Knowledge that Transforms

The revenue-equivalence theorem 1 for auctions predicts that expected seller revenue is independent of the bidding rules, as long as equilibrium has the properties that the buyer with the highest reservation price wins and any buyer with the lowest possible reservation price has zero expected surplus. Thus, in particular, the two most common auction institutions- the open "English " auction and the sealed high-bid auction- are equivalent despite their rather different strategic properties. This strong prediction of equivalence seems at odds, however, with the empirical observation that rarely is any given kind of commodity sold through more than one sort of auction. Thus, for example, art is nearly always auctioned off according to the English rules, whereas job contracts are normally awarded through sealed bids. Admittedly, in the public sector, there have been a few attempts to use both methods (lumber contracts in the Pacific Northwest) or to switch from one to the other (Treasury Bills). But changes have typically met great resistance. This is also in conflict with theory, since a corollary of the revenue equivalence theorem is that the expected surplus for any buyer is the same in the two auctions.

In markets where prices are determined by the intersection of supply and demand curves, standard identification results require the presence of instruments that shift one curve but not the other. These results are typically presented in the context of linear models with fixed coefficients and additive residuals. The first contribution of this paper is an investigation of the consequences of relaxing both the linearity and the additivity assumption for the interpretation of linear instrumental variables estimators. Without these assumptions, the standard linear instrumental variables estimator identifies a weighted average of the derivative of the behavioural relationship of interest. A second contribution is the formulation of critical identifying assumptions in terms of demand and supply at different prices and instruments, rather than in terms of functional-form specific residuals. Our approach to the simultaneous equations problem and the average-derivative interpretation of instrumental variables estimates is illustrated by estimating the demand for fresh whiting at the Fulton fish market. Strong and credible instruments for identification of this demand function are available in the form of weather conditions at sea.

We consider the dynamic private provision of funds to projects that generate public benefits. Participants have complete information about the environment, but imperfect information about individual actions: each period they observe only the aggregate contribution. Each player may contribute any amount in any period before the contributing horizon is reached. All Nash equilibrium outcomes are characterized. In many cases they are all also perfect Bayesian equilibrium outcomes. If the horizon is long, if the players' preferences are similar, and if they are patient or the period length is short, perfect Bayesian equilibria exist that essentially complete the project. In some of them the completion time shrinks to zero with the period length—efficiency is achieved in the limit.

Previous work on information and financial markets has focused on a special set of assumptions: agents have exponential utility, and random variables are normally distributed. These assumptions are often necessary to obtain closed-form solutions. We present an example with alternative assumptions, and demonstrate that some of the conclusions from previous literature fail to hold. In particular, we show that in our example, as more agents acquire information, prices do not necessarily become more informative, and agents may have greater incentive to acquire information. Learning can therefore be a strategic complement, allowing for the possibility of multiple equilibria.

In a local interaction game agents play an identical stage game against their neighbours over time. For nearest neighbour interaction, it is established that, starting from a random initial configuration in which each agent has a positive probability of playing the risk dominant strategy, a sufficiently large population coordinates in the long-run on the risk dominant equilibrium almost surely. Our result improves on Blume (1995), Ellison (2000), and Morris (2000) by showing that the risk dominant equilibrium spreads to the entire population in a two dimensional lattice and without the help of mutation, as long as there is some randomness in the initial configuration.

This paper analyses optimal auctions of several objects. In the first model bidders have a binary distribution over their valuations for each object, in which case the optimal auction is efficient. The optimal auction takes one of two formats: either objects are sold in independent auctions, or a degree of bundling is introduced in the sense that the probability a bidder wins one object is increasing in her value for the other. The format of the optimal auction may depend upon the number of bidders. In the second model the restriction to binary distributions is relaxed, and the optimal auction is then inefficient.

The paper examines the behaviour of “evolutionary” models with ɛ-noise like those which have been used recently to discuss the evolution of social conventions. The paper is built around two main observations: that the “long run stochastic stability” of a convention is related to the speed with which evolution toward and away from the convention occurs, and that evolution is more rapid (and hence more powerful) when it may proceed via a series of small steps between intermediate steady states. The formal analysis uses two new measures, the radius and modified coradius, to characterize the long run stochastically stable set of an evolutionary model and to bound the speed with which evolutionary change occurs. Though not universally powerful, the result can be used to make many previous analyses more transparent and extends them by providing results on waiting times. A number of applications are also discussed. The selection of the risk dominant equilibrium in 2 × 2 games is generalized to the selection of ½-dominant equilibria in arbitrary games. Other applications involve two-dimensional local interaction and cycles as long run stochastically stable sets.

We present a model of entry and exit with Bayesian learning and price competition. A new product of initially unknown quality is introduced in the market, and purchases of the product yield information on its true quality. We assume that the performance of the new product is publicly observable. As agents learn from the experiments of others, informational externalities arise. We determine the Markov Perfect Equilibrium prices and allocations. In a single market, the combination of the informational externalities among the buyers and the strategic pricing by the sellers results in excessive experimentation. If the new product is launched in many distinct markets, the path of sales converges to the efficient path in the limit as the number of markets grows.