I review the uses of economic theory in the initial design and later improvement of the ‘‘simultaneous ascending auction,’ ’ which was developed initially for the sale of radio spectrum licenses in the United States. I analyze some capabilities and limitations of the auction, the roles of various detailed rules, the possibilities for introducing combinatorial bidding, and some considerations in adapting the auction for sales in which revenue, rather than efficiency, is the primary goal. I.

A benchmark "package auction" is introduced in which bidders may determine their own packages on which to bid. If all bidders bid straightforwardly, then the outcome is a point in the core of the exchange economy that minimizes the seller's revenue. When goods are substitutes, straightforward bidding strategies comprise an ex post Nash equilibrium. Compared to the Vickrey auction, the benchmark ascending package auction has cheaper information processing, better handling of budget constraints, and less vulnerability to joint bidding strategies among bidders who would otherwise be losers. Improvements are suggested that speed the auction and limit opportunities for collusion.

We combine Nagel’s “step-k” model of boundedly rational players with a “law of effect” learning model. Players begin with a disposition to use one of the step-k rules of behavior, and over time the players learn how the available rules perform and switch to better performing rules. We offer an econometric specification of this dynamic process and fit it to Nagel’s experimental data. We find that the rule of learning model vastly outperforms other nested and nonnested learning models. We find strong evidence for diverse dispositions and reject the Bayesian rule-learning model.

We examine the force of three types of behavioral dynamics in quantity-setting triopoly experiments: (1) mimicking the successful firm, (2) rules based on following the exemplary firm, and (3) rules based on belief learning. Theoretically, these three types of rules lead to the competitive, the collusive, and the CournotNash outcome, respectively. In the experiment we employ three information treatments, each of which is hypothesized to be conducive to the force of one of the three dynamic rules. To a large extent, the results are consistent with the hypothesized relationships between treatments, behavioral rules, and outcomes.

This study clarifies the conditions under which learning in games produces convergence to Nash equilibria in practice. We experimentally investigate the role of supermodularity, which is closely related to the more familiar concept of strategic complementarities, in achieving convergence through learning. Using a game from the literature on solutions to externalities, we find that supermodular and “nearsupermodular” games converge significantly better than those far below the threshold of supermodularity. From a little below the threshold to the threshold, the improvement is statistically insignificant. Increasing the parameter far beyond the threshold does not significantly improve convergence. (JEL C91, D83) When do players learn to play Nash equilibria? The answer to this important question will help us identify when the outcomes predicted by theory will be realized in competitive environments involving real people. This question has been examined both theoretically (see Drew Fudenberg and David Levine, 1998, for a survey) and experimentally (see Colin Camerer, 2003, for a survey). According to the theoretical literature, games with strategic complementarities (Paul Milgrom and John Roberts, 1991; Milgrom and Chris Shannon, 1994) have robust dynamic stability properties: under numerous learning dynamics,

In the framework of symmetric Cournot oligopoly, this paper provides two minimal sets of assumptions on the demand and cost functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to (i) decreasing industry price and increasing or decreasing per-firm output; and (ii) increasing industry price (and decreasing per-firm output.) In both cases, per-firm profits are decreasing. The analysis relies crucially on lattice-theoretic methods and yields general, unambiguous and easily interpretable conclusions of a global nature. As a byproduct of independent interest, new insight into existence of Cournot equilibrium is developed.

Nick Vriend and seminar audiences at UPF, Munich, Stockholm for helpful comments. Cabrales and Nagel

this paper for a conference on "Democratization in Poland and Eastern Europe: Progress and Prospects," at Jagiellonian University, Krakow, May 1997. 1 Thus Offe, for instance, contends that the "core problem" in current East European states "resides in their lack of any non-contingent 'givens' which would be suitable fixed parameters of the politics of reform. Precisely because the system is at such a deadlock, everything becomes contingent and nothing can self-evidently remain as it is" (Offe 1997, 41). 2 Interpretation and Coordination in Constitutional Politics Randall L. Calvert and James Johnson 1. Introduction Rampant uncertainty, fluidity, and indeterminacy are central, perhaps defining, features of politics in post-communist Eastern Europe (Bunce and Csanadi 1993). Analyses of politics in the region regularly stress what one writer refers to as "the helter-skelter of post-communism, . . . the bewilderment of life since 1989"

Ascending auctions with package bidding and their economic uses are explained and the main results of recent FCC-sponsored experiments with such auctions are summarized. A benchmark model is formulated that accounts for the experimental results. In the benchmark, if each bidder bids "straightforwardly" at each round for its potentially most profitable package, then the total payoff is approximately maximized by the final allocation---all payoff approximations here have error bounds proportional to the bid increment. With just two bidders, straightforward bidding strategies constitute an approximate equilibrium, but there can also be other equilibria. A bidder whose competitors all bid straightforwardly has a best reply that entails bidding straightforwardly but with maximal delays, suggesting a concern for the auctions time-to-completion. A new class of simple "bid improvement rules" is introduced that prevents such delays and accelerates the auction without unnecessarily degrading auction performance relative to the unmodified benchmark. The results are used to formulate recommendations for the FCC auction design. 1.

Self-tuning experience weighted attraction (EWA) is a one-parameter theory of learning in games. It replaces the key parameters in an earlier model (EWA) with functions of experience that “self-tune ” over time. The theory was tested on seven different games, and compared to the earlier model and a one-parameter stochastic equilibrium theory. The more parsimonious self-tuning EWA does as well as EWA in predicting behavior in new games, and reliably better than an equilibrium benchmark. The economic value of a learning theory is measured by how much more subjects would have earned in an experimental session if they followed the theory’s recommendations. Economic values for several learning and equilibrium theories were estimated (controlled for boomerang effects of following a model’s advice in one period, on future earnings). Most models have economic value. Self-tuning The power of equilibrium models of games comes from their ability to produce precise predictions using only the structure of a game and assumptions about players ’ rationality. Statistical models of learning, on the other hand, often need data to calibrate free parameters, and use