Perfectly competitive bilateral exchange without discounting

In a random-matching economy of traders who maximize cumulative consumption (overtaking criterion), the stationary, Markov, Bayesian-perfect equilibrium is studied. At such equilibrium, two results hold: (1) perfect substitutability between current and future consumption implies a no-surplus condition; and (2) by the no-surplus condition, there is a nominal price at which all trades must occur. These results strengthen the seminal results of regarding monetary bilateral exchange in two ways: the incentive compatibility of the equilibrium trading pattern is established and a less roundabout trading pattern enhances welfare by enabling consumption to occur more frequently.