Call a Vickrey-Clarke-Groves (VCG) mechanism to assign p identical objects among n agents, feasible if cash transfers yield no deficit. The efficiency loss of such a mechanism is the worst (largest) ratio of the budget surplus to the efficient surplus, over all profiles of non negative valuations. The optimal (smallest) efficiency loss � L(n, p) satisfies is strictly smaller or strictly �L(n, p) ≤ �L(n, { n 4

In the traffic assignment problem, commuters select the shortest available path to travel from their origins to their destinations. This system has been studied for over 50 years since Wardrop’s seminal work (1952). Motivated by freight companies, we study a generalization of the traffic assignment problem in which competitors, who may control a non-negligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which some of the freight companies have market power. Other applications include intelligent transportation systems, competition of telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully-efficient solution from the system’s point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency, which depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino (1991), we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, all Nash equilibria of an

We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we construct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.

Users share an increasing marginal cost technology. A cost sharing method charges non negative cost shares covering costs. We look at the worst surplus (relative to the efficient surplus) in a Nash equilibrium of the demand game, where the minimum is taken over all convex preferences quasi-linear in cost shares. We compare average cost pricing and serial cost sharing, two budget-balanced methods, and incremental cost sharing, a method collecting a budget surplus, that we count as a welfare loss. For any convex cost function, the average cost and serial methods guarantee a (relative) surplus no less than 1,wherenis the number of n users. For some cost functions incremental cost sharing guarantees no positive gain. With quadratic costs, the surplus guaranteed by serial cost sharing is θ ( 1

Computational grids offer users a simple access to tremendous computer resources for solving large scale computing problems. Traditional performance analysis of scheduling algorithms considers overall system performance while fairness analysis focuses on the individual performance each user receives. Until recently, only few grids and cluster systems provided preemptive migration (e.g. [2]), which is the ability of dynamically moving computational tasks across machines during runtime. The emergent technology of virtualization (e.g. [4]) provides off-the-shelf support for migration, thus making the use of this feature more accessible (even across different OS’s). In this paper, we study the close relation between migration and fairness. We present fairness and quality of service properties for economic online scheduling algorithms. Under mild assumptions we show that it is impossible to achieve these properties without the use of migration. On the other hand, if zero cost migration is used, then these properties can be satisfied.

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Abstract—This paper presents a theoretic framework of optimal resource allocation and admission control for peer-topeer networks. Peer’s behavioral rankings are incorporated into the resource allocation and admission control to provide differentiated services and even to block peers with bad rankings. These peers may be free-riders or suspicious attackers. A peer improves her ranking by contributing resources to the P2P system or deteriorates her ranking by consuming services. Therefore, the ranking-based resource allocation provides necessary incentives for peers to contribute their resources to the P2P systems. We define a utility function which captures the best wish for the source peer to serve competing peers, who request services from the source peer. Although the utility function is convex, Harsanyi-type social welfare functions are devised to obtain a unique optimal resource allocation that achieves maxmin fairness. The parameters used in our model can be derived from the nature of the services or chosen by the source peer. No private information is required to reveal from individual peers. This prevents selfish peers to play the system strategically and cheat the resource allocation mechanism for their own benefits. The resource allocation and admission control are fully distributed and linearly scalable. I.

While efficiency of mechanisms for control of communication networks has been extensively investigated, little attention has been paid to the critical metric of revenue generation. In this paper, we pursue such an investigation within a class of allocation schemes with the minimal signaling and computation costs necessary in communication network domains. We show that, within this space, linear cost rules for proportional allocation mechanisms are optimal for symmetric agent populations and reserving a portion of the resource can increase revenue even though less of the resource is being sold. While nonlinear cost functions can be better for asymmetric populations, intelligent agents can undermine this via signal splitting. We show how a resource can counter this phenomenon by declaring a linear cost. Most current approaches to control of communication networks incorporate economic models to deal with the decentralization necessitated by the domain. Ideas such as “smart markets ” where packets bid for service [3] and proportionally fair pricing [2] promoted market-based control to induce efficient use of network resources. While the success of various schemes at achieving efficiency has been studied extensively [1,5,7,8], little attention has been paid to revenue generation as a performance metric. Clearly, for many network resource owners, revenue generation is a critical motivation as illustrated by the emergence of bandwidth auctions and exchanges. In this paper, we investigate various aspects of revenue generation through analysis of a class of mechanisms with minimal signaling and computational costs for the resource, which is vital in communication network settings and obtain several key results. We show that for symmetric populations of buyers (e.g. band-

Motivated by market design for electric power systems, we consider a model where a finite number of producers compete to meet an infinitely divisible but inelastic demand for the product. Each firm is characterized by a production cost that is convex in the output produced, and firms act as profit maximizers. We consider a uniform price market design that uses supply function bidding [22]: firms declare the amount they would supply at any positive price, and a single price is chosen to clear the market. We are interested in evaluating the impact of price anticipating behavior both on the allocative efficiency of the market, and on the prices seen at equilibrium. We show that by restricting the strategy space of the firms to parameterized supply functions, we can provide upper bounds on both the inflation of aggregate cost at the Nash equilibrium relative to the socially optimal level, as well as the markup of the Nash equilibrium price above the competitive level: as long as N> 2 firms are competing, these quantities are both upper bounded by 1 + 1/(N − 2). This result holds even in the presence of asymmetric cost structure across firms. We also discuss several extensions, generalizations, and related issues. 1