a dynamic game for the study of partial information and obtain the equilibrium policies and equilibrium performance. In [39] , [79] the results are further extended for the wireless context.

Stochastic geometry methods for wireless design issues

Stochastic geometry seems to be the adequate tool in order to model correctly randomness in the location of networks elements such as the mobile terminals and the fixed base stations. Modeling the locations of both as independent spatial processes, In [66] and [25] , M. K. Hanawal and E. Altman study in collaboration with F. Baccelli (Trec , Inria - ENS) properties of Nash equilibria obtained in a multiple access game. They also derive the saddle point obtained in jamming games [68] .

In which content to specialize

E. Altman considers in [40] the question of how should a content provider decide in which content to specialize. He shows that the problem is equivalent to the so called “Crowding” games, which allows him to prove the existence of a pure equilibrium. The conclusion is then that there is no gain by diversifying in several contents.

Cognitive radio

In collaboration with J. Elias (Univ. Paris Descartes-Sorbonne) and F. Martignon (LRI-Univ. Paris-Sud), E. Altman study in [56] the question of which priority level to use in a cognitive radio network: higher priority (primary user) or lower one (secondary user). The utilities are function of both the price and the quality of service. After deriving an equilibrium in this game problem, the authors study the question of how to choose prices so as to induce efficient equilibria.

Constrained games

In collaboration with A. Galindo-Serrano and L. Guipponi (CTTC, Spain), E. Altman studies in [60] a game theoretical problem of power control in several base stations with a coupled constraint: the interference at a given point in space should be upper bounded by some constant. The authors establish the existence of a continuum of constrained equilibria to this type of games and show that there is a unique one with some desirable scaling properties (i.e. that consitutes a normalized Nash equilibrium).

Dynamic coalition games

In collaboration with M. K. Panda and T. Chahed (Telecom SudParis, France), E. Altman considers the question of whether to join a multicast session or not. In contrast to many queueing problems, the congestion here is a desirable property, since the cost per user decreases as the number of users connected to the multicast session increases. In [74] the equilibrium policies are derived; these exhibit a surprising structure.

Evolutionary games

The relatively young theory of Evolutionary games considers a large number of interactions between pairs of randomly selected players. It is thus based on a relatively narrow scope in which the one that interacts is the player. In collaboration with Y. Hayel (Univ. Avignon/LIA) and E. V. Belmega (ETIS/ENSEA - Univ. Cergy-Pontoise - CNRS), E. Altman has been developing in [26] an alternative theory of evolutionary game in which a player consists of a group of interacting agents. This is in line with today's understanding of evolution of species (e.g. Dawkins' book “The Selfish Gene” in which the player is the gene of the species). We plan to apply this to energy dependent power control in wireless systems. We also plan to apply these in other areas such as the evolution of languages over social networks, in which some preliminary results (over Twitter) were already obtained in [81] by E. Altman and Y. Portilla (Univ. Avignon/LIA).