20 | January | 2016 | A MAN OF ACTION

This morning I had a discussion with A, mainly on the pooling equilibrium.

The basic model is as follows. The supplier S has two distribution channels: direct sell to the end consumers, and through a retailer R. The retailer is more efficient in retail operations with less retail cost. However, the retail channel suffers efficiency loss due to double marginalization (DM) (we assume that the channel is managed by the wholesale price contract). In addition, the supplier’s type of retail cost $c_i$ is his private information, high or low. The consumer demand is linear. Both parties are risk-neutral and profit maximizing.

We frame the problem as a signaling game. First, S learns his type $c_i$ and sets wholesale price $w(c_i)$ . Second, R orders quantity $q_R$ . Finally, S delivers $q_R$ and sells $q_S$ directly to the market. Hence the market clearing price is $P= a - b(q_R+ q_S)$ . The payoffs for R and S are
$(P-w)q_R$ and $Pq_S + c_i(q_S + q_R)$ , respectively.