Non-clairvoyant Scheduling Games

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 the jobs in parallel using time-multiplexing, assigning each job an equal fraction of CPU time

Approximate Strong Equilibrium in Job Scheduling Games

A Nash Equilibrium (NE) is a strategy profile resilient to unilateral deviations, and is predominantly used in the analysis of multiagent systems. A downside of NE is that it is not necessarily stable against deviations by coalitions. Yet, as we show in this paper, in some cases, NE does exhibit stability against coalitional deviations, in that the benefits from a joint deviation are bounded. In this sense, NE approximates strong equilibrium. Coalition formation is a key issue in multiagent systems. We provide a framework for quantifying the stability and the performance of various assignment policies and solution concepts in the face of coalitional deviations. Within this framework we evaluate a given configuration according to three measures: (i) IR_min: the maximal number alpha, such that there exists a coalition in which the minimal improvement ratio among the coalition members is alpha, (ii) IR_max: the maximal number alpha, such that there exists a coalition in which the maximal improvement ratio among the coalition members is alpha, and (iii) DR_max: the maximal possible damage ratio of an agent outside the coalition. We analyze these measures in job scheduling games on identical machines. In particular, we provide upper and lower bounds for the above three measures for both NE and the well-known assignment rule Longest Processing Time (LPT). Our results indicate that LPT performs better than a general NE. However, LPT is not the best possible approximation. In particular, we present a polynomial time approximation scheme (PTAS) for the makespan minimization problem which provides a schedule with IR_min of 1+epsilon for any given epsilon. With respect to computational complexity, we show that given an NE on m >= 3 identical machines or m >= 2 unrelated machines, it is NP-hard to determine whether a given coalition can deviate such that every member decreases its cost

Do Capacity Constraints Constrain Coalitions?

We study strong equilibria in symmetric capacitated cost-sharing games. In these games, a graph with designated source $s$ and sink $t$ is given, and each edge is associated with some cost. Each agent chooses strategically an $s$-$t$ path, knowing that the cost of each edge is shared equally between all agents using it. Two variants of cost-sharing games have been previously studied: (i) games where coalitions can form, and (ii) games where edges are associated with capacities; both variants are inspired by real-life scenarios. In this work we combine these variants and analyze strong equilibria (profiles where no coalition can deviate) in capacitated games. This combination gives rise to new phenomena that do not occur in the previous variants. Our contribution is two-fold. First, we provide a topological characterization of networks that always admit a strong equilibrium. Second, we establish tight bounds on the efficiency loss that may be incurred due to strategic behavior, as quantified by the strong price of anarchy (and stability) measures. Interestingly, our results are qualitatively different than those obtained in the analysis of each variant alone, and the combination of coalitions and capacities entails the introduction of more refined topology classes than previously studied

Generalized selfish bin packing

Standard bin packing is the problem of partitioning a set of items with positive sizes no larger than 1 into a minimum number of subsets (called bins) each having a total size of at most 1. In bin packing games, an item has a positive weight, and given a valid packing or partition of the items, each item has a cost or a payoff associated with it. We study a class of bin packing games where the payoff of an item is the ratio between its weight and the total weight of items packed with it, that is, the cost sharing is based linearly on the weights of items. We study several types of pure Nash equilibria: standard Nash equilibria, strong equilibria, strictly Pareto optimal equilibria, and weakly Pareto optimal equilibria. We show that any game of this class admits all these types of equilibria. We study the (asymptotic) prices of anarchy and stability (PoA and PoS) of the problem with respect to these four types of equilibria, for the two cases of general weights and of unit weights. We show that while the case of general weights is strongly related to the well-known First Fit algorithm, and all the four PoA values are equal to 1.7, this is not true for unit weights. In particular, we show that all of them are strictly below 1.7, the strong PoA is equal to approximately 1.691 (another well-known number in bin packing) while the strictly Pareto optimal PoA is much lower. We show that all the PoS values are equal to 1, except for those of strong equilibria, which is equal to 1.7 for general weights, and to approximately 1.611824 for unit weights. This last value is not known to be the (asymptotic) approximation ratio of any well-known algorithm for bin packing. Finally, we study convergence to equilibria

Evolutionary Solutions and Internet Applications for Algorithmic Game Theory

The growing pervasiveness of the internet has created a new class of algorithmic problems: those in which the strategic interaction of autonomous, self-interested entities must be accounted for. So motivated, we seek to (1) use game theoretic models and techniques to study practical problems in load balancing, data streams and internet traffic congestion, and (2) demonstrate the usefulness of evolutionary game theory's adaptive learning model as an analytical and evaluative tool.First we consider the evolutionary game theory concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of anarchy for quantifying the cost of having no central authority. Unlike Nash equilibria, stochastically stable states are the result of natural dynamics of large populations of computationally bounded agents, and are resilient to small perturbations from ideal play. To illustrate the utility of stochastic stability, we study the load balancing game on related machines, which has an unbounded price of anarchy, even in the case of two jobs and two machines. We show that in contrast, even in the general case, the price of stochastic anarchy is bounded.Next, we propose auction-based mechanisms for admission control of continuous queries to a Data Stream Management System. When submitting a query, each user also submits a bid: how much she is willing to pay for her query to run. Our mechanisms must admit queries and set payments in a way that maximizes system revenue while incentivizing customers to use the system honestly. We propose several manipulation-resistant payment mechanisms and prove that one guarantees a profit close to a standard profit benchmark, and the others perform well experimentally.Finally, we study the long standing problem of congestion control at bottleneck routers on the internet. We examine the effectiveness of commonly-used queuing policies when each network endpoint is self-interested and has no information about the other endpoints' actions or preferences. By employing evolutionary game theory, we find that while bottleneck routers face heavy congestion at stochastically stable states under policies being currently deployed, a practical policy that was recently proposed yields fair and efficient conditions with no congestion

Strong Price of Anarchy for Machine Load Balancing

Abstract. As defined by Aumann in 1959, a strong equilibrium is a Nash equilibrium that is resilient to deviations by coalitions. We give tight bounds on the strong price of anarchy for load balancing on related machines. We also give tight bounds for k-strong equilibria, where the size of a deviating coalition is at most k