Decentralized Trading, Strategic Behaviour and the Walrasian Outcome

For a market with a finite number of agents, pairwise matching and bargaining, it is shown that, even when the market is frictionless, the equilibrium is not necessarily competitive. It depends on the amount of information agents use. If their behaviour is conditioned only on the sets of agents present and the time, the competitive solution is the unique subgame perfect equilibrium. If agents have full information and condition their behaviour on some of it, there are also noncompetitive equilibria in which behaviour depends on specific information such as the identity of the trading partner and past events.