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Nash proved in 1951 that every game has a mixed Nash equilibrium [6]; whether such an equilibrium can be found in polynomial time has been open since that time. We review here certain recent results which shed some light to this old problem. Even though a mixed Nash equilibrium is a continuous object, the problem is essentially combinatorial, since it suffices to identify the support of a mixed...
The sensitivity of Nash equilibrium to strategic and informational details presents a difficulty in applying it to games which are not fully specified. Structurally-robust Nash equilibria are less sensitive to such details. Moreover, they arise naturally in important classes of games that have many semi-anonymous players. The paper describes this condition and its implications.
This paper studies the equilibrium property and algorithmic complexity of the exchange market equilibrium problem with more general utility functions: piece-wise linear functions, which include Leontief’s utility functions. We show that the Fisher model again reduces to the general analytic center problem, and the same linear programming complexity bound applies to approximating its equilibrium. However,...
We provide the first strongly polynomial time exact combinatorial algorithm to compute Fisher equilibrium for the case when utility functions do not satisfy the Gross substitutability property. The motivation for this comes from the work of Kelly, Maulloo, and Tan [15] and Kelly and Vazirani [16] on rate control in communication networks. We consider a tree like network in which root is the source...
In pay-per-click online advertising systems like Google, Overture, or MSN, advertisers are charged for their ads only when a user clicks on the ad. While these systems have many advantages over other methods of selling online ads, they suffer from one major drawback. They are highly susceptible to a particular style of fraudulent attack called click fraud. Click fraud happens when an advertiser or...
We present a simple model in which the worldwide web (www) is created by the interaction of selfish agents, namely document authors, users, and search engines. We show experimentally that power law statistics emerge very naturally in this context, and that the efficiency of the system has certain monotonicity properties.
In machine scheduling, a set of n jobs must be scheduled on a set of m machines. Each job i incurs a processing time of pij on machine j and the goal is to schedule jobs so as to minimize some global objective function, such as the maximum makespan of the schedule considered in this paper. Often in practice, each job is controlled by an independent selfish agent...
In this paper we present a cooperative game theoretic interpretation of the shortest path problem. We consider a buying agent who has a budget to go from a specified source node s to a specified target node t in a directed acyclic network. The budget may reflect the level of utility that he associates in going from node s to node t. The edges in the network are owned by individual utility maximizing...
We present a mechanism for reservations of bursty resources that is both truthful and robust. It consists of option contracts whose pricing structure induces users to reveal the true likelihoods that they will purchase a given resource. Users are also allowed to adjust their options as their likelihood changes. This scheme helps users save cost and the providers to plan ahead so as to reduce the risk...
We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the...
We present an auction-based algorithm for the computing market equilibrium prices in a production model, in which producers have a single linear production constraint, and consumers have linear utility functions. We provide algorithms for both the Fisher and Arrow-Debreu versions of the problem.
The assessment of credibility and reputation of contractors in online auctions is the key issue in providing reliable environment for customer-to-customer e-commerce. Confident reputation rating system is an important factor in managing risk and building customer satisfaction. Unfortunately, most online auction sites employ a very simple reputation rating scheme that utilizes user feedbacks and comments...
We give a simple characterization of all single-item truth-revealing auctions under some mild (and natural) assumptions about the auctions. Our work opens up the possibility of using variational calculus to design auctions having desired properties.
We introduce a new class of mechanism design problems called prediction games. There are n self interested agents. Each agent i has a private input xi and a cost of accessing it. Given are a function f(x1, ..., xn) which predicts whether a certain event will occur and an independent distribution on the agents’ inputs...
We study the complexity issues for Walrasian equilibrium in a special case of combinatorial auction, called single-minded auction, in which every participant is interested in only one subset of commodities. Chen et al. [5] showed that it is NP-hard to decide the existence of a Walrasian equilibrium for a single-minded auction and proposed a notion of approximate Walrasian equilibrium called relaxed...
We study an intensively studied resource allocation game introduced by Koutsoupias and Papadimitriou where n weighted jobs are allocated to m identical machines. It was conjectured by Gairing et al. that the fully mixed Nash equilibrium is the worst Nash equilibrium for this game w. r. t. the expected maximum load over all machines. The known algorithms for approximating the so-called “price of anarchy”...
A sharing community prospers when participation and contribution are both high. We suggest the two, while being related decisions every peer makes, should be given separate rational bases. Considered as such, a basic issue is the viability of club formation, which necessitates the modelling of two major sources of heterogeneity, namely, peers and shared content. This viability perspective clearly...
We study a model of interdomain routing in which autonomous systems’ (ASes’) routing policies are based on subjective cost assessments of alternative routes. The routes are constrained by the requirement that all routes to a given destination must be confluent. We show that it is NP-hard to determine whether there is a set of stable routes. We also show that it is NP-hard to find a set of confluent...
Providing network connectivity to rural regions in the developing world is an economically challenging problem especially given the low income levels and low population densities in such regions. Many existing connectivity technologies incur a high deployment cost that limits their affordability. Leveraging several emerging wireless technologies, this paper presents the case for economically viable...
In this work, we introduce and study a simple, graph-theoretic model for selfish scheduling among m non-cooperative users over a collection of nmachines; however, each user is restricted to assign its unsplittable load to one from a pair of machines that are allowed for the user. We model these bounded interactions using an interaction graph, whose vertices and edges are the machines and the users,...
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