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International audience; This paper considers different pricing models for a platform based rental system, such as Airbnb. A linear model is assumed for the demand response to price, and existence and uniqueness conditions for Nash equilibria are obtained. The Stackelberg equilibrium prices for the game are also obtained, and an iterative scheme is provided, which converges to the Nash equilibrium. Different cooperative pricing schemes are studied, and splitting of revenues based on the Shapley value is discussed. It is shown that a division of revenue based on the Shapley value gives a revenue to the platform proportional to its control of the market. The demand response function is modified to include user response to quality of service. It is shown that when the cost to provide quality of service is low, both renter and the platform will agree to maximize the quality of service. However, if this cost is high, they may not always be able to agree on what quality of service to provide.

International audience; We consider the problem of 'fair' scheduling the resources to one of the many mobile stations by a centrally controlled base station (BS). The BS is the only entity taking decisions in this framework based on truthful information from the mobiles on their radio channel. We study the well-known family of parametric -fair scheduling problems from a gametheoretic perspective in which some of the mobiles may be noncooperative. We first show that if the BS is unaware of the noncooperative behavior from the mobiles, the noncooperative mobiles become successful in snatching the resources from the other cooperative mobiles, resulting in unfair allocations. If the BS is aware of the noncooperative mobiles, a new game arises with BS as an additional player. It can then do better by neglecting the signals from the noncooperative mobiles. The BS, however, becomes successful in eliciting the truthful signals from the mobiles only when it uses additional information (signal statistics). This new policy along with the truthful signals from mobiles forms a Nash Equilibrium (NE) which we call a Truth Revealing Equilibrium. Finally, we propose new iterative algorithms to implement fair scheduling policies that robustify the otherwise non-robust (in presence of noncooperation) fair scheduling algorithms.

Forming, in a decentralized fashion, an optimal network topology while balancing multiple, possibly conflicting objectives like cost, high performance, security and resiliency to viruses is a challenging endeavor. In this paper, we take a game-formation approach to network design where each player, for instance an autonomous system in the Internet, aims to collectively minimize the cost of installing links, of protecting against viruses, and of assuring connectivity. In the game, minimizing virus risk as well as connectivity costs results in sparse graphs. We show that the Nash Equilibria are trees that, according to the Price of Anarchy (PoA), are close to the global optimum, while the worst-case Nash Equilibrium and the global optimum may significantly differ for small infection rate and link installation cost. Moreover, the types of trees, in both the Nash Equilibria and the optimal solution, depend on the virus infection rate, which provides new insights into how viruses spread: for high infection rate τ, the path graph is the worst- and the star graph is the best-case Nash Equilibrium. However, for small and intermediate values of τ, trees different from the path and star graphs may be optimal.

International audience; Is it profitable for players to unite and merge to a single player? Obviously, the sum of utilities at an equilibrium cannot exceed the sum obtained if all players join together. But what happens if only a subset of players join together? Previous work on collusion have already shown that the society may either gain or loose from collusion of a subset of players. In this paper we show for a simple load balancing example that not only the society may loose, but also the subset of players that collude may end up with a worse performance than without collusion. In doing so, we introduce new concepts that measure the price of collusion.

The area of networking games has had a growing impact on wireless networks. This reflects the recognition in the important scaling advantages that the service providers can benefit from by increasing the autonomy of mobiles in decision making. This may however result in inefficiencies that are inherent to equilibria in non-cooperative games. Due to the concern for efficiency, centralized protocols keep being considered and compared to decentralized ones. From the point of view of the network architecture, this implies the co-existence of network-centric and terminal centric radio resource management schemes. Instead of taking part within the debate among the supporters of each solution, we propose in this paper hybrid schemes where the wireless users are assisted in their decisions by the network that broadcasts aggregated load information. We derive the utilities related to the Quality of Service (QoS) perceived by the users and develop a Bayesian framework to obtain the equilibria. Numerical results illustrate the advantages of using our hybrid game framework in an association problem in a network composed of HSDPA and 3G LTE systems., Comment: 5 pages, 4 figures, IEEE Infocom, San Diego, USA, March 2010.

When routing dynamically randomly arriving messages, the controller of a high-speed communication network very often gets the information on the congestion state of down stream nodes only after a considerable delay, making that information irrelevant at decision epochs. We consider the situation where jobs arrive according to a Poisson process and must be routed to one of two (parallel) queues with exponential service time distributions (possibly with different means), without knowing the congestion state in one of the queues. However, (the conditional) probability distribution of the state of the unobservable queue can be computed by the router. We derive the joint probability distribution of the congestion states in both queues as a function of the routing policy. This allows us to identify optimal routing schemes for two types of frameworks: global optimization, in which the weighted sum of average queue lengths is minimized, and individual optimization, in which the goal is to minimize the expected delay of individual jobs.

The goal of this paper is to study pricing of differential services and its impact on the choice of service priority at equilibrium. We consider both TCP connections as well as non controlled (real time) connections. The performance measures (such as through-put and loss rates) are determined according to the operational parameters of a RED buffer management. The latter is assumed to be able to give differentated services to the applications according to their choice of service class. We consider a best effort type of service differentiation for both TCP as well as real-time traffic where the QoS of connections is not guaranteed, but by choosing a better (more expensive) service class, the QoS parameters of a session can improve (as long as the service class of other sessions are fixed). The choice of a service class of an application will depend both on the utility as well as on the cost it has to pay. We first study the performance of the system as a function of the connections'parameters and their choice of service classes. We then study the decision problem of how to choose the service classes. We model the problem as a noncooperative game. We etablish conditions for an equilibrium to exist and to be uniquely defined. We further provide conditions for convergence to equilibrium from non equilibria initial states. We finally study the pricing problem of how to choose prices so that the resulting equilibrium would maximize the network benefit.

The paper studies routing in loss networks in the framework of a non-cooperati- ve game with selfish users. Two solution concepts are considered: the Nash equilibrium, corresponding to the case of a finite number of agents (such as service providers) that take routing decisions, and the Wardrop equilibrium, in which routing decisions are taken by a very large number of individual users. We show that these equilibria do not fall into the standard frameworks of non-cooperative routing games. As a result, we show that uniqueness of equilibria or even of utilizations at equilibria may fail even in the case of simple topology of parallel links. However, we show that some of the problems disappear in the case in which the bandwidth required by of all connections is the same. For the special case of a parallel link topology, we obtain some surprisingly simple way of solving the equilibrium for both cases of Wardrop as well as Nash equilibrium.

Network equilibrium models that have traditionally been used for transportati- on planning have penetrated in recent years to other scientific fields. These models have recently been introduced in the telecommunication networks literature, as well as in the field of game theory. Researchers in the latter fields are not always aware of the very rich literature on equilibrium models outside of their application area. On the other hand, researchers that have used network equilibrium models in transportation may not be aware of new application areas of their tools. The aim of this paper is to present some central research issues and tools in network equilibria and pricing that could bring closer the three mentioned research communities.

International audience; We consider a coalition formation among players, in an $n$-player strategic game, over infinite horizon. At each time a randomly selected coalition makes a joint deviation, from a current action profile to a new action profile, which is strictly beneficial for all the players belonging to the coalition.Such deviations define a stochastic coalitional better-response (CBR) dynamics. The stochastic CBR dynamics either converges to a $\cal{K}$-stable equilibrium or becomes stuck in a closed cycle.We also assume that at each time a selected coalition makes mistake in deviation with small probability. We prove that all $\cal{K}$-stable equilibria and all action profiles from closed cycles, having minimum stochastic potential, are stochastically stable. Similar statement holds for strict $\cal{K}$-stable equilibrium. We apply the stochastic CBR dynamics to the network formation games. We show that all strongly stable networks and closed cycles of networks are stochastically stable.

Designing an optimal network topology while balancing multiple, possibly conflicting objectives like cost, performance, and resiliency to viruses is a challenging endeavor, let alone in the case of decentralized network formation. We therefore propose a game-formation technique where each player aims to minimize its cost in installing links, the probability of being infected by a virus and the sum of hopcounts on its shortest paths to all other nodes. In this article, we (1) determine the Nash Equilibria and the Price of Anarchy for our novel network formation game, (2) demonstrate that the Price of Anarchy (PoA) is usually low, which suggests that (near-)optimal topologies can be formed in a decentralized way, and (3) give suggestions for practitioners for those cases where the PoA is high and some centralized control/incentives are advisable., accepted for publication in IEEE Transactions on Control of Network Systems

International audience; We consider a scenario where an Internet Service Provider (ISP) serves users that choose digital content among M Content Providers (CP). In the status quo, these users pay both access fees to the ISP and content fees to each chosen CP; however, neither the ISP nor the CPs share their profit. We revisit this model by introducing a different business model where the ISP and the CP may have motivation to collaborate in the framework of caching. The key idea is that the ISP deploys a cache for a CP provided that they share both the deployment cost and the additional profit that arises due to caching. Under the prism of coalitional games, our contributions include the application of the Shap-ley value for a fair splitting of the profit, the stability analysis of the coalition and the derivation of closed-form formulas for the optimal caching policy. Our model captures not only the case of non-overlapping contents among the CPs, but also the more challenging case of overlapping contents; for the latter case, a non-cooperative game among the CPs is introduced and analyzed to capture the negative externality on the demand of a particular CP when caches for other CPs are deployed.