We are indebted to many people for their encouragement and advice in undertaking this project. Above all, however, we must thank the editor of this journal, whose practical and scientifc judgment kept us on track through what turned out to be a long and at times difficult task. In addition, we must thank William Baumol, Gerald Faulhaber, Michael Intriligator, George Lee, Stephen Littlechild, Fritz Machlup, Thomas Marschak, Herve Moulin, Andrew Postlewaite, Juan Eugenio de la Rama, Robert Rosenthal, David Schmeidler, Anne Schotter, and Martin Shubik, all of whom have read the manuscript either in part or in whole and have given us extremely useful scientific and editorial advice. Professor Schotter's participation in the project was made possible by a grant from the Office of Naval Research Contract No. N00014-78-C-0598, whose support is gratefully acknowledged. All errors in the work that follows are those of the authors alone.

Economics and the Theory of Games: A Survey

In revenue management research and practice, demand models are used that describe how demand for a seller's products depends on the decisions, such as prices, of that seller. Even in settings where the demand for a seller's products also depends on decisions of other sellers, the models often do not explicitly account for such decisions. It has been conjectured in the revenue management literature that such monopoly models may incorporate the effects of competition, because the parameter estimates of the monopoly models are based on data collected in the presence of competition. In this paper we take a closer look at such a setting to investigate the behavior of parameter estimates and decisions if monopoly models are used in the presence of competition. We consider repeated pricing games in which two competing sellers use mathematical models to choose the prices of their products. Over the sequence of games, each seller attempts to estimate the values of the parameters of a demand model that expresses demand as a function only of its own price using data comprised only of its own past prices and demand realizations. We analyze the behavior of the sellers' parameter estimates and prices under various assumptions regarding the sellers' knowledge and estimation procedures, and we identify situations in which a the sellers' prices converge to the Nash equilibrium associated with knowledge of the correct demand model, b the sellers' prices converge to the cooperative solution, and c the sellers' prices have many potential limit points that are neither the Nash equilibrium nor the cooperative solution and that depend on the initial conditions. We compare the sellers' revenues at potential limit prices with their revenues at the Nash equilibrium and the cooperative solution, and we show that it is possible for sellers to be better off when using a monopoly model than at the Nash equilibrium.

Learning and Pricing with Models That Do Not Explicitly Incorporate Competition

Learning is investigated using experimental methods. Agents have no information about demand conditions. The same oligopoly market is finitely repeated, and the only link between successive markets is that agents acquire experience over time as the game is played. Adaptive as well as least squares learning are tested. The model of price adjustment followed by firms indicates that the non-cooperative Bertrand–Nash equilibrium constitutes an attractor to players' strategies.

Oligopoly experimentation of learning with simulated markets

https://pure.uva.nl/ws/files/8077646/119331_390015.pdf

Learning Cycles in Bertrand Competition with Differentiated Commodities and Competing Learning Rules

In this paper we study a model of a quantity-setting duopoly market where firms lack knowledge of the market demand. Using a misspecified demand function firms determine their profit-maximizing choices of their corresponding perceived market game. For illustrative purposes we assume that the (true) demand function is linear and that the reaction functions of the players are quadratic. We then investigate the global dynamics of this game and characterize the number of steady states and their welfare properties. We study the basins of attraction of these steady states and present situations in which global bifurcations of their basins occur when model parameters are varied. The economic significance of our result is to show that in situations where players choose their actions based on a misspecified model of the environment, additional self-confirming steady states may emerge, despite the fact that the Nash-equilibrium of the game under perfect knowledge is unique. As a consequence the long run outcome of the game and overall welfare is highly dependent upon initial conditions.

/pdf/the-long-run-outcomes-and-global-dynamics-of-a-duopoly-game-2o7yi13z0k.pdf

D. J. Wilson

Papers

A Convergent Adjustment Process for Firms in Competition

Convergence of a market related game strategy