Three theorems state conditions sufficient for the inessentiality of equilibrium in a pure exchange, sequence economy. The agents have uncommon priors, state-contingent utility functions, and asymmetric information in every trading period, and they trade different sets of event-contingent claims in different periods. The theorems provide alternative interpretations of the concept of market completeness, reveal two fundamentally different ways to obtain inessentiality, and shed light on the conditions permitting speculation and the role of price-contingent trading. None of the theorems requires ex ante Pareto optimality or the absence of arbitrage opportunities. Copyright 1993 by The Econometric Society.

In this paper, small firms sell a homogeneous good to small consumers under conditions of free entry, but consumers receive price information only through firms' advertising. In equilibrium, every firm on the continuous price distribution buys less advertising than is socially optimal. The result is robust if firms advertise in just one medium. If readers of different advertising media are positively correlated, excess advertising can occur in media used exclusively to advertise discount prices. Copyright 1991 by American Economic Association.

In this paper, small firms sell a homogeneous good to small consumers under conditions of free entry, but consumers receive price information only through firms' advertising. In equilibrium, every firm on the continuous price distribution buys less advertising than is socially optimal. The result is robust if firms advertise in just one medium. If readers of different advertising media are positively correlated, excess advertising can occur in media used exclusively to advertise discount prices.

mutation.) Kandori, Mailath, and Rob (henceforth KMR) first provide a useful general theorem concerning the stationary distribution of strategies under Darwinian dynamics. They then divide the analysis of the 2 x 2 game into three cases: dominant strategy games (e.g., prisoners' dilemma), coordination games, and games with no symmetric pure strategy equilibrium (e.g., battle of the sexes). We refer to these as DS, C, and NP games. In each case, KMR claim that, as the rate of mutation vanishes, the stationary distribution of strategies converges to a symmetric Nash equilibrium. They emphasize C games, which have two symmetric Nash equilibria, and characterize the conditions under which the distribution converges to the risk dominant equilibrium. In this note, we argue that while their formal conclusions for C games are correct, their results for DS and NP games are valid only for large populations of players. In small populations, Darwinian dynamics may produce non-Nash outcomes in these two cases. Section 1 summarizes the KMR model, and Section 2 provides examples of 2 x 2 games in which Darwinian dynamics generate non-Nash outcomes. A theorem in Section 3 describes the Darwinian equilibrium of any 2 x 2 game.

An organization makes collective decisions through neither markets nor contracts. Instead, rational agents voluntarily choose to follow a leader. In many cases, incentive problems are solved: the unique nondegenerate equilibrium achieves the first best, even though every agent has incentives to free ride. The leader has no special talents but is distinguished by getting exclusive access to information. A crucial feature is that the leader reveals part but not all of her information. It is this maintenance of informational asymmetry that permits achieving the first best. (JEL D23, M54)

Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well–defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better–reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator.