Theoretical Economics 10 (2015), 597–648
Price discrimination through communication
Itai Sher, Rajiv Vohra
We study a seller's optimal mechanism for maximizing revenue when a buyer may present evidence relevant to her value. We show that a condition very close to transparency of buyer segments is necessary and sufficient for the optimal mechanism to be deterministic--hence akin to classic third degree price discrimination--independently of non-evidence characteristics. We also find another sufficient condition depending on both evidence and valuations, whose content is that evidence is hierarchical. When these conditions are violated, the optimal mechanism contains a mixture of second and third degree price discrimination, where the former is implemented via sale of lotteries. We interpret such randomization in terms of the probability of negotiation breakdown in a bargaining protocol whose sequential equilibrium implements the optimal mechanism.
Keywords: Price discrimination, communication, bargaining, commitment, evidence, network flows
JEL classification: C78, D82, D83
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