On Cobb-Douglas Preferences in Bilateral Oligopoly

Bilateral oligopoly is a simple model of exchange in which a finite set of sellers seek to exchange the goods they are endowed with for money with a finite set of buyers, and no price-taking assumptions are imposed. If trade takes place via a strategic market game bilateral oligopoly can be thought of as two linked proportional-sharing contests: in one the sellers share the aggregate bid from the buyers in proportion to their supply and in the other the buyers share the aggregate supply in proportion to their bids. The analysis can be separated into two ‘partial games’. First, fix the aggregate bid at B; in the first partial game the sellers contest this fixed prize in proportion to their supply and the aggregate supply in the equilibrium of this game is X˜ (B). Next, fix the aggregate supply at X; in the second partial game the buyers contest this fixed prize in proportion to their bids and the aggregate bid in the equilibrium of this game is ˜B (X). The analysis of these two partial games takes into account competition within each side of the market. Equilibrium in bilateral oligopoly must take into account competition between sellers and buyers and requires, for example, ˜B (X˜ (B)) = B. When all traders have Cobb-Douglas preferences ˜ X(B) does not depend on B and ˜B (X) does not depend on X: whilst there is competition within each side of the market there is no strategic interdependence between the sides of the market. The Cobb-Douglas assumption provides a tractable framework in which to explore the features of fully strategic trade but it misses perhaps the most interesting feature of bilateral oligopoly, the implications of which are investigated.

Self-Fulfilling Price Cycles

This paper presents a model of a self-fulfilling price cycle in an asset market. Price oscillates deterministically even though the underlying environment is stationary. The mechanism that we uncover is driven by endogenous variation in the investment horizons of the different market participants, informed and uninformed. On even days, the price is high; on odd days it is low. On even days, informed traders are willing to jettison their good assets, knowing that they can buy them back the next day, when the price is low. The anticipated drop in price more than offsets any potential loss in dividend. Because of these asset sales, the informed build up their cash holdings. Understanding that the market is flooded with good assets, the uninformed traders are willing to pay a high price. But their investment horizon is longer than that of the informed traders: their intention is to hold the assets they purchase, not to resell. On odd days, the price is low because the uninformed recognise that the informed are using their cash holdings to cherry-pick good assets from the market. Now the uninformed, like the informed, are investing short-term. Rather than buy-and-hold as they do with assets purchased on even days, on odd days the uninformed are buying to sell. Notice that, at the root of the model, there lies a credit constraint. Although the informed are flush with cash on odd days, they are not deep pockets. On each cherry that they pick out of the market, they earn a high return: buying cheap, selling dear. However they don't have enough cash to strip the market of cherries and thereby bid the price up.