Karl H. Schlag

Robust Monopoly Pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.

Pricing without Priors

We consider the problem of pricing a single object when the seller has only minimal information about the true valuation of the buyer. Specifically, the seller only knows the support of the possible valuations and has no further distributional information. The seller is solving this choice problem under uncertainty by minimizing her regret. The pricing policy hedges against uncertainty by randomizing over a range of prices. The support of the pricing policy is bounded away from zero. Buyers with low valuations cannot generate substantial regret and are priced out of the market. We generalize the pricing policy without priors to encompass many buyers and many qualities.

Minimax Regret and Strategic Uncertainty

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)).

On the Evolutionary Selection of Sets of Nash Equilibria

Abstract It is well established for evolutionary dynamics in asymmetric games that a pure strategy combination is asymptotically stable if and only if it is a strict Nash equilibrium. We use an extension of the notion of a strict Nash equilibrium to sets of strategy combinations called ‘strict equilibrium set’ and show the following. For a large class of evolutionary dynamics, including all monotone regular selection dynamics, every asymptotically stable set of rest points that contains a pure strategy combination in each of its connected components is a strict equilibrium set. A converse statement holds for two-person games, for convex sets and for the standard replicator dynamic.

A New Method for Constructing Exact Tests Without Making Any Assumptions

We present a new method for constructing exact distribution-free tests (and confidence intervals) for variables that can generate more than two possible outcomes. This method separates the search for an exact test from the goal to create a non- randomized test. Randomization is used to extend any exact test relating to means of variables with finitely many outcomes to variables with outcomes belonging to a given bounded set. Tests in terms of variance and covariance are reduced to tests relating to means. Randomness is then eliminated in a separate step. This method is used to create confidence intervals for the difference between two means (or variances) and tests of stochastic inequality and correlation.

Does Noise Undermine The First-Mover Advantage? An Evolutionary Analysis Of Bagwell'S Example

Bagwell (1995) considered a simple Stackelberg-type game in which one player benefits from the others ability to observe his move, assuming they play the unique subgame perfect equilibrium. He showed that introducing noise in the observability of the move eliminates that equilibrium, and thus the advantage. Van Damme and Hurkens (1997) objected that the noisy game also has a mixed strategy equilibrium close to the pure strategy one Bagwell had eliminated. However, we analyse the noisy game with a wide variety of evolutionary and learning dynamics, and find that almost all admit the no-first-mover-advantage equilibrium as a possible outcome, and often they select it uniquely.

Can sanctions induce pessimism? An experiment

We run an experiment in which two subjects play a two-round minimum effort game in the presence of a third player (principal) who is the only one informed about past effort choices and benefits from a higher minimum effort of the others. Sanctions introduced in the second round by the experimenter lead to more optimistic beliefs and higher efforts. This is not true when sanctions have been imposed by the principal. The possibility that the choice of a sanction is a signal of low effort levels causes players who chose high effort in the first round to be less optimistic.

Evolutionary insights on the willingness to communicate

AbstractWhile in previous models of pre-play communication players are forced to communicate, we investigate what happens if players can choose not to participate in this cheap talk. Outcomes are predicted by analyzing evolutionary stability in a population of a priori identical players. If the game following the communication rewards players who choose the same action then an efficient outcome is only guaranteed when participation in the pre-play communication is voluntary. If however players aim to coordinate on choosing different actions in the underlying game and there are sufficiently many messages then the highest payoff is selected when players are forced to talk to each other before playing the game.

Communication, Coordination, and Efficiency in Evolutionary One-Population Models

We analyze the role of commitment in pre-play communication for ensuring efficient evolutionarily stable outcomes in coordination games. All players are a priori identical as they are drawn from the same population. In games where efficient outcomes can be reached by players coordinating on the same action we find commitment to be necessary to enforce efficiency. In games where efficienct outcomes only result from play of different actions, communication without commitment is most effective although efficiency can no longer be guaranteed. Only when there are many messages then inefficient outcomes are negligible as their basins of attraction become very small.

Who Gives Direction to Statistical Testing? Best Practice Meets Mathematically Correct Tests

We are interested in statistical tests that are able to uncover that one method is better than another one. The Wilcoxon-Mann-Whitney rank-sum and the Wilcoxon sign-rank test are the most popular tests for showing that two methods are di¤erent. Yet all of the 32 papers in Economics we surveyed misused them to claim evidence that one method is better, without making any additional assumptions. We present eight nonparametric tests that can correctly identify which method is better in terms of a stochastic inequality, median di¤erence and di¤erence in medians or means, without adding any as- sumptions. We show that they perform very well in the data sets from the surveyed papers. The two tests for comparing medians are novel, constructed in the spirit of Mood?s test.