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A game theoretic approach to promotion design in two-sided platforms

Two-sided platforms often face a high degree of uncertainty in the availability of their service providers, which can harm the profit of the platform as it may result in too many or too few providers available for service. We propose a game-theoretic approach to optimal promotion design as a means by which platforms can influence providers' availability. We consider a mass of service providers in a two-sided market, each can be either active or not. The price paid for a service is decreasing with the number of active providers and increasing with a known demand. A provider participates only if his expected earning, that is the expected price less a fixed percentage held as the commission by the platform, passes his reserved price. There are two types of uncertainties in reserved prices. An idiosyncratic uncertainty which models the variation of reserved prices across providers; And a systematic uncertainty, representing the uncertainty in the overall average reserved price, which also accounts for the uncertainty in the number of active providers. We view the decision making of providers as a global game of strategic substitutes. Focusing on the threshold equilibria of the game, we formulate the optimal promotion design as an infinite dimensional convex optimization problem, where we show that the optimal decreasing promotion program is a combination of a bonus at all prices and a low-price-only bonus.