We examine a general class of adaptive behavior models in which the distant past has only a weak effect on current actions, and assume that agents sometimes make mistakes, to show that average behavior (averaged over time) converges, with probability one, to a unique limit. Mistakes generate global convergence and are an equilibrium selection device; for small mistake probabilities the equilibr...

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...

In this paper we examine a representative agent forecasting prices in a first-order self-referential overlapping generations model. We first consider intermediate stage learning, where agents update the forecasting rule every m periods. We show that, in theory and simulations, the learning rule does not converge to the rational expectations equilibrium (REE). We next consider two stage learning...

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...

Decentralized scheduling is the problem of allocating resources to alternative possible uses over time, where competing uses are represented by autonomous agents. Market mechanisms use prices derived through distributed bidding protocols to determine schedules. We investigate the existence of equilibrium prices for some general classes of scheduling problems, the quality of equilibrium solution...

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...