A major challenge in 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 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 non-cooperative power control game where users maximize their utility. The outcome of the game results in a Nash equilibrium that is ine#cient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the non-cooperative 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.

This paper analyzes a class of games of incomplete information where each agent has

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We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoffs. Specifically, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs. We show that these conditions are satisfied by a number of games of economic importance, and discuss the implications of these …ndings for the evolutionary theory of preference formation and the theory of Cournot competition.

In the past few decades multi-store retailers, especially those with a hundred or more stores, have experienced substantial growth. At the same time, there is widely reported public outcry over the impact of these chain stores on small retailers and local communities. This paper develops an empirical model to assess the impact of chain stores on the profitability and entry/exit decisions of small discount retailers and to quantify the size of the scale economies within a chain. The model has two key features. First, it allows for flexible competition patterns among all players. Second, for chains, it incorporates the scale economies that arise from operating multiple stores in nearby regions. In doing so, the model relaxes the commonly used assumption that entry in different markets is independent. The estimation exploits a unique data set that covers the discount retail industry from 1988 to 1997 and yields interesting results. First, Wal-Mart’s expansion from the late 1980s to the late 1990s explains about fifty to seventy percent of the net change in the number of small discount retailers. Failure to address the endogeneity of the firms ’ entry decisions would result in underestimating this impact by fifty to sixty percent. Second, scale economies were important for both Kmart and Wal-Mart, but the magnitude did not grow proportionately with the chains ’ sizes. Finally, direct government subsidies to either chains or small retailers are unlikely to be cost effective in increasing the number of firms or the level of employment.

We present a model of labor markets that accounts for the social network through which agents hear about jobs. We show that an improvement in the wage or employment status of either an agent's direct or indirect contacts leads to an increase in the agent's employment probability and expected wages, in the sense of first order stochastic dominance. A similar effect results from an increase in the network contacts of an agent. In terms of dynamics and patterns, we show that both wages and employment are positively associated (a strong form of correlation) across time and agents. We also analyze the decisions of agents regarding staying in the labor market or dropping out. If there are costs to staying in the labor market, and we compare two networks of agents that are identical except that one group starts with a worse wage status, then that group's drop-out rate will be higher than the other's and there will be a persistent di#erence in wages between the groups.

This paper develops necessary and sufficient conditions for monotone comparative statics predictions in several classes of stochastic optimization problems. The results are formulated so as to highlight the tradeoffs between assumptions about payoff functions and assumptions about probability distributions; they characterize “minimal sufficient conditions” on a pair of functions (for example, a utility function and a probability distribution) so that the expected utility satisfies necessary and sufficient conditions for comparative statics predictions. The paper considers two main classes of assumptions on primitives: single crossing properties and log-supermodularity. Single crossing properties arise naturally in portfolio investment problems and auction games. Logsupermodularity is closely related to several commonly studied economic properties, including decreasing absolute risk aversion, affiliation of random variables, and the monotone likelihood ratio property. The results are used to extend the existing literature on investment problems and games of incomplete information, including auction games and pricing games.

The goal of this paper is to study pricing of differentiated services and its impact on the choice of service priority at equilibrium. We consider both TCP connections as well as non controlled (real time) connections. The performance measures (such as throughput and loss rates) are determined according to the operational parameters of a RED buffer management. The latter is assumed to be able to give differentiated services to the applications according to their choice of service class. We consider a best effort type of service differentiation where the QoS of connections is not guaranteed, but by choosing a better (more expensive) service class, the QoS parameters of a session can improve (as long as the service class of other sessions are fixed). The choice of a service class of an application will depend both on the utility as well as on the cost it has to pay. We first study the performance of the system as a function of the connections' parameters and their choice of service classes. We then study the decision problem of how to choose the service classes. We model the problem as a noncooperative game. We establish conditions for an equilibrium to exist and to be uniquely defined. We further provide conditions for convergence to equilibrium from non equilibria initial states. We finally study the pricing problem of how to choose prices so that the resulting equilibrium would maximize the network benefit. Keywords: TCP, Buffer Management, RED/AQM, Nash equilibrium, Pricing, Mathematical programming /optimization, Economics I.

This paper formalizes the relation between comparative statics and the out-of-equilibrium explanation for how a system evolves after a change in parameters. The paper has two main results. First, an increase in an exogenous parameter sets o# learning dynamics that involve larger values of the endogenous variables. Second, equilibrium selections that are not monotone increasing in the exogenous variables must be predicting unstable equilibria. Moreover, under some conditions monotone comparative statics and stability are equivalent. JEL Classification: C61, C62, C72, C73 Keywords: Monotone comparative statics, supermodularity, strategic complements, learning, correspondence principle. # Discussions with Ilya Segal and Chris Shannon were very important for this work, I am very grateful for all their help. For comments and advice, I also thank Robert Anderson, Juan Dubra, Nestor Gandelman, Ernesto Lopez Cordova, Marcelo Moreira, Charles Pugh, Matthew Rabin, Tarun Sabarwal and Miguel Villa...

This paper studies the competitive and cooperative selection of inventory policies in a two-echelon supply chain with one supplier and N retailers. Stochastic demand is monitored continuously. Retailers incur inventory holding and backorder penalty costs. The supplier incurs holding costs for its inventory and backorder penalty costs for backorders at the retailers. The latter cost reflects the supplier’s desire to maintain adequate availability of its product to consumers. Previous research finds the supply chain cost minimizing reorder point policies, the cooperative solution. The competitive solution is a Nash equilibrium, a set of reorder points such that no firm can deviate from the equilibrium and lower its cost. It is shown that Nash equilibria exist and a method is presented to find all of them. In some settings the cooperative solution is a Nash equilibrium; competition does not necessarily lead to supply chain inefficiency. In other settings, competition leads to costs that are substantially higher than optimal. Usually (but not always), the competitive supply chain carries too little inventory. Three cooperation strategies are discussed: change incentives, change equilibrium, and change control. A set of contracts is provided that changes the firms ’ incentives so that the optimal policy is a Nash equilibrium. An equilibrium change can improve performance but does not guarantee optimal performance. To change control, the firms let the supplier choose all reorder points, a key component in vendor managed inventory. That change leads to optimal supply chain performance. 1.