Taxing Subnetworks

In this work we study weighted network congestion games with player-specific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic. Our main findings are as follows. For routing games on parallel links with linear latency functions, we introduce two new potential functions for unsplittable and for splittable traffic, respectively. We use these functions to derive results on the convergence to pure Nash equilibria and the computation of equilibria. For several generalizations of these routing games, we show that such potential functions do not exist. We prove tight upper and lower bounds on the price of anarchy for games with polynomial latency functions. All our results on the price of anarchy translate to general congestion games.

We study congestion games where players aim to access a set of resources. Each player has a set of possible strategies and each resource has a function associating the latency it incurs to the players using it. Players are non–cooperative and each wishes to follow strategies that minimize her own latency with no regard to the global optimum. Previous work has studied the impact of this selfish behavior to system performance. In this paper, we study the question of how much the performance can be improved if players are forced to pay taxes for using resources. Our objective is to extend the original game so that selfish behavior does not deteriorate performance. We consider atomic congestion games with linear latency functions and present both negative and positive results. Our negative results show that optimal system performance cannot be achieved even in very simple games. On the positive side, we show that there are ways to assign taxes that can improve the performance of linear congestion games by forcing players to follow strategies where the total latency suffered is within a factor of 2 of the minimum possible; this result is shown to be tight. Furthermore, even in cases where in the absence of taxes the system behavior may be very poor, we show that the total disutility of players (latency plus taxes) is not much larger than the optimal total latency. Besides existential results, we show how to compute taxes in time polynomial in the size of the game by solving convex quadratic programs. Similar questions have been extensively studied in the model of non-atomic congestion games. To the best of our knowledge, this is the first study of the efficiency of taxes in atomic congestion games.KeywordsNash EquilibriumCongestion GameIdentical MachinePure Nash EquilibriumConvex Quadratic ProgramThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We investigate the speed of convergence of congestion games with linear latency functions under best response dynamics. Namely, we estimate the social performance achieved after a limited number of rounds, during each of which every player performs one best response move. In particular, we show that the price of anarchy achieved after krounds, defined as the highest possible ratio among the total latency cost, that is the sum of all players latencies, and the minimum possible cost, is $O(\sqrt[2^{k-1}] {n})$, where nis the number of players. For constant values of ksuch a bound asymptotically matches the $\Omega(\sqrt[2^{k-1}] {n}/k)$ lower bound that we determine as a refinement of the one in [7]. As a consequence, we prove that order of loglognrounds are not only necessary, but also sufficient to achieve a constant price of anarchy, i.e. comparable to the one at Nash equilibrium. This result is particularly relevant, as reaching an equilibrium may require a number of rounds exponential in n. We then provide a new lower bound of $\Omega(\sqrt[2^k-1] {n})$ for load balancing games, that is congestion games in which every strategy consists of a single resource, thus showing that a number of rounds proportional to loglognis necessary and sufficient also under such a restriction. Our results thus solve the important left open question of the polynomial speed of convergence of linear congestion games to constant factor solutions.

Stackelberg thresholds in network routing games or the value of altruism

Introduction, 342. — I. Theoretical development, 343; constant cost, 344; decreasing cost, 345; increasing cost, 353. — II. Electric light and power industry, 355. — III. The railroads, 363. — IV. The telephone industry, 369. — V. Conclusion, 371.

We study the inefficiency of equilibrium outcomes in Bottleneck Congestion games. These games model situations in which strategic players compete for a limited number of facilities. Each player allocates his weight to a (feasible) subset of the facilities with the goal to minimize the maximum (weight-dependent) latency that he experiences on any of these facilities. We analyze the (strong) Price of Anarchy of these games for a natural load balancing social cost objective, i.e., minimize the maximum latency of a facility. In our studies, we focus on Bottleneck Congestion games with linear latency functions. These games still constitute a rich class of games and generalize, for example, Load Balancing games with identical or uniformly related machines (with or without restricted assignments). We derive upper and (asymptotically) matching lower bounds on the (strong) Price of Anarchy of these games. We also derive more refined bounds for several special cases of these games, including the cases of identical player weights, identical latency functions and symmetric strategy sets. Further, we provide lower bounds on the Price of Anarchy for k-strong equilibria.

ABSTRACTA dynamic model for marginal cost pricing of port infrastructures links costs to system performance by combining a power-law function with time-dependent queueing analysis. Additionally, the model incorporates the marginal cost of capacity, including the effects of economies of scale. This allows the calculation of the marginal cost price under a dynamic framework. The model accounts for nonlinear behaviour of port demand, which is sensitive to price and service levels. The effects over time of cost and service levels on the port’s operational performance are quantified. The proposed model allows determining the optimal timing for capacity investment. The model is a starting point for the application of marginal cost pricing to ports. However, for practical application of such pricing method it is necessary to apply a system’s approach, as productivity and costs must be assessed at the terminal’s component level. This should allow the derivation of a marginal cost function at the terminal’s component level.

It is by now well known that in an economy with increasing returns, first‐best efficiency may be impossible to attain through an equilibrium concept based on market prices, even if firms are regulated to follow marginal cost pricing. We examine the efficiency issue in a special but important class of economies in which the only source of nonconvexities is the presence of fixed costs. Even in this context, it is possible that none of the equilibria based on marginal cost pricing are efficient (unless additional, strong assumptions are made). We argue that available results on the existence of an efficient two‐part tariff equilibrium rely on very strong assumptions, and we provide a positive result using a weak surplus condition. Our approach can also be used to establish the existence of an efficient marginal cost pricing equilibrium with endogenously chosen lump‐sum taxes if the initial endowment is efficient in the economy without the production technology.

This paper is concerned with the allocation of cost and benefits from regional cooperation, with respect to reuse of municipal effluent for irrigation at the Ramla region of Israel. An efficient regional solution provides the maximal regional income which has to be redistributed among the town and several farms. Different allocations based on marginal cost pricing and schemes from cooperative game theory like the core, Shapley value, generalized Shapley value, and nucleolus are applied. The town and farm A have the main additional gains according to all allocation schemes presented. Advantages and disadvantages of these allocation schemes are examined in order to suggest a fair and acceptable allocation of the regional cooperative gains. Although no method has been preferred, the marginal cost pricing was found to be unacceptable by the participants. The conclusion is that the theory of cooperative games may provide guidelines while comparing the different solutions.

Optimal Conditions of Financing and Pricing for a Public FIRM

It is well known that chargingmarginal cost tolls (MCT) from self interested agents participating in a congestion game leads to optimal system performance, i.e., minimal total latency. However, it is not generally possible to calculate the correct marginal costs tolls precisely, and it is not known what the impact is of charging incorrect tolls. This uncertainty could lead to reluctance to adopt such schemes in practice. This paper studies the impact of charging MCT with some fixed factor error on the system's performance. We prove that under-estimating MCT results in a system performance that is at least as good as that obtained by not applying tolls at all. This result might encourage adoption of MCT schemes with conservative MCT estimations. Furthermore, we prove that no local extrema can exist in the function mapping the error value, r, to the system's performance, $T(r)$. This result implies that accurately calibrating MCT for a given network can be done by identifying an extremum in $T(r)$ which, consequently, must be the global optimum. Experimental results from simulating several large-scale, real-life traffic networks are presented and provide further support for our theoretical findings.

In this paper, an optimal airport-pricing model is derived, both with and without a constraint on the revenues, that includes all relevant external marginal costs. Given the results of the model, the implications on the profit of airports are discussed. It was found that, given that proceeds of the environmental charges are seen as revenue for the airport, it is not obvious that a marginal cost-pricing scheme would result in financial deficits for the airports, despite the reasonable assumption of increasing returns to scale in airport capacity. Using relatively crude estimates of the marginal costs, the current pricing scheme is compared with a marginal cost pricing scheme. Findings show that the effect on revenues of moving towards a marginal cost pricing scheme may not be so dramatic; especially not if the marginal external costs include estimated marginal costs of carbon dioxide emissions.

What did Coase teach in the classroom? Coase’s articles reprinted in The Firm, the Market, and the Law make up 4 of 11 articles assigned in Coase’s 1972 course on “Economic Analysis and Public Policy.” This article reconstructs Coase’s 1972 syllabus, describes Coase as a teacher, reviews the part of his course devoted to the marginal cost controversy, and presents the lessons learned by a student in Coase’s course. Coase taught practical analysis, useful in law, business, and administration to law students. In addition to teaching the important ideas found in The Firm, the Market, and the Law, Coase taught the controversy surrounding marginal cost pricing. He assigned articles which criticized his views severely. His students learned about strongly opposing views and were expected to decide for themselves what they thought. Thus, Coase taught how discourse on public policy should be conducted. His classroom was a model of the “marketplace for ideas.” A close reading of the assigned materials on the marginal cost controversy reveals the connection Coase made between pricing schemes and economic development, revealing Coase’s view that marginal cost pricing would retard growth. Coase wrote about microeconomic policy decisions with an eye on the macroeconomic consequences. Coase taught that theory should not be allowed to stand in the way of progress.

The issues that Bernard and Cairns raise in their paper deal primarily with the importance of using marginal cost pricing to improve efficiency in the consumption of electricity and ultimately in its production. While their policy recommendations have had a long and noble tradition in the economics literature, marginal cost pricing cannot be separated from the question of what is, the appropriate cost of capital for public electric utilities to use to determine the correct mix of generation and transmission investments that will minimize their long run marginal cost. (This abstract was borrowed from another version of this item.)

The author finds that marginal cost pricing leads to slower expansion of capacity than either higher or lower pricing. transport planners are advised how to find the same optimum expansion dates under common forms of user fees as under marginal cost pricing.