We define and discuss several notions of potential functions for games in strategic form. We characterize games that have a potential function, and we present a variety of applications.

Distributed Algorithmic Mechanism Design (DAMD) combines theoretical computer science’s traditional focus on computational tractability with its more recent interest in incentive compatibility and distributed computing. The Internet’s decentralized nature, in which distributed computation and autonomous agents prevail, makes DAMD a very natural approach for many Internet problems. This paper first outlines the basics of DAMD and then reviews previous DAMD results on multicast cost sharing and interdomain routing. The remainder of the paper describes several promising research directions and poses some specific open problems.

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 examine the force of three types of behavioural 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 Cournot-Nash 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, behavioural rules, and outcomes.

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.

This paper studies myopic Bayesian learning processes for finite-player, finitestrategy normal form games. Initially, each player is presumed to know his own payoff function but not the payoff functions of the other players. Assuming that the common prior distribution of payoff functions satisfies independence across players, it is proved that the conditional distributions on strategies converge to a set of Nash equilibria with probability one. Under a further assumption that the prior distributions are sufficiently uniform, convergence to a set of Nash equilibria is proved for every profile of payoff functions, that is, every normal form game.

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.

The performance of the Japanese economy in the last forty-five years, during which it has gone from post-war destitution and near collapse to one of the richest and most productive in the world, is unmatched in human history. Between 1950 and 1990, real GNP per capita increased from $1,230 to $23,970 (both calculated in 1990 prices), rising from one-eighth of the level in the United States to surpass it. Since the War, life expectancies have increased by half, from 50 years for males to 75, and from 54 to 81 years for females.2 Naturally, Japan's experience has attracted much attention among those concerned with economic growth: How did Japan do it? Can other nations replicate the Japanese success? What are the key lessons from Japan for countries seeking economic growth? A unique set of institutional arrangements, organizational structures and managerial practices are characteristic of Japanese economic organization, and many observers have seen various of these as important causal elements in Japan's economic success. They have consequently advocated imitating these features elsewhere, both in the practices of individual firms and at an economy-wide level. Very often, however, attempts to import elements of Japanese practice to other countries have been partial or complete failures.

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,