Section: New Results

Network Engineering Games

Participants : Eitan Altman, Ilaria Brunetti, Majed Haddad, Alexandre Reiffers.

The association problem

In [57] , M. Haddad, S. Habib (Orange Labs, Issy les Moulineaux), and P. Wiecek (Wroclaw Univ. of Technology, Poland) and E. Altman develop a hierarchical Bayesian game framework for automated dynamic offset selection. Users compete to maximize their throughput by picking the best locally serving radio access network (RAN) with respect to their own measurement, their demand and a partial statistical channel state information of other users. In particular, they investigate the properties of a Stackelberg game, in which the base station is a player on its own. They derive analytically the utilities related to the channel quality perceived by users to obtain the equilibria. They study the Price of Anarchy of such system, which is defined as the ratio of the social welfare attained when a network planner chooses policies to maximize social welfare versus the social welfare attained at a Nash/Stackeleberg equilibrium when users choose their policies strategically.

Cognitive radio

In [26] , M. Haddad, P. Wiecek (Wroclaw Univ. of Technology, Poland), O. Habachi and Y. Hayel (both with Univ. of Avignon) propose a game theoretical approach that allows cognitive radio pairs, namely the primary user (PU) and the secondary user (SU), to update their transmission powers and frequencies simultaneously. Specifically, a Stackelberg game model in which individual users attempt to hierarchically access to the wireless spectrum while maximizing their energy efficiency was addressed. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium was conducted. In particular, it was shown that a spectrum coordination naturally occurs when both actors in the system decide sequentially about their powers and their transmitting carriers. As a result, spectrum sensing in such a situation turns out to be a simple detection of the presence/absence of a transmission on each sub-band. An algorithmic analysis on how the PU and the SU can reach such a spectrum coordination using an appropriate learning process is provided.

In [59] , the same authors present a hierarchical game to model distributed joint power and channel allocation for multi-carrier energy efficient cognitive radio systems. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. It was proved that, at the Stackelberg equilibrium, each of the two users transmits on only one carrier depending on the fading channel gains. This results contrast with capacity-based approaches in which a certain number of carriers is exploited depending on the channel gains. Interestingly, it was shown that, for the vast majority of cases, introducing a certain degree of hierarchy in a multi-carrier system induces a natural coordination pattern where users have incentive to choose their transmitting carriers in such a way that they always transmit on orthogonal channels. Analytical results were provided for assessing and improving the performances in terms of energy efficiency between the non-cooperative game with synchronous decision makers and the proposed Stackelberg game.

Routing Games

In [39] , E. Altman, J. Kuri (Indian Institute of Science, Bangalore, India) and R. El-Azouzi (Univ. of Avignon) study a routing game that models competition over a simple network with losses. Packets may be lost in the network due to either congestion losses or to channel random losses. They compute the equilibrium and establish its properties. They identify a Braess type paradox in which by adding a link the loss probabilities of all players increase.

G. Accongiagioco (Institute for Advanced Studies, Lucca, Italy), E. Altman, E. Gregori (Italian National Research Council, Italy) and L. Lenzini (Univ. of Pisa, Italy) analyze in [36] the decisions taken by an Autonomous System (AS) when joining the Internet. They first define a realistic model for the interconnection costs incurred and then they use this cost model to perform a game theoretic analysis of the decisions related to the creation of new links in the Internet. The proposed model does not fall into the standard category of routing games, hence they devise new tools to solve it by exploiting peculiar properties of the game. They prove analytically the existence of multiple equilibria for specific cases, and provide an algorithm to compute the stable ones. The analysis of the model's outcome highlights the existence of a Price of Anarchy and a Price of Stability.

Network neutrality and collusion

Representatives of several Internet access providers have expressed their wish to see a substantial change in the pricing policies of the Internet. In particular, they would like to see content providers pay for use of the network, given the large amount of resources they use. This would be in clear violation of the “network neutrality” principle that had characterized the development of the wireline Internet. In [14] , E. Altman, M. K. Hanawal (former PhD student in Maestro ) and R. Sundaresan (Indian Institute of Science, Bangalore, India) proposed and studied possible ways of implementing such payments and of regulating their amount. The results were reported already in a previous report, but were substantially revised during the period of this project.

Competition over popularity in social networks

We have pursued our analysis of competition over popularity and visibility in social networks. In [68] , A. Reiffers and E. Altman, together with Y. Hayel (Univ. of Avignon) study a game model that arises when the rate of transmission of packets of each source can be accelerated in order to optimize a weighted sum of its acceleration cost and the expected number of its contents on the timelines of those who follow that content. While this paper considers equilibrium within static policies (in which the acceleration rate does not change in time), the same authors study in [51] the structure of dynamic equilibrium policies which are allowed to change as a function of the time (or of the state). A problem with a similar tradeoff is studied by E. Altman in a mobile context in [13] where the question of accelerating the transmission rate of content arises in a context of competition over content where it is assumed that if a content reaches a given destination then that destination will not be interested any more in receiving competing content.

In [67] , A. Reiffers, E. Altman and Y. Hayel (Univ. of Avignon) extend the work in [68] , and model the situation in which several social networks are available and a source may control not only the rate of transmission (acceleration) but may also decide how to split its content to the various social networks.

A competition over the timing of the transmission of a content was studied by E. Altman and N. Shimkin (Israel Institute of Technology, Israel) in [41] . Uniqueness of a symmetric equilibrium was established under the assumption of Poisson arrival of requests.