## Section: New Results

### Game theory applied to networking

Participants : Eitan Altman, Konstantin Avrachenkov, Majed Haddad, Manoj Panda, Giovanni Neglia.

#### Resource allocation in wireless networks

##### Power control

In [14] E. Altman, K. Avrachenkov and A. Garnaev (St. Petersburg State University, Russia), study power control for Gaussian interference channel in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The authors enhance the water-filling technique with explicit analytic solutions. The authors also provide an alternative simple proof of the convergence of the Iterative Water Filling Algorithm. Finally, the authors compare the non-cooperative approach with the cooperative approach and show that the non-cooperative approach results in a more fair resource distribution.

There has been a debate between those proposing protocols based on a centralized controller and those favoring decentralized protocols based on non-cooperative game theory. In [26] E. Altman and M. Haddad, together with S.-E. Elayoubi and Z. Altman (both from Orange Labs, Issy les Moulineaux), consider a situation where a base station lets mobiles take power control decisions in some system states and imposes actions in other states. The authors study how best to choose what information to make available and how mobiles should react.

##### Joint power and rate allocation

In [63] X. Lei and L. Cottatellucci (both from Institut Eurecom ) and K. Avrachenkov consider a block fading interference channels with partial channel state information and address the issue of joint power and rate allocation in a game theoretic framework. Resource allocation algorithms based on Bayesian games are proposed. The existence, uniqueness, and some stability properties of Nash equilibria are analyzed. For some asymptotic setting, closed-form expressions of Nash equilibria are also provided.

##### Jamming in wireless networks

Jamming is a form of a denial of service attack in which an adversary can degrade the quality of the reception by creating interference. One can study jamming both in the purpose of protecting a wireless network against such attack or, on the contrary, in order to efficiently disrupt the communications of some adversary. In both cases jamming is part of a conflict for which game theory is an appropriate tool. In [15] E. Altman, K. Avrachenkov and A. Garnaev (St. Petersburg State University), investigate the effect of partially available information in which the user does not even know whether or not the jammer is indeed present. The problem is formulated as a zero-sum game. The authors find the equilibrium strategies in closed-form and specify the range of sub-carriers where the user can expect the jamming attack.

##### Channel access

In WiFi networks, mobile nodes compete for accessing the shared channel by means of a random access protocol called Distributed Coordination Function (DCF), which is long term fair. Selfish nodes could benefit from violating the protocol and increasing their transmission probability. G. Neglia, I. Tinnirello and L. Giarré (University of Palermo, Italy) have been studying the interaction of selfish nodes in the last two years (the research activity is described in Maestro 2009 and Maestro 2010 activity reports). [31] , [74] further extend the results to a heterogeneous scenario, where nodes have different requirements in terms of uplink/downlink ratios.

#### Network formation games

The continued growth of computer networks such as the Internet has raised the interest in understanding how networks get formed. The design of such networks is generally carried out by a large number of self-interested actors (users, Internet Service Providers ...), all of whom seek to optimize the quality and cost of their own operation. Previous works have addressed the “Network Formation” problem considering almost exclusively networks designed by selfish users, which can be consistently suboptimal. In [46] K. Avrachenkov and G. Neglia, together with J. Elias (University Paris Descartes), F. Martignon (University Paris-Sud 11), and L. Petrosyan (St. Petersburg State University, Russia), address the network formation issue using cooperative game theory, which permits to study ways to enforce and sustain cooperation among agents. Both the Nash bargaining solution and the Shapley value are investigated. After the comparison of these two approaches, the authors conclude that the Nash bargaining solution is more suitable to enforce cooperation in the network formation game in terms of cost allocation to users and computation time to get the solution.

##### Network design with socially-aware users

In many scenarios network design is not enforced by a central authority, but arises from the interactions of several self-interested agents. This is the case of the Internet itself. K. Avrachenkov and G. Neglia, in collaboration with J. Elias (University Paris Descartes) and F. Martignon (University Paris-Sud 11), have proposed two novel socially-aware network design games. The research has been described in Maestro 2010 activity reports. [24] extends the results for the case when users' utility functions incorporate a socially-aware component.

##### Stochastic games for cooperative network routing

In [64] K. Avrachenkov, L. Maggi and L. Cottatellucci (both from Institut Eurecom ) consider a system where several providers share the same network and control the routing in disjoint sets of nodes. They provide connection toward a unique server (destination) to their customers. The objective is to facilitate the design of the available network links and their costs such that all network providers are interested in cooperating and none of them withdraw from the coalition. More specifically, the authors establish the framework of a coalition game by providing an algorithm to compute the transferable coalition values. As by-product, the authors apply the proposed algorithm to two-player games both in networks subject to hacker attacks and in epidemic networks.

##### Association games

Using tools from coalition game theory, E. Altman, in cooperation with C. Singh (IISc Bangalore, India), considers in [72] a wireless framework in which several mobile terminals can receive and decode the same signal of the base station, and where the cost for broadcasting is taken to be the transmission power. They begin by proposing various schemes to share the cost and study their properties. Then, they study the association with partial information: an arriving user knowing its location has to decide without knowledge of the location of the other users and their number whether to join the multicast tree and pay according to a given cost sharing scheme, or to have a unicast connection at a given cost. The unicast alternative that each mobile has, results in a limitation on the coverage (area covered by the multicast session) and on the capacity (number of mobiles connected to the multicast session). The authors derive the expected capacity and coverage as a function of the cost sharing policy. This work is extended in [58] to the case of several base stations by E. Altman in collaboration with C. Hasan and J. M. Gorce (both from INSA Lyon and Inria project-team Swing ).

#### Routing games

In [40] , E. Altman, M. Panda and A. Estanisla (Master student at UPMC) study ring networks extensively used in both road traffic and telecommunications (in local area networks) in which each source with a given origin and destination on the ring, can split its traffic and send some part in one direction of the ring and some other part in the other direction. They compute the equilibria and find out that due to non-cooperation, much traffic is sent at equibrium along long paths.

In [16] , E. Altman, O. Pourtallier (Inria project-team Coprin ), T. Jimenez (Univ. Avignon/LIA) and H. Kameda (Univ. Tsukuba, Japan) study a load balancing processor sharing problem. The classical framework of routing games turned out not to apply here. Indeed, it had been used to model situations where the flow from each class of users is split among paths without any information on the realization of the sizes of each packet. In contrast, in this paper, each individual knows its size. The authors have succeeded in computing the equilibrium within the new setting.

Collusion is the situation where several players decide to cooperate and to choose their actions as if they were a single player - each player maximizes the sum of utilities of that group instead of only its own utility. In [90] , E. Altman in collaboration with Y. Hayel (Univ. Avignon/LIA) and H. Kameda (Univ. Tsukuba, Japan), has proposed various concepts that evaluate the impact of collusions. The authors have further studied collusions in routing games and identified situations where collusions are bad for all players: both those that collide loose in performance as well as those who remain independent.