Bilateral trading in divisible double auctions

Existing models of divisible double auctions typically require three or more traders-when there are two traders, the usual linear equilibria imply market breakdowns unless the traders' values are negatively correlated. This paper characterizes a family of nonlinear ex post equilibria in a divisible double auction with only two traders, who have interdependent values and submit demand schedules. The equilibrium trading volume is positive but less than the first best. Closed-form solutions are obtained in special cases. Moreover, no nonlinear ex post equilibria exist if: (i) there are n≥4 symmetric traders or (ii) there are 3 symmetric traders with pure private values. Overall, our nonlinear equilibria fill the “n=2” gap in the divisible-auction literature and could be a building block for analyzing strategic bilateral trading in decentralized markets.