Quantal response equilibria for models of price competition

Lopez Acevedo, Gladys Cristina, Department of Economics, University of Virginia
Holt, Charles, Department of Economics, University of Virginia
Anderson, Simon, Department of Economics, University of Virginia

There is a growing body of data from game theory and industrial organization experiments that reveals systematic deviations from Nash equilibrium behavior. In this thesis, the perfectly rational decision-making embodied in Nash equilibrium is generalized to allow for endogenously determined decision errors. Firms choose among strategies based on their expected payoffs, but make decision errors based on a probabilistic or quantal choice model. Such errors may either be due to mistakes or to unobserved random variations in payoff functions. For a given error distribution a quantal response equilibrium is a fixed point in choice probabilities. Closed-form solutions for equilibrium price distributions with endogenous errors are derived for models of price competition. Numerical methods are used to examine more complex market models. This thesis establishes differences in the qualitative properties of Nash and quantal response equilibria in models of price competition.

This thesis consists of two parts. In the first part, chapters 3 and 4, a parametric class of quantal response functions is derived from a model of multiplicative random errors. This "power function" decision rule is used to derive the equilibrium price distribution with endogenous errors in a simple model of price competition. The power-function quantal response equilibrium is appealing since it thereby accounts for systematic deviations from the Bertrand-Nash equilibrium.

The second part of this thesis, chapters 5 and 6, applies the quantal response equilibrium to a series of increasingly complex models, with step-function demand and supply structures, of the type used in market experiments. In some of these models, the price distribution in a quantal response equilibrium is affected by changes in structural variables although the Nash equilibrium remains unaltered. It is also shown that the quantal response equilibrium stochastically dominates the Nash equilibrium in mixedstrategies in a model with market power and increasing costs. The Nash and quantal response equilibria differ in a model with market power and constant costs. In other models, however, it is shown that the Nash and quantal response equilibria are identical. This is the case in a (first-price) all-pay auction presented in chapter 6.

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PHD (Doctor of Philosophy)
quantal response, Nash equilibrium

Digitization of this thesis was made possible by a generous grant from the Jefferson Trust, 2015.

Thesis originally deposited on 2016-02-18 in version 1.28 of Libra. This thesis was migrated to Libra2 on 2017-03-23 16:33:28.

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