We examine the bid-ask quotes offered by specialists (or dealers) who face indirect competition from other specialists who trade in related assets. In the context of a simple model where investors have mean variance preferences, we characterize the equilibrium bids and asks quoted by K...

We provide an overview of the workings of the National Science Foundation and the proposal review process, as well as some guidance in writing proposals for funding.

We consider discontinuous games with incomplete information. Auctions are a leading example. With standard tie breaking rules (or more generally, sharing rules), these games may not have equilibria. We consider sharing rules that depend on the private information of players. We show that there...

We analyze bidding behavior in large discriminatory price auctions where the number of objects is a non-trivial proportion of the number of bidders. Bidders observe private signals that are affiliated with the common value. We show that the average price in the auction is biased downward from...

A simple example shows that equilibria can fail to exist in second price (Vickrey) and English auctions when there are both common and private components to bidders' valuations and private information is held on both dimensions. The example shows that equilibrium only exists in the extremes of...

We show existence of equilibria in istributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of quilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard pricing...

We examine a legislative voting game where decisions are being made over both ideological and distributive dimensions, and legislators' preferences are separable over the two dimensions. In equilibrium legislators prefer to make proposals for the two dimensions together, rather than offering...