Many natural games have both high and low cost Nash equilibria: their Price of Anarchy is high and yet their Price of Stability is low. In such cases, one could hope to move behavior from a high cost equilibrium to a low cost one by a “public service advertising campaign ” encouraging players to follow the low-cost equilibrium, and if every player follows the advice then we are done. However, the assumption that everyone follows instructions is unrealistic. A more natural assumption is that some players will follow them, while other players will not. In this paper we consider the question of to what extent can such an advertising campaign cause behavior to switch from a bad equilibrium to a good one even if only a fraction of people actually follow the given advice, and do so only temporarily. Unlike

In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their cost and therefore their behaviors do not necessarily lead the game to an equilibrium. Even in the case there is an equilibrium, its makespan might be much larger than the social optimum, and this inefficiency is measured by the price of anarchy – the worst ratio between the makespan of an equilibrium and the optimum. Coordination mechanisms aim to reduce the price of anarchy by designing scheduling policies that specify how jobs assigned to a same machine are to be scheduled. Typically these policies define the schedule according to the processing times as announced by the jobs. One could wonder if there are policies that do not require this knowledge, and still provide a good price of anarchy. This would make the processing times be private information and avoid the problem of truthfulness. In this paper we study these so-called non-clairvoyant policies. In particular, we study the RANDOM policy that schedules the jobs in a random order without preemption, and the EQUI policy that schedules

We study the degree to which small fluctuations in costs in wellstudied potential games can impact the result of natural best-response and improved-response dynamics. We call this the Price of Uncertainty and study it in a wide variety of potential games (including fair cost-sharing games, set-cover games, routing games, and jobscheduling games), finding a number of surprising results. In particular, we show that in certain cases, even extremely small fluctuations can cause these dynamics to spin out of control and move to states of much higher social cost, whereas in other cases these dynamics are much more stable even to large degrees of fluctuation. We also consider the resilience of these dynamics to a small number of Byzantine players about which no assumptions are made. We show again a contrast between different games. In certain cases (e.g., fair cost-sharing, set-covering, job-scheduling) even a single Byzantine

We consider a dynamic load balancing scenario in which users allocate resources in a non-cooperative and selfish fashion. The perceived performance of a resource for a user decreases with the number of users that allocate the resource. In our dynamic, concurrent model, users may reallocate resources in a round-based fashion. As opposed to various settings analyzed in the literature, we assume that users have quality of service (QoS) demands. A user has zero utility when falling short of a certain minimum performance threshold and having positive utility otherwise. Whereas various load-balancing protocols have been proposed for the setting without quality of service requirements, we consider protocols that satisfy an additional locality constraint: The behavior of a user depends merely on the state of the resource it currently allocates. This property is particularly useful in scenarios where the state of other resources is not readily accessible. For instance, if resources represent channels in a mobile network, then accessing channel information may require time-intensive measurements. We consider several variants of the model, where the quality of service demands may depend on the user, the resource, or both. For all cases we present protocols for which the dynamics converge to a state in which all users are satisfied. More importantly, the time to reach such a state scales nicely. It is only logarithmic in the number of users, which makes our protocols applicable in large-scale systems.

The generous financial help of the Israeli Ministry of Science (Eshkol Scholarship), the Prof.

We consider a game-theoretic bin packing problem with identical items, and we study the convergence time to a Nash equilibrium. In the model proposed, users choose their strategy simultaneously. We deal with two bins and multiple bins cases. We consider the case when users know the load of all bins and cases with less information. We consider two approaches, depending if the system can undo movements that lead to infeasible states. In the two bins case, we show an O(log log n) and an O(n) bounds when undo movements are allowed and when they are not allowed, resp. In multiple bins case, we show an O(log n) and an O(nm) bounds when undo movements are allowed and when they are not allowed, resp. In the case with less information, we show an O(m log n) and an O(n³ m) bounds when undo movements are allowed and when they are not allowed, resp. Also, in the case with less information where the information about completely filled/empty bins is not available, we show an O(m² log n) and an O(n³ m³) bounds when undo movements are allowed and when they are not allowed, resp.

We prove N P-hardness of pure Nash equilibrium for some problems of scheduling games and connection games. The technique is standard: first, we construct a gadget without the desired property and then embed it to a larger game which encodes a N P-hard problem in order to prove the complexity of the desired property in a game. This technique is very efficient in proving NP-hardness for deciding the existence of Nash equilibria. In the paper, we illustrate the efficiency of the technique in proving the N P-hardness of deciding the existence of pure Nash equilibria of Matrix Scheduling Games and Weighted Connection Games. Moreover, using the technique, we can settle the complexity not only of the existence of equilibrium but also of the existence of good cost-sharing protocol.

We study how to reach a Nash equilibrium in a load balancing scenario where each task is managed by a selfish agent and attempts to migrate to a machine which will minimize its cost. The cost of a machine is a function of the load on it. The load on a machine is the sum of the weights of the jobs running on it. We prove that Nash equilibria can be learned on that games with incomplete information, using some Lyapunov techniques.

In this note we report recent results on the problem of leading natural dynamics to good behavior in games that have both high-quality and low-quality equilibria. We show how a central agency can use a public-service advertising campaign to help “nudge ” players ’ behavior towards a high-quality equilibrium, even if only a fraction of players pay attention. We also discuss results analyzing how well-motivated learning rules, when given additional global information about a game, can be used to effectively reach high-quality equilibria.