/pdf/the-theory-of-industrial-organization-19bejph0ej.pdf

The Theory of Industrial Organization

We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times---the total latency---is minimized.In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a "selfishly motivated" assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance.In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total latency of the routes chosen by unregulated selfish network users may be arbitrarily larger than the minimum possible total latency; however, we prove that it is no more than the total latency incurred by optimally routing twice as much traffic.

/pdf/how-bad-is-selfish-routing-g644vu88rg.pdf

How bad is selfish routing

Information, trade and common knowledge

A major challenge in the operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With the increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash (1951) equilibrium that is inefficient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e., to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system.

/pdf/efficient-power-control-via-pricing-in-wireless-data-34gk0jwxel.pdf

Efficient power control via pricing in wireless data networks

The History of Economic Analysis

The Banzhaf index of power in a voting situation depends on the number of ways in which each voter can effect a “swing” in the outcome. It is comparable—but not actually equivalent—to the better-known Shapley-Shubik index, which depends on the number of alignments or “orders of support” in which each voter is pivotal. This paper investigates some properties of the Banzhaf index, the main topics being its derivation from axioms and its behavior in weighted-voting models when the number of small voters tends to infinity. These matters have previously been studied from the Shapley-Shubik viewpoint, but the present work reveals some striking differences between the two indices. The paper also attempts to promote better communication and less duplication of mathematical effort by identifying and describing several other theories, formally equivalent to Banzhaf’s, that are found in fields ranging from sociology to electrical engineering. An extensive bibliography is provided.

Mathematical Properties of the Banzhaf Power Index

Introduction The study of methods for measuring the “value” of playing a particular role in an n -person game is motivated by several considerations One is to determine an equitable distribution of the wealth available to the players through their participation in the game Another is to help an individual assess his prospects from participation in the game When a method of valuation is used to determine equitable distributions, a natural defining property is “efficiency”: The sum of the individual values should equal the total payoff achieved through the cooperation of all the players However, when the players of a game individually assess their positions in the game, there is no reason to suppose that these assessments (which may depend on subjective or private information) will be jointly efficient This chapter presents an axiomatic development of values for games involving a fixed finite set of players We primarily seek methods for evaluating the prospects of individual players, and our results center around the class of “probabilistic” values (defined in the next section) In the process of obtaining our results, we examine the role played by each of the Shapley axioms in restricting the set of value functions under consideration, and we trace in detail (with occasional excursions) the logical path leading to the Shapley value

/pdf/probabilistic-values-for-games-1yktsj00bh.pdf

Probabilistic Values for Games

We extend the standard model of general equilibrium with incomplete markets to allow for default and punishment by thinking of assets as pools. The equilibrating variables include expected delivery rates, along with the usual prices of assets and commodities. By reinterpreting the variables, our model encompasses a broad range of adverse selection and signalling phenomena in a perfectly competitive, general equilibrium framework. Perfect competition eliminates the need for lenders to compute how the size of their loan or the price they quote might affect default rates. It also makes for a simple equilibrium refinement, which we propose in order to rule out irrational pessimism about deliveries of untraded assets. We show that refined equilibrium always exists in our model, and that default, in conjunction with refinement, opens the door to a theory of endogenous assets. The market chooses the promises, default penalties, and quantity constraints of actively traded assets.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID274514_code010621530.pdf?abstractid=274514&mirid=3

Default and Punishment in General Equilibrium

It is shown that Nash Equilibria of smooth games generally tend to be inefficient in the Pareto sense.

/pdf/inefficiency-of-nash-equilibria-3dk4hjoqol.pdf

Inefficiency of Nash Equilibria

L.S. Shapley [1953] showed that there is a unique value defined on the classD of all superadditive cooperative games in characteristic function form (over a finite player setN) which satisfies certain intuitively plausible axioms. Moreover, he raised the question whether an axiomatic foundation could be obtained for a value (not necessarily theShapley value) in the context of the subclassC (respectivelyC′, C″) of simple (respectively simple monotonic, simple superadditive) gamesalone. This paper shows that it is possible to do this. Theorem I gives a new simple proof ofShapley's theorem for the classG ofall games (not necessarily superadditive) overN. The proof contains a procedure for showing that the axioms also uniquely specify theShapley value when they are restricted to certain subclasses ofG, e.g.,C. In addition it provides insight intoShapley's theorem forD itself. Restricted toC′ orC″, Shapley's axioms donot specify a unique value. However it is shown in theorem II that, with a reasonable variant of one of his axioms, a unique value is obtained and, fortunately, it is just theShapley value again.

Pradeep Dubey

Papers

Mathematical Properties of the Banzhaf Power Index

Probabilistic Values for Games

Default and Punishment in General Equilibrium

Inefficiency of Nash Equilibria

On the Uniqueness of the Shapley Value