We experimentally study decentralized one-to-one matching markets with transfers. We vary the information available to participants, complete or incomplete, and the surplus structure, supermodular or submodular. Several insights emerge. First, while markets often culminate in efficient matchings, stability is more elusive, reflecting the difficulty of arranging attendant transfers. Second, incomplete information and submodularity present hurdles to efficiency and especially stability; their combination drastically diminishes stability’s likelihood. Third, matchings form “from the top down” in complete-information supermodular markets, but exhibit many more and less-obviously ordered offers otherwise. Last, participants’ market positions matter far more than their dynamic bargaining styles for outcomes.

We consider an economy in which long-lived experts are matched with short-lived clients. Experts choose the type of client with whom they match, unobserved by the market. The interaction outcome depends on both the expert's and the client's type. We study the effects of supplying information about otherwise unobservable outcomes, such as "medical report cards," to help clients identify better experts. Such information can lead to inefficient matches, as experts reject risky clients to build their reputation. Hence, information can reduce welfare. Withholding information can mitigate these perverse incentives at the cost of misallocating experts known to be inept.

We investigate the impact of wealth redistribution on economic growth, building on Kelly’s (1956) optimal investment portfolio theory. A growth-optimal policy redistributes wealth from “lucky” overperforming individuals to underperforming ones, minimizing the systematic component of this redistribution in a myopic fashion. That is, the optimal policy minimizes the discrepancy between endowments and outcomes, counterfactually taking outcomes as independent of endowments. The myopia in this result follows from a decoupling argument that allows us to model the planner as independently choosing a growth-maximizing policy and a pattern of wealth circulation. (JEL D31, E23, G41, G51, H23, O41)

We introduce a notion of substitutability for correspondences and establish a monotone comparative static result. More precisely, we introduce the notions of unified gross substitutes and nonreversingness and show that if Q: P ⇉ Q is a supply correspondence defined on a set of prices P , which is a sublattice of R N , and Q satisfies these two properties, then the set of equilibrium prices Q −1 ( q ) associated with a vector of quantities q ∈ Q is a sublattice of P and is increasing (in the strong set order) in q . We establish connections between our notion of substitutes and existing notions, and examine applications such as the structure of inverse demand, profit maximization, the structure of competitive equilibria, matching games, hedonic pricing, and routing problems.

We examine an economy in which interactions are more productive if agents can trust others to refrain from cheating. Some agents are scoundrels, who cheat at every opportunity, while others cheat only if the cost of cheating, a decreasing function of the proportion of cheaters, is sufficiently low. The economy exhibits multiple equilibria. As the proportion of scoundrels in the economy declines, the high-trust equilibrium can be disrupted by arbitrarily small perturbations or by arbitrarily small infusions of low-trust agents, while the low-trust equilibrium becomes impervious to perturbations and infusions of high-trust agents. Scoundrels may thus have the effect of making trust more robust.

We explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity-averse and hence chooses an action that maximizes their minimum utility, the principal can strictly gain from using an ambiguous contract, and this gain can be arbitrarily high. We characterize the structure of optimal ambiguous contracts, showing that ambiguity drives optimal contracts toward simplicity. We also provide a characterization of ambiguity-proof classes of contracts, where the principal cannot gain by infusing ambiguity. Finally, we show that when the agent can engage in mixed actions, the advantages of ambiguous contracts disappear.

In this paper, we establish conditions for the existence of an equilibrium in the equilibrium flow problem studied by Galichon et al. (2024). The problem nests several classical economic models such as bipartite matching models, hedonic pricing models, shortest-path and minimum-cost flow problems, and time-dependent routing problems.

In this work we explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity-averse and chooses an action that maximizes their max-min utility, then the principal can strictly gain from using an ambiguous contract. We provide insights into the structure of optimal contracts, and establish that optimal ambiguous contracts are composed of simple contracts. We also provide a geometric characterization of ambiguity-proof classes of contracts. Finally, we show that when the agent considers mixed strategies, then there is no advantage in using an ambiguous contract.

We study markets in which agents first make investments and are then matched into potentially productive partnerships. Equilibrium investments and the equilibrium matching will be efficient if agents can simultaneously negotiate investments and matches, but we focus on markets in which agents must first sink their investments before matching. Additional equilibria may arise in this sunk-investment setting, even though our matching market is competitive. These equilibria exhibit inefficiencies that we can interpret as coordination failures. All allocations satisfying a constrained efficiency property are equilibria, and the converse holds if preferences satisfy a separability condition. We identify sufficient conditions (most notably, quasiconcave utilities) for the investments of matched agents to satisfy an exchange efficiency property as well as sufficient conditions (most notably, a single crossing property) for agents to be matched positive assortatively, with these conditions then forming the core of sufficient conditions for the efficiency of equilibrium allocations.

We offer an approach to cooperation in repeated games of private monitoring in which players construct models of their opponents' behavior by observing the frequencies of play in a record of past plays of the game in which actions but not signals are recorded. Players construct models of their opponent's behavior by grouping the histories in the record into a relatively small number of analogy classes for which they estimate probabilities of cooperation. The incomplete record and the limited number of analogy classes lead to misspecified models that provide the incentives to cooperate. We provide conditions for the existence of equilibria supporting cooperation and equilibria supporting high payoffs for some nontrivial analogy partitions.

This paper examines connections between stochastic growth and decision problems. We use tools from the theory of large deviations to show that wishful thinking decision problems are equivalent to utility maximization problems, both of which are equivalent to growth maximization under idiosyncratic risk. Rational inattention problems are equivalent to growth-optimal portfolio problems, both of which are equivalent to growth maximization under aggregate risk. Stochastic growth generates extreme inequality, with nearly all wealth eventually held by those who happen to have faced empirical distributions that match the solution to the wishful thinking or rational inattention problem. (JEL D31, D81, D82, D83, G51, O41)

We examine the evolutionary selection of attitudes toward aggregate risk in an age structured population. Aggregate shocks perturb the population's consumption possibilities. Consumption is converted to fertility via a technology that exhibits first increasing and then decreasing returns to scale, captured in the simplest case by a fertility threshold. We show that evolution will select preferences that exhibit arbitrarily high aversion to aggregate risks with even very small probabilities of sufficiently low outcomes. These findings complement the familiar result that evolution will select for greater aversion to aggregate than idiosyncratic risks by identifying circumstances under which the difference can be extreme.

We introduce a notion of substitutability for correspondences and establish a monotone comparative static result, unifying results such as the inverse isotonicity of M-matrices, Berry, Gandhi and Haile's identification of demand systems, monotone comparative statics, and results on the structure of the core of matching games without transfers (Gale and Shapley) and with transfers (Demange and Gale). More specifically, we introduce the notions of 'unified gross substitutes' and 'nonreversingness' and show that if Q is a supply correspondence defined on a set of prices P which is a sublattice of R^N, and Q satisfies these two properties, then the set of prices yielding supply vector q is increasing (in the strong set order) in q; and it is a sublattice of P.

Economic theory comprises three types of inquiry. One examines economic phenomena, one develops analytical tools, and one studies the scientific endeavor in economics in general and in economic theory in particular. We refer to the first as economics, the second as the development of economic methods, and the third as the methodology of economics. The same mathematical result can often be interpreted as contributing to more than one of these categories. We discuss and clarify the distinctions between these categories, and argue that drawing the distinctions more sharply can be useful for economic research.

Galichon, Samuelson and Vernet (2022) introduced a class of problems, equilibrium flow problems, that nests several classical economic models such as bipartite matching models, minimum-cost flow problems and hedonic pricing models. We establish conditions for the existence of equilibrium prices in the equilibrium flow problem, in the process generalizing Hall's theorem.

Decision theory can be used to test the logic of decision making—one may ask whether a given set of decisions can be justified by a decision‐theoretic model. Indeed, in principal–agent settings, such justifications may be required—a manager of an investment fund may be asked what beliefs she used when valuing assets and a government may be asked whether a portfolio of rules and regulations is coherent. In this paper we ask which collections of uncertain‐act evaluations can be simultaneously justified under the maxmin expected utility criterion by a single set of probabilities. We draw connections to the fundamental theorem of finance (for the special case of a Bayesian agent) and revealed‐preference results.

The interpretation of economic theories varies along several dimensions. First, models can describe reality, illustrate a recommended state of affairs, or analyze the structure and implications of a theory. Second, theories can be used for prediction or for explanation. Third, theories can relate to reality in a rule-based or case-based manner. Fourth, theories can be statements about economic reality or about the act of economic reasoning itself. Fifth, theories can offer predictions or merely critique reasoning. We argue that theories are often open to multiple interpretations which can shift depending on the context in which the theory is applied, the surrounding economic literature, and the argument made by the interpreter.

It has been argued that Pareto-improving trade is not as compelling under uncertainty as it is under certainty. The former may involve agents with different beliefs, who might wish to execute trades that are no more than betting. In response, the concept of no-betting Pareto dominance was introduced, requiring that putative Pareto improvements must be rationalizable by some common probabilities, even though the participants’ beliefs may differ. In this paper, we argue that this definition might be too narrow for use when agents are not Bayesian. Agents who face ambiguity might wish to trade in ways that can be justified by common ambiguity, though not necessarily by common probabilities. We accordingly extend the notion of no-betting Pareto dominance to characterize trades than are “no-betting Pareto” ranked according to the maxmin expected utility model.