In a duopoly with lotteries, a Stackelberg leader offering one lottery guarantees 1/4 of monopoly revenue for regular distributions, and in the worst case no leader can guarantee more than 1/e.
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abstract
We study scenarios where multiple sellers of a homogeneous good compete on prices, where each seller can only sell to some subset of the buyers. Crucially, sellers cannot price-discriminate between buyers. We model the structure of the competition by a graph (or hyper-graph), with nodes representing the sellers and edges representing populations of buyers. We study equilibria in the game between the sellers, prove that they always exist, and present various structural, quantitative, and computational results about them. We also analyze the equilibria completely for a few cases. Many questions are left open.
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Approximately Optimal Mechanism Design for Competing Sellers
In a duopoly with lotteries, a Stackelberg leader offering one lottery guarantees 1/4 of monopoly revenue for regular distributions, and in the worst case no leader can guarantee more than 1/e.