arXiv subjects
Publications and source records attributed to Mark Whitmeyer.
Every statistic on laws with finite pth moment that is additive across independent risks and monotone in mean-preserving spreads depends only on an additive function of the mean when p is strictly less than 2, and only on such a function and a nonnegative multiple of the variance when p is no less than 2.
I argue that there is a sense in which universal equilibrium (defined loosely) existence in games is incompatible with eschewing strictly dominated strategies and a sense in which it isn't.
We prove that every mean-zero probability law on the real line is the law of X-Y for some identically distributed real-valued random variables X and Y.
We study joint decision-making when agents agree on all primitives other than signal likelihoods. We propose a decision-theoretic measure of interpretive disagreement: a pair of subjective models is more agreeable than another if, uniformly across decision problems, it supports a larger set of signal-contingent plans that both agents weakly prefer ex-ante to the common reservation payoff. We show that this measure is prior independent and can be represented as an inclusion preorder over pairs of subjective models: each model in the more agreeable pair is a convex combination of the two models in the less agreeable pair. We then show that the measure's unique rotation-invariant scalar completion is cosine similarity. Applications show that greater agreement reduces speculative-trade wedges, expands a normalized version of the ex-ante Pareto frontier, and enlarges the set of single-model rationalizations. Our order is independent of Blackwell dominance and selects quadratic over KL-type Bregman divergences.
Suppose we want to assign a certainty equivalent--one number--to a multivariate risk. Which such assignments are law-invariant, monotone with respect to vector stochastic dominance, and invariant to independent background risk? I show that every such certainty equivalent is a positive mixture of scalar entropic certainty equivalents applied to positive projections of the vector risk. The same representation yields a robust-order characterization: unanimity across such certainty equivalents is equivalent, up to closure, to dominance after adding independent multidimensional background risk. In a social-welfare specialization, the corresponding shadow valuations are welfare weights.
The marginal degree of sums in dimension \(n\) is the smallest integer \(k\) such that the joint distributions of all subcollections of at most \(k\) coordinates of a real-valued random vector \(\left(X_1,\ldots,X_n\right)\) determine the value of \(\E\left(X_1+\cdots+X_n\right)\), whenever this expectation is defined. For every \(n\ge2\), we prove that this marginal degree is \(\left\lceil n/2\right\rceil\). The upper bound follows from a theorem of Simons (1977). The lower bound is proved by constructing, for every \(1\le k<\left\lceil n/2\right\rceil\), two joint laws whose marginals of dimension at most \(k\) agree, but for which the corresponding expectations of \(X_1+\cdots+X_n\) are defined and unequal.
Labels -- grades, credentials, scores, ratings, ranks -- do two things. They inform receivers, and they give agents something to chase. I study optimal classification when labels must be earned through costly self-selection. I show that exact certification is inefficiently fine: pooling a small bottom interval saves first-order signaling costs while losing only higher-order decision value. I provide sufficient conditions for lower censorship to maximize efficiency as well as for every optimal classification to use finitely many categories.
I study transformations of returns in the growth-optimal (Kelly) portfolio problem. In the one-safe-one-risky-asset problem, a return transform f universally produces a more conservative portfolio if and only if f is concave and strictly increasing and r/f is convex. As a corollary, I characterize comparative risk aversion for a rationally-inattentive agent: a more risk-averse agent is one who is sufficiently more risk averse in the Pratt (1964) sense.
We study a population-wide tournament in which agents, who care both about their absolute and relative wealth, experiment by searching over correlated objects. We explore the role of the agents' beliefs about the environment; namely, the stochastic processes corresponding to their experimentation. We find that although optimism leads to higher output, it also produces greater inequality. We connect these observations with empirical evidence suggesting a positive relationship between inequality and entrepreneurship.
We provide a unifying way to analyze how risk aversion changes bidding in auctions by asking which bids become more attractive as bidders become more risk averse. In first-price auctions, under two payoff conditions--winning is never worse than the outside option, and winning with a low bid is preferable to winning only with a high bid--greater risk aversion makes high bids more appealing. In second-price auctions with a known outside option, bidding more increases risk exposure conditional on winning, so greater risk aversion favors lower bids. We show these bid-level forces translate into corresponding equilibrium comparative statics.
Price controls kill the incentive for arbitrage. We prove a Chaos Theorem: under a binding price ceiling, suppliers are indifferent across destinations, so arbitrarily small cost differences can determine the entire allocation. The economy tips to corner outcomes in which some markets are fully served while others are starved; small parameter changes flip the identity of the corners, generating discontinuous welfare jumps. These corner allocations create a distinct source of cross-market misallocation, separate from the aggregate quantity loss (the Harberger triangle) and from within-market misallocation emphasized in prior work. They also create an identification problem: welfare depends on demand far from the observed equilibrium. We derive sharp bounds on misallocation that require no parametric assumptions. In an efficient allocation, shadow prices are equalized across markets; combined with the adding-up constraint, this collapses the infinite-dimensional welfare problem to a one-dimensional search over a common shadow price, with extremal losses achieved by piecewise-linear demand schedules. Calibrating the bounds to station-level AAA survey data from the 1973--74 U.S. gasoline crisis, misallocation losses range from roughly 1 to 9 times the Harberger triangle.
I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must possess, and provide a characterization via the first-order approach. Manifold applications--to R\&D competition, oligopolistic competition with product design, and rank-order contests--follow.
How do cost shocks pass through to prices in markets with price dispersion? We decompose the problem into two layers. In the competition layer, consumers' consideration sets determine equilibrium distributions of normalized margins. In the curvature layer, demand elasticity maps these margins into prices and pass-through rates. We prove the pricing game is strategically equivalent to a game over normalized margins, so equilibrium margin distributions are invariant to demand and costs. This separation yields closed-form pass-through formulas at each quantile of the price distribution, robust bounds across demand specifications, and sharp comparative statics linking market structure to incidence.
We study continuous-time persuasion where a sender controls both how informative a signal is over time and when to stop providing information to a receiver. There is an exogenous signal process, which the sender both garbles and stops, delaying the receiver's decision at a convex, increasing cost of time. We show that, although both instruments are available, under natural regularity conditions, full transparency is always optimal: the sender keeps the signal fully informative and persuades solely by choosing when to stop.
In finite problems comprising objects, cases, and an object- and case-contingent payoff function, we study the comparative statics of the set of undominated objects, meaning those for which there exists no mixture over objects that is superior in every case. We consider both weak and strict dominance (corresponding to different degrees of 'strictness' in the definition of superiority). Our main theorem characterises those payoff transformations which robustly expand the not-weakly-dominated and not-strictly-dominated sets: the necessary and sufficient condition is that payoffs be transformed separately across cases, in either a monotone-concave or a constant manner. We apply our results to Pareto frontiers and games.
In choice under risk, there is a standard notion of 'less risk-averse than', due to Yaari (1969). In the theory of comparative statics, the single-crossing property is satisfied by all weighted averages of a family of single-crossing functions if and only if the family satisfies a property called signed-ratio monotonicity (Quah & Strulovici, 2012). We establish a close link between 'less risk-averse than' and signed-ratio monotonicity.
We study welfare analysis for policy changes when supply and demand behavior are only partially known. We augment the robust approach pioneered by Kang and Vasserman (2025) by incorporating the supply side. We posit intervals of feasible pass-through and conduct (market-power) parameters, then apply them to two equilibrium snapshots to characterize the extremal supply-side terms entering welfare. We show that the supply-side bounds are attained by inverse pass-through functions that take only the two endpoint values of the specified interval, separated by a single price cutoff. Combining these supply-side extrema with demand-side shape restrictions, we produce simple bounds for consumer surplus, producer surplus, total surplus, and deadweight loss.
We uncover a close link between outside options and risk attitude: when a decision-maker gains access to an outside option, her behaviour becomes less risk-averse, and conversely, any observed decrease of risk-aversion can be explained by an outside option having been made available. We characterise the comparative statics of risk-aversion, delineating how effective risk attitude (i.e. actual choice among risky prospects) varies with the outside option and with the decision-maker's 'true' risk attitude. We prove that outside options are special: among transformations of a decision problem, those that amount to adding an outside option are the only ones that always reduce risk-aversion.