Price discrimination through communication - Itai Sher; Rakesh Vohra (Theoretical Economics, 2015)
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: C78; D82; D83; 330; Price discrimination; communication; bargaining; commitment; evidence; network flows