Intermediation with Costly Bilateral Exchange

This paper was motivated in part by questions of optimal regulation of financial institutions such as intermediaries. It is believed that an analysis of such questions should take place in a model in which financial institutions emerge endogenously as the choice of agents of the model. Yet there appear to be few models which explain institutions in this way. The absence of such models is due in part to the acceptance of what are often thought of as necessary conditions for tractable mathematical analysis. In particular, speaking rather loosely, the technologies of production and exchange are usually assumed to be convex. This is true of the standard competitive model as described for example in ArrowHahn (1971). It is also true of recent attempts to obtain a theory of more limited exchange as in Foley (1970), Hahn (1971) and Kurz (1974). In these analyses convexity is used in establishing the continuity of choice functions upon which standard fixed point theorems rely. Yet, to repeat, convexity prevents the models from explaining specialization. There have been several attempts to weaken the convexity assumptions. In Starr (1969) and in Arrow-Hahn (1971) non-convex sets are replaced by their convex hulls, standard existence theorems are applied to the convexified economy, and the excess demands of the resulting social-approximate equilibrium are then shown to have limit zero as the number of agents is increased. The thrust of this work is that the competitive equilibrium is a good approximation for non-convex economies with a large number of agents. This approach has been modified somewhat by Heller (1972) and by Heller and Starr (forthcoming) to allow for various strong non-convexities associated with set-up costs and to explain the use of money. This paper proposes a simple theory of intermediation and, in contrast to the literature described above, circumvents the difficulties associated with non-convex technologies by a game theoretic approach. A model is described in which exchange is motivated by risksharing considerations. But exchange is also resource using; for each bilateral deal there is a fixed cost. This creates the non-convexity.' Then, having specified the set of agents, their preferences and the technology available to them, core allocations are characterized. As noted by Shapley and Shubik (1966), core allocations are in some sense socially stable; one might expect to observe institutions and exchange arrangements which support such allocations.2 Indeed, a non-cooperative game is proposed for the model, and it is shown that the equilibrium allocations of the game are equivalent to core allocations. In this non-cooperative game agents announce strategies under which they are willing to act as intermediaries, buying shares in investment projects and selling shares in the resulting portfolio. In an equilibrium only a subset of agents act as intermediaries, and in this sense the model may be said to explain specialization. These intermediaries emerge endogenously because they are able to economize on the fixed cost of exchange. The game theoretic approach adopted here also enables one to dispense with the Walrasian auctioneer. Agents of the model propose the exchange arrangements. Moreover the strategies of active intermediaries may include per unit prices with fixed fees or a