/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

We consider abstract exchange mechanisms wherein individuals submit "diversified" offers in m commodities, which are then redistributed to them. Our first result is that if the mechanism satisfies certain natural conditions embodying "fairness" and "convenience" then it admits unique prices, in the sense of consistent exchange-rates across commodity pairs ij that equalize the valuation of offers and returns for each individual.We next define certain integers tau_{ij}, pi_{ij}, and k_{i} which represent the "time" required to exchange i for j, the "difficulty" in determining the exchange ratio, and the "dimension" of the offer space in i; we refer to these as time-, price- and message-complexity of the mechanism. Our second result is that there are only a finite number of minimally complex mechanisms, which moreover correspond to certain directed graphs G in a precise sense. The edges of G can be regarded as markets for commodity pairs, and prices play a stronger role in that the return to a trader depends only on his own offer and the prices.Finally we consider "strongly" minimal mechanisms, with smallest "worst case" complexities tau = max tau_{ij} and pi = max pi_{ij}. Our third main result is that for m > 3 commodities that there are precisely three such mechanisms, which correspond to the star, cycle, and complete graphs, and have complexities (pi,tau) = (4,2), (2,m - 1), (m^{2} - m, 1) respectively. Unlike the other two mechanisms, the star mechanism has a distinguished commodity -- the money -- that serves as the sole medium of exchange. As m approaches infinity it is the only mechanism with bounded (pi,tau).

/pdf/minimally-complex-exchange-mechanisms-emergence-of-prices-22cw2b0w8s.pdf

Minimally Complex Exchange Mechanisms: Emergence of Prices, Markets, and Money

We build a model of competitive pooling, which incorporates adverse selection and signalling into general equilibrium. Pools are characterized by their quantity limits on contributions. Households signal their reliability by choosing which pool to join. In equilibrium, pools with lower quantity limits sell for a higher price, even though each household's deliveries are the same at all pools. The Rothschild-Stiglitz model of insurance is included as a special case. We show that by recasting their hybrid oligopolistic-competitive story into our perfectly competitive framework, their separating equilibrium always exists (even when they say it doesn't) and is unique.

Competitive Pooling: Rothschild-Stiglitz Reconsidered

We consider a principal who is keen to induce his agents to work at their maximal effort levels. To this end, he samples n days at random out of the T days on which they work, and awards a prize of B dollars to the most productive agent. The principal's policy (B,n) induces a strategic game Gamma(B,n) between the agents. We show that to implement maximal effort levels weakly (or, strongly) as a strategic equilibrium (or, as dominant strategies) in Gamma(B,n), at the least cost B to himself, the principal must choose a small sample size n. Thus less scrutiny by the principal induces more effort from the agents. The need for reduced scrutiny becomes more pronounced when agents have information of the history of past plays in the game. There is an inverse relation between information and optimal sample size. As agents acquire more information (about each other), the principal -- so to speak -- must "undo" this by reducing his information (about them) and choosing the sample size n even smaller.

Competitive Prizes: When Less Scrutiny Induces More Effort

We show that if limit orders are required to vary smoothly, then strategic (Nash) equilibria of the double auction mechanism yield competitive (Walras) allocations. It is not necessary to have competitors on any side of any market: smooth trading is a substitute for price wars. In particular, Nash equilibria are Walrasian even in a bilateral monopoly.

/pdf/perfect-competition-in-a-bilateral-monopoly-265v46x1it.pdf

Perfect Competition in a Bilateral Monopoly

Status is greatly valued in the real world, yet it has not received much attention from economic theorists. We examine how the owner of a firm can best combine money and status together to get his employees to work hard for the least total cost. We find that he should motivate workers of low skill mostly by status and high skill mostly by money. Moreover, he should do so by using a small number of titles and wage levels. This often results in star wages to the elite performers.

/pdf/games-with-money-and-status-how-best-to-incentivize-work-36v8o641w3.pdf

Pradeep Dubey

Papers

Minimally Complex Exchange Mechanisms: Emergence of Prices, Markets, and Money

Competitive Pooling: Rothschild-Stiglitz Reconsidered

Competitive Prizes: When Less Scrutiny Induces More Effort

Perfect Competition in a Bilateral Monopoly

Games with Money and Status: How Best to Incentivize Work