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Abstract
We study Butters's (1977. "Equilibrium Distributions of Sales and Advertising Prices." The Review of Economic Studies 44 (3): 465–91) model under concave advertising costs, and determine a class of cost functions such that each seller sends the same finite number of ads in equilibrium. Then we consider the limit economy where the number of buyers and sellers grow indefinitely, and show that the equilibrium of the finite economy does not converge to an equilibrium in the limit economy.

AbstractWe study a large economy where capacity-constrained sellers post prices to attract buyers. Capacity is costly and each seller chooses how many units to stock, which allows us to study the relationship between search frictions and capacity. We show that no equilibrium exists with linear costs; however, sufficiently convex costs are enough for existence. There may be several equilibria, but we show that the equilibrium payoffs to the agents are unique as well as constrained efficient. Finally, we numerically analyze how the magnitude of search frictions is affected by the capacity choices of the firms.

We apply the von Neumann-Morgenstern stable set to the n-player cake division problem. Only time-preferences á la Rubinstein (1982) are assumed. The stable set is defined with respect to the following dominance relation: x dominates y if there is a player who prefers x over y even with one period lag. The Nash bargaining solution is characterized in the language of stable sets. Through the characterization, we establish the existence and uniqueness of the Nash solution.