Pseudo-Competitive Games and Algorithmic Pricing

68 Pages Posted: 21 Sep 2021 Last revised: 29 Sep 2021

See all articles by Chamsi Hssaine

Chamsi Hssaine

Cornell University - School of Operations Research and Information Engineering

Vijay Kamble

University of Illinois at Chicago - Department of Information and Decision Sciences

Siddhartha Banerjee

Cornell University - School of Operations Research and Information Engineering

Date Written: September 2, 2021

Abstract

We study a game of price competition amongst firms selling homogeneous goods defined by the property that a firm's revenue is independent of any competing prices that are strictly lower. This property is induced by any customer choice model involving utility-maximizing choice from an adaptively determined consideration set, encompassing a variety of empirically validated choice models studied in the literature.

For these games, we show a one-to-one correspondence between pure-strategy local Nash equilibria with distinct prices and the prices generated by the firms sequentially setting local best-response prices in different orders. In other words, despite being simultaneous-move games, they have a sequential-move equilibrium structure. Although this structure is attractive from a computational standpoint, we find that it makes these games particularly vulnerable to the existence of strictly-local Nash equilibria, in which the price of a firm is only a local best-response to competitors' prices when a globally optimal response with a potentially unboundedly higher payoff is available. Our results thus suggest that strictly-local Nash equilibria may be more prevalent in competitive settings than anticipated. We moreover show, both theoretically and empirically, that price dynamics resulting from the firms utilizing gradient-based dynamic pricing algorithms to respond to competition may often converge to such an undesirable outcome. We finally propose an algorithmic approach that incorporates global experimentation to address this concern under certain regularity assumptions on the revenue curves.

Keywords: price competition, algorithmic pricing, learning in games

Suggested Citation

Hssaine, Chamsi and Kamble, Vijay and Banerjee, Siddhartha, Pseudo-Competitive Games and Algorithmic Pricing (September 2, 2021). Available at SSRN: https://ssrn.com/abstract=3925242 or http://dx.doi.org/10.2139/ssrn.3925242

Chamsi Hssaine (Contact Author)

Cornell University - School of Operations Research and Information Engineering ( email )

Ithaca, NY 14853
United States

Vijay Kamble

University of Illinois at Chicago - Department of Information and Decision Sciences ( email )

Chicago, IL 60607-7124
United States

Siddhartha Banerjee

Cornell University - School of Operations Research and Information Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

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