Proceedings Article•
The Price of Anarchy of Affine Congestion Games with Similar Strategies.
01 Jan 2018-pp 48-59
TL;DR: In this article, the authors investigated to what extent these bounds depend on the similarities among the players' strategies in affine congestion games and showed that for the non-atomic case, better bounds can always be obtained for any finite value of θ, while for the atomic case, θ 3 / 2 and θ 2 are necessary and sufficient conditions to obtain better bounds in games played on general graph topologies and on parallel link graphs, respectively.
Abstract: Affine congestion games are a well-studied model for selfish behavior in distributed systems, such as transportation and communication networks. Seminal influential papers in Algorithmic Game Theory have bounded the worst-case inefficiency of Nash equilibria, termed as price of anarchy, in several variants of these games. In this work, we investigate to what extent these bounds depend on the similarities among the players' strategies. Our notion of similarity is modeled by assuming that, given a parameter θ ≥ 1 , the costs of any two strategies available to a same player, when evaluated in absence of congestion, are within a factor θ one from the other. It turns out that, for the non-atomic case, better bounds can always be obtained for any finite value of θ. For the atomic case, instead, θ 3 / 2 and θ 2 are necessary and sufficient conditions to obtain better bounds in games played on general graph topologies and on parallel link graphs, respectively. It is worth noticing that small values of θ model the behavioral attitude of players who are partially oblivious to congestion and are not willing to significantly deviate from what is their best strategy in absence of congestion.
Citations
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Journal Article•
TL;DR: In a system where noncooperative agents share a common resource, the price of anarchy is proposed, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system.
Abstract: In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.
46 citations
16 Sep 2020
TL;DR: In this paper, the authors consider congestion games where players are partitioned into p priority classes and resources schedule their users according to a priority-based policy, breaking ties uniformly at random.
Abstract: We reconsider atomic and non-atomic affine congestion games under the assumption that players are partitioned into p priority classes and resources schedule their users according to a priority-based policy, breaking ties uniformly at random. We derive tight bounds on both the price of anarchy and the price of stability as a function of p, revealing an interesting separation between the general case of \(p\ge 2\) and the priority-free scenario of \(p=1\). In fact, while non-atomic games are more efficient than atomic ones in absence of priorities, they share the same price of anarchy when \(p\ge 2\). Moreover, while the price of stability is lower than the price of anarchy in atomic games with no priorities, the two metrics become equal when \(p\ge 2\). Our results hold even under singleton strategies. Besides being of independent interest, priority-based scheduling shares tight connections with online load balancing and finds a natural application within the theory of coordination mechanisms and cost-sharing policies for congestion games. Under this perspective, a number of possible research directions also arises.
7 citations
Posted Content•
TL;DR: This work provides an exhaustive analysis of traffic routing by providing provably tight bounds on PoA for arbitrary classes of cost functions both in the case of general congestion/routing games as well as in the special case of path-disjoint networks.
Abstract: We investigate traffic routing both from the perspective of real world data as well as theory. First, we reveal through data analytics a natural but previously uncaptured regularity of real world routing behavior. Agents only consider, in their strategy sets, paths whose free-flow costs (informally their lengths) are within a small multiplicative $(1+\theta)$ constant of the optimal free-flow cost path connecting their source and destination where $\theta\geq0$. In the case of Singapore, $\theta=1$ is a good estimate of agents' route (pre)selection mechanism. In contrast, in Pigou networks the ratio of the free-flow costs of the routes and thus $\theta$ is infinite, so although such worst case networks are mathematically simple they correspond to artificial routing scenarios with little resemblance to real world conditions, opening the possibility of proving much stronger Price of Anarchy guarantees by explicitly studying their dependency on $\theta$. We provide an exhaustive analysis of this question by providing provably tight bounds on PoA($\theta$) for arbitrary classes of cost functions both in the case of general congestion/routing games as well as in the special case of path-disjoint networks. For example, in the case of the standard Bureau of Public Roads (BPR) cost model, $c_e(x)= a_e x^4+b_e$ and more generally quartic cost functions, the standard PoA bound for $\theta=\infty$ is $2.1505$ (Roughgarden, 2003) and it is tight both for general networks as well as path-disjoint and even parallel-edge networks. In comparison, in the case of $\theta=1$, the PoA in the case of general networks is only $1.6994$, whereas for path-disjoint/parallel-edge networks is even smaller ($1.3652$), showing that both the route geometries as captured by the parameter $\theta$ as well as the network topology have significant effects on PoA (Figure 1).
5 citations
Journal Article•
TL;DR: In this paper, the authors study the impact of selfishness and greediness on the performance of load balancing in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers.
Abstract: We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it selects to run its job to the server among its permissible servers having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness. We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy and price of stability of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions.
4 citations
Journal Article•
TL;DR: In this paper, exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions are given. And the given values also hold for weighted and non-unweighted network congestion games.
Abstract: We show exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions. The given values also hold for weighted and unweighted network congestion games.
4 citations
References
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TL;DR: A concept of an n -person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n -tuple ofpure strategies, one strategy being taken for each player.
Abstract: One may define a concept of an n -person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n -tuple of pure strategies, one strategy being taken for each player. For mixed strategies, which are probability distributions over the pure strategies, the pay-off functions are the expectations of the players, thus becoming polylinear forms …
7,047 citations
Book•
01 Jan 1920
TL;DR: Aslanbeigui et al. as mentioned in this paper discussed the relationship between the national dividend and economic and total welfare, and the size of the dividend to the allocation of resources in the economy and the institutional structure governing labor market operations.
Abstract: The Economics of Welfare occupies a privileged position in economics. It contributed to the professionalization of economics, a goal aggressively and effectively pursued by Pigou's predecessor and teacher Alfred Marshall. The Economics of Welfare also may be credited with establishing welfare economics, by systematically analyzing market departures and their potential remedies. In writing The Economics of Welfare, Pigou built a bridge between the old and the new economics at Cambridge and in Britain. Much of the book remains relevant for contemporary economics. The list of his analyses that continues to play an important role in economics is impressive. Some of the more important include: public goods and externalities, welfare criteria, index number problems, price discrimination, the theory of the firm, the structure of relief programs for the poor, and public finance. Pigou's discussion of the institutional structure governing labor-market operations in his Wealth and Welfare prompted Schumpeter to call the work "the greatest venture in labor economics ever undertaken by a man who was primarily a theorist." The Economics of Welfare established welfare economics as a field of study. The first part analyzes the relationship between the national dividend and economic and total welfare. Parts II and III link the size of the dividend to the allocation of resources in the economy and the institutional structure governing labor-market operations. Part IV explores the relationship between the national dividend and its distribution. In her new introduction, Nahid Aslanbeigui discusses the life of Pigou and the history of The Economics of Welfare. She also discusses Pigou's theories as expressed in this volume and some of the criticisms those theories have met as well as the impact of those criticisms. The Economics of Welfare is a classic that repays careful study.
5,145 citations
TL;DR: In this paper, a class of noncooperative games (of interest in certain applications) is described and each game in the class is shown to possess at least one Nash equilibrium in pure strategies.
Abstract: A class of noncooperative games (of interest in certain applications) is described Each game in the class is shown to possess at least one Nash equilibrium in pure strategies
2,161 citations
2,036 citations