Eric Rasmusen

We revisit a classic question of Fenchel from 1953: Which quasiconcave functions can be concavified by post-composition with a monotonic transformation? This question has a long history in economic utility theory. While many authors have given partial answers under various assumptions, we offer a complete characterization for quasiconcave functions without a priori assumptions on regularity. The answer hinges on the local regularity class of the function. We establish this characterization of concavifiability for continuous functions whose domain is any arbitrary geodesic metric space. Under the additional assumption of twice differentiability, we also provide simpler necessary and sufficient conditions for concavifiability on Riemannian manifolds which essentially generalize those given by Kannai for the Euclidean case.

Is it better to move first, or second—to innovate, or to imitate? We show that if one player's information about the profitability of new markets is only modestly superior, the possibility of foreclosing the market can lead to a first‐mover advantage. On the other hand, more extreme information superiority can reverse this, leading to a second‐mover advantage. Knowing more surely what is the best choice, the better‐informed player wants to delay to keep his information private and the less‐informed player wants to delay to learn. Because of this, more accurate information can actually lead to inefficiency by increasing the incentive to delay, and exogenous costs of delay can aid efficiency by neutralizing that strategic incentive. In fact, in some circumstances a player may purposely coarsen his information to deter imitation.

It is natural to suppose that a prosecutor's conviction rate—the ratio of convictions to cases prosecuted—is a sign of his competence. Prosecutors, however, choose which cases to prosecute. If they prosecute only the strongest cases, they will have high conviction rates. Any system that pays attention to conviction rates, as opposed to the number of convictions, is liable to abuse. As a prosecutor's budget increases, he allocates it between prosecuting more cases and putting more effort into existing cases. Either can be socially desirable, depending on particular circumstances. We model the tradeoffs theoretically in two models, one of a benevolent social planner and one of a prosecutor who values not just the number of convictions but the conviction rate and unrelated personal goals. We apply the model to U.S. data drawn from county-level crime statistics and a survey of all state prosecutors by district. Conviction rates do have a small negative correlation with prosecutorial budgets, but conditioning on other variables in regression analysis, higher budgets are associated both with more prosecutions and higher conviction rates.

It is well known that risk increases the value of options. This article makes that precise in a new way. The conventional theorem says that the value of an option does not fall if the underlying asset becomes riskier in the conventional sense of the mean-preserving spread. This article uses two new definitions of “riskier” to show that the value of an option strictly increases (i) if the underlying asset becomes “pointwise riskier,” and (ii) only if the underlying asset becomes “extremum riskier.”

A rational bidder in a private-value auction should be reluctant to incur the cost of perfectly estimating his value if it might not matter to the success of his bidding strategy. This can explain sniping---flurries of bids at the end of auctions---as the result of other bidders trying to avoid stimulating the victim into learning more about his value. The idea of value discovery also explains why a bidder might increase his bid ceiling in the course of an auction and why he would like to know the private values of other bidders.

We look at a Bertrand model in which each firm may be inactive with a known probability, so the number of active firms is uncertain. The model has a mixed‐strategy equilibrium, in which industry profits are positive and decline with the number of firms, the same features which make the Cournot model attractive. Unlike those in a Cournot model with similar uncertainty, Bertrand profits always increase in the probability that firms are inactive. Profits decline more sharply than in the Cournot model, the pattern found empirically in Bresnahan and Reiss [1991].

Much real-world contracting involves finding new clauses to add to a basic agreement, clauses which may or may not increase the welfare of both parties. The parties must decide which complications to propose, how closely to examine the other side's proposals, and whether to accept them. This suggests a reason why contracts are incomplete in the sense of lacking Pareto-improving clauses: contract-reading costs matter as much as contract-writing costs. Fine print that is cheap to write can be expensive to read carefully enough to understand the value to the reader, and especially to verify the absence of clauses artfully written to benefit the writer at the reader's expense. As a result, complicated clauses may be rejected outright even if they really do benefit both parties, and this will deter proposing such clauses in the first place.