We show existence of equilibria in distributional strategies for a wide class of private value auctions, including the rst general existence result for double auctions. The set of equilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard pricing rules, reserve prices, entry costs, and stochastic demand and supply. Valuations can be correlated a...

This paper analyzes a stochastic model of evolution in normal form games. The long-run behavior of individuals in this model is investigated in the limit where mutation rates tend to zero, while the expected number of mutations, and hence population sizes, tend to infinity. It is shown that weakly dominated strategies do not survive evolution. Also strategies which are not rationalizable in the...

We examine the structure of the core of a trading economy with three competitive equilibria as the number of traders (N) is varied. The core first splits into two pieces at N = 5 and then splits a second time into three pieces at N = 12. Both of these splits occur not at a point but as a contiguous gap. We find that the speed of convergence of the core toward the three competitive equilibria is...

A dynamic model of financial markets with learning is demonstrated to produce a selforganized system that displays critical behavior. The price contains private information that traders learn to extract and employ to forecast future value. Since the price reflects the beliefs of the traders, the learning process is self referencing. As the market learns to correctly extract information from the...

The winner-take-all nature of all-pay auctions makes the outcome sensitive to decision errors, which we introduce with a logit formulation. The equilibrium bid distribution is a fixed point: the belief distributions that determine expected payoffs equal the choice distributions determined by expected payoffs. We prove existence, uniqueness, and symmetry properties. In contrast to the Nash equil...

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually ratio...

In the many-to-one matching model with contracts, I show that there is no restriction on preferences weaker than substitutable preferences which guarantees that the set of stable matches is a lattice. Thus, when contracts are not substitutes, removing agents from the economy may decrease the payoffs to existing agents on both sides of the market. I introduce a new necessary condition to guarant...

Commodity money arises endogenously in a general equilibrium model with separate budget constraints for each transaction. Transaction costs imply differing bid and ask (selling and buying) prices. The most liquid good—with the smallest proportionate bid/ask spread—becomes commodity money. General equilibrium may not be Pareto efficient. If zero-transaction-cost money is available then the equil...

Earlier studies of the seigniorage inflation model have found that the high-inflation steady state is not stable under adaptive learning. We reconsider this issue and analyze the full set of solutions for the linearized model. Our main focus is on stationary hyperinflationary paths near the high-inflation steady state. The hyperinflationary paths are stable under learning if agents can utilize ...