Pseudo-Competitive Games and Algorithmic Price Competition

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 undesirable outcomes. We finally propose an algorithmic approach that incorporates global experimentation to address this concern under certain regularity assumptions on the revenue curves.

Bio: Chamsi Hssaine is a final-year Ph.D. student in the School of Operations Research and Information Engineering at Cornell University, where she is advised by Professor Sid Banerjee. She graduated from Princeton University in 2016, with a B.S. in Operations Research and Financial Engineering and a minor in Applied and Computational Mathematics. Her research interests lie broadly in algorithm and incentive design for large-scale e-commerce marketplaces, with a focus on integrated mobility marketplaces. She was selected for the 2020 Rising Stars in EECS workshop at UC Berkeley, as well as the 2020 Rising Scholars conference at the Stanford Graduate School of Business.