Stochastic Stability in a Double Auction

Abstract:     
In a k-double auction, a buyer and a seller must simultaneously announce a bid and an ask price respectively. Exchange of the indivisible good takes place if and only if the bid is at least as high as the ask, the trading price being the bid price with probability k and the ask price with probability (1-k). We show that the stochastically stable equilibria of a complete information k-double approximate an asymmetric Nash Bargaining solution with the seller's bargaining power decreasing in k.

Note that ceteris paribus, the payoffs of the seller of the one-shot game increase in k. Nevertheless, as the stochastically stable equilibrium price decreases in k, choosing the seller's favorite price with a relatively higher probability in individual encounters makes him worse off in the long run.

Number of Pages in PDF File: 24

Keywords: k-double auction, multiple equilibria, risk potential, stochastic stability, Nash Bargaining Solution

JEL Classification: C78, D83

working papers series