On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure strategy equilibria in Bayesian games. We allow action spaces to be compact locally-complete metrizable semilattices and type spaces to be partially ordered probability spaces. Our proof is based upon contractibility rather than convexity of best reply sets. Several examples illustrate the scope of the result, including new applications to multi-unit auctions with risk-averse bidders.

The Better Half of Selling Separately

Separate selling of two independent goods is shown to yield at least 62% of the optimal revenue, and at least 73% when the goods satisfy the Myerson regularity condition. This improves the 50% result of Hart and Nisan (2017, originally circulated in 2012)

Existence of subgame perfect equilibrium with public randomization: A short proof

Consider a multi-stage game where each player has a compact choice set and payoffs are continuous in all such choices. Harris, Reny and Robson (1995) prove existence of a subgame perfect equilibrium as long as a public correlation device is added to each stage. They achieve this by showing that the subgame perfect equilibium path correspondence is upper hemicontinuous. The present paper gives a short proof of existence that focuses on equilibrium payoffs rather than paths.Existence

How to count citations if you must

Citation indices are regularly used to inform critical decisions about promotion, tenure, and the allocation of billions of research dollars. Nevertheless, most indices (e.g., the h-index) are motivated by intuition and rules of thumb, resulting in undesirable conclusions. In contrast, five natural properties lead us to a unique new index, the Euclidean index, that avoids several shortcomings of the h-index and its successors. The Euclidean index is simply the Euclidean length of an individual's citation list. Two empirical tests suggest that the Euclidean index outperforms the h-index in practice

A Stone-Weierstrass Theorem without Closure under Suprema

For a compact metric space X, consider a linear subspace A of C (X) containing the constant functions. One version of the Stone-Weierstrass theorem states that, if A separates points, then the closure of A under both minima and maxima is dense in C (X). Similarly, by the Hahn-Banach theorem, if A separates probability measures, A is dense in C (X). We show that if A separates points from probability measures, then the closure of A under minima is dense in C (X). This theorem has applications in Economic Theory

Why sex? and why only in pairs?

Understanding the purpose of sex is a fundamental unresolved problem in evolutionary biology. The difficulty is not that there are too few theories of sex, the difficulty is that there are too many and none stand out. To distinguish between theories, we ask: Why are there no triparental species with offspring composed of the genetic material of three individuals? A successful theory should confer an advantage to biparental sex over asexual reproduction without conferring an even greater advantage to triparental sex. Of two leading theories (red queen and mutational) we show that only one is successful in this sense