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Pseudo-Competitive Games and Algorithmic Pricing
Chamsi Hssaine · Vijay Kamble · Siddhartha Banerjee

We study a new game of price competition amongst firms selling identical goods, whose defining property is that the revenue of a firm at a price is independent of any competing prices that are strictly lower. This game is motivated by a variety of customer choice models that induce this property, prominently those stemming from the well-known satisficing heuristic for decision-making. Under a mild condition, we show that every pure-strategy local Nash equilibrium in this game corresponds to a set of prices generated by the firms sequentially setting local best-response prices in a fixed order. In other words, despite being simultaneous-move games, equilibria have a sequential-move equilibrium structure. We thus call these games pseudo-competitive games. We find that these games are often plagued by strictly-local Nash equilibria, in which the price of a firm is only a local best-response to the competitor's price, when a globally optimal response with a potentially unboundedly higher payoff is available. We show that price dynamics resulting from the firms utilizing gradient-based pricing algorithms may often converge to such undesirable outcomes. We propose a new online learning approach to address this concern under certain regularity assumptions on the revenue curves.

Author Information

Chamsi Hssaine (Cornell University)
Vijay Kamble (University of Illinois, Chicago)
Siddhartha Banerjee (Cornell University)

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