A game is better-reply secure if for every nonequilibrium strategy x U and every payoff vector limit u U resulting from strategies approaching x U , some player i has a strategy yielding a payoff strictly above u U even if the others deviate slightly from x U . If strategy i spaces are compact and convex, payoffs are quasiconcave in the owner's strategy, and the game is better-reply secure, then a pure strategy Nash equilibrium exists. Better-reply security holds in many economic games. It also permits new results on the existence of symmetric and mixed strategy Nash equilibria.

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Citation indices attempt to provide useful information about a researcher's publication record by summarizing it with a single numerical score. They provide government agencies, departmental and university committees, administrators, faculty, and students with a simple and potentially informative tool for comparing one researcher to another, and are regularly used to inform critical decisions about funding, promotion, and tenure. With decisions of this magnitude on the line, one should approach the problem of developing a good index as systematically as possible. Doing so here, we are led to a unique new index.

Consider the problem of maximizing the revenue from selling a number of goods to a single buyer. We show that, unlike the case of one good, when the buyer's values for the goods increase, the seller's maximal revenue may well decrease. We then identify two circumstances where monotonicity does obtain: when optimal mechanisms are deterministic and symmetric, and when they have submodular prices. Next, through simple and transparent examples, we clarify the need for and the advantage of randomization when maximizing revenue in the multiple‐good versus the one‐good case. Finally, we consider “seller‐favorable” mechanisms, the only ones that matter when maximizing revenue. They are essential for our positive monotonicity results, and they also circumvent well known nondifferentiability issues.

A step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information. If there are sufficiently many buyers and sellers, and their bids are restricted to a sufficiently fine discrete set of prices, then, generically, there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents. In particular, the large double-auction equilibrium is almost efficient and almost fully aggregates the agents' information. Copyright The Econometric Society 2006.