We consider an auction in which k identical objects of unknown value are auctioned off to n bidders. The k highest bidders get an object and pay the k+1st bid. Bidders receive a signal that provides information about the value of the object. We characterize the unique symmetric equilibirum of...

We consider discriminatory auctions for multiple identical units of a good. Players have private values, possibly for multiple units. None of the usual assumptions about symmetry of players' distributions over values or of their equilibrium play are made. Because of this, equilibria will...

We define and explore the No-Upward-Crossing NUC, a condition satisfied by every parameterized family of distributions commonly used in economic applications. Under smoothness assumptions, NUC is equivalent to log-supermodularity of the negative of the derivative of the distribution with respect...

Consider an agent who can costlessly add mean-preserving noise to his output. To deter such risk-taking, the principal optimally offers a contract that makes the agent's utility concave in output. If the agent is risk-neutral and protected by limited liability, this concavity constraint binds...

We consider the problem of providing a risk averse manager effort incentives in a setting where there is a binding minimum that can be paid. An implication is that the contract may be strictly preferred by the manager to outside opportunities. We show that stocks can dominate options as a means...

We consider the choice between stocks and options to provide effort incentives to a risk-averse manager. We show that stocks can dominate options as a means of motivation only if nonviability risk is substantial, as in financially distressed firms or start-ups. Options dominate stocks for other...

Human utility embodies a number of seemingly irrational aspects. The leading example in this paper is that utilities often depend on the presence of salient unchosen alternatives. Our focus is to understand <i>why</i> an evolutionary process might optimally lead to such seemingly dysfunctional features...