Abstract
Real markets evolve over time. They often exhibit complex behaviors, such as auto-correlation, continuity, and non-stationarity. How do these behaviors affect channel contracting? We study the problem in a bilateral channel where the retailer has private information on evolving market conditions. We characterize the optimal contract under arbitrary market evolution. The central notion is market inertia: it prices retailer's information advantage, dictates price and quantity response over time, and determines the contract complexity. Using market inertia, we identify a general property - stochastic linearity - that justifies the use of simple contracts for a much larger class of channel conditions. For practitioners, we offer refined guidance: (i) when the market has linear dynamics, simple contracts are sufficient; (ii) when the market is continuous, the quantity distortion should be pervasive; (iii) when the market is non-stationary, the distortion can vanish, intensify, stay constant, or even go non-monotonic over time. By highlighting the central role of realistic market behaviors, this paper advances our understanding of channel theory and practice.
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