Efficient Random Assignment under a Combination of Ordinal and Cardinal Information on Preferences

Consider a collection of m indivisible objects to be allocated to n agents, where m = n. Each agent falls in one of two distinct categories: either he (a) has a complete ordinal ranking over the set of individual objects, or (b) has a set of “plausible” benchmark von Neumann-Morgenstern (vNM) utility functions in whose non-negative span his “true” utility is known to lie. An allocation is undominated if there does not exist a preference-compatible profile of vNM utilities at which it is Pareto dominated by another feasible allocation. Given an undominated allocation, we use the tools of linear duality theory to construct a profile of vNM utilities at which it is ex-ante welfare maximizing. A finite set of preference-compatible vNM utility profiles is exhibited such that every undominated allocation is ex-ante welfare maximizing with respect to at least one of them. Given an arbitrary allocation, we provide an interpretation of the constructed vNM utilities as subgradients of a function which measures worst-case domination.Random Assignment, Efficiency, Duality, Linear Programming

House allocation with fractional endowments

This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extend to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain.house allocation, fractional endowments, fairness, individual rationality

Pollution Control: When, and How, to be Precautious

The precautionary principle (PP) applied to environmental policy stipulates that, in the presence of physical uncertainty, society must take robust preventive action to guard against worst-case outcomes. It follows that the higher the degree of uncertainty, the more aggressive this preventive action should be. This normative maxim is explored in the case of a stylized dynamic model of pollution control under Knightian uncertainty. At time 0 a decision-maker makes a one-time investment in damage-control technology and subsequently decides on a desirable dynamic emissions policy. Adopting the robust control framework of Hansen and Sargent [10], we investigate optimal damage-control and mitigation policies. We show that optimal investment in damage control is always increasing in the degree of uncertainty, thus confirming the conventional PP wisdom. Optimal mitigation decisions, however, need not always comport with the PP and we provide analytical conditions that sway the relationship one way or the other. This result is interesting when contrasted to a model with fixed damage-control technology, in which it can be easily shown that a PP vis-a-vis mitigation unambiguously holds. We conduct a set of numerical experiments to determine the sensitivity of our results to specific functional forms of damage-control cost. We find that when the cost of damage-control technology is low enough, damage-control investment and mitigation may act as substitutes and a PP with respect to the latter can be unambiguously irrational.Risk, Ambiguity, Robust Control, Precautionary Principle, Pollution Control

Minimizing regret when dissolving a partnership

We study the problem of dissolving an equal-entitlement partnership when the objective is to minimize maximum regret. We initially focus on the family of linear-pricing mechanisms and derive regret-optimizing strategies. We also demonstrate that there exist linear-pricing mechanisms satisfying ex-post efficiency. Next, we analyze a binary-search mechanism which is ex-post individually rational. We discuss connections with the standard Bayesian-Nash framework for both linear and binary-search mechanisms. On a more general level, we show that if entitlements are unequal, ex-post efficiency and ex-post individual rationality impose significant restrictions on permissible mechanisms. In particular, they rule out both linear and binary-search mechanisms.Partnership dissolution; minimax regret; fair division; allocative efficiency

Optimal Mechanisms for Heterogeneous Multi-cell Aquifers

Standard economic models of groundwater management impose restrictive assumptions regarding perfect transmissivity (i.e., the aquifer behaves as a bathtub), no external effects of groundwater stocks, observability of individual extraction rates, and/or homogenous agents. In this article, we derive regulatory mechanisms for inducing the socially optimal extraction path in Markov perfect equilibrium for aquifers in which these assumptions do not hold. In spite of the complexity of the underlying system, we identify an interesting case in which a simple linear mechanism achieves the social optimum. To illustrate potential problems that can arise by erroneously imposing simplifying assumptions, we conduct a simulation based on data from the Indian state of Andhra Pradesh.Common Property Resource, Differential Games, Groundwater Extraction, Imperfect Monitoring, Markov Perfect Equilibrium

Ambiguous Aggregation of Expert Opinions: The Case of Optimal R&D Investment

How should a decision-maker allocate R&D funds when a group of experts provides divergent estimates on a technology's potential effectiveness? To address this question, we propose a simple decision-theoretic framework that takes into account ambiguity over the aggregation of expert opinion and a decision-maker's attitude towards it. In line with the paper's focus on R&D investment, decision variables in our model may affect experts' subjective probability distributions of the future potential of a technology. Using results from convex optimization, we are able to establish a number of analytical results including a closed-form expression of our model's value function, as well as a thorough investigation of its differentiability properties. We apply our framework to original data from a recent expert elicitation survey on solar technology. The analysis suggests that more aggressive investment in solar technology R&D is likely to yield significant dividends even, or rather especially, after taking ambiguous aggregation into account.Aggregation, Ambiguity, R&D, Expert Opinions, Convex/Conic Optimization

Minimizing Regret when Dissolving a Partnership

We study the problem of dissolving an equal-entitlement partnership when the objective is to minimize maximum regret. We initially focus on the family of linear-pricing mechanisms and derive regret-optimizing strategies. We also demonstrate that there exist linear-pricing mechanisms satisfying ex-post efficiency. Next, we analyze a binary-search mechanism which is ex-post individually rational. We discuss connections with the standard Bayesian-Nash framework for both linear and binary-search mechanisms. On a more general level, we show that if entitlements are unequal, ex-post efficiency and ex-post individual rationality impose significant restrictions on permissible mechanisms. In particular, they rule out both linear and binary-search mechanisms

Dynamic nonpoint-source pollution control policy: ambient transfers and uncertainty

When a regulator cannot observe or infer individual emissions, corrective policy must rely on ambient pollution data. Assuming this kind of environment, we study a class of differential games of pollution control with profit functions that are polynomial in the global pollution stock. Given an open-loop emissions strategy satisfying mild regularity conditions, an ambient transfer scheme is exhibited that induces it in Markov-perfect equilibrium (MPE). Proposed transfers are a polynomial function of the difference between actual and desired pollution levels; moreover, they are designed so that in MPE no tax or subsidy is ever levied. Their applicability under stochastic pollution dynamics is studied for a symmetric game of polluting oligopolists with linear demand. We discuss a quadratic scheme that induces agents to adopt Markovian emissions strategies that are stationary and linearly decreasing in total pollution. Total expected ambient transfers are non-positive and their magnitude is linearly increasing in physical volatility, the size of the economy, and the absolute value of the slope of the inverse demand function. However, if the regulator is interested in inducing a constant emissions strategy then, in expectation, transfers vanish. The total expected ambient transfer is compared to its point-source equivalent

Contract farming with possible reneging in a developing country: Can it work?

Abstract We consider a processed-food manufacturer that faces uncertain exogenous demand and procures a farm crop either from the outside market or from local farmers via contract farming. The contract price is determined at the beginning of the season when the market price is still uncertain. When the market price is realised, we allow the farmer the possibility of reneging from the contract, which occurs if the market price is sufficiently high. We show that granting farmers the option of reneging on the contract may improve the manufacturer's expected profit, and identify the conditions under which such an improvement can be expected

Investing in Mobility: Freight Transport in the Hudson Region

Proposes a framework for assessing alternative investments in freight rail, highway, and transit capacity that would increase the ability to improve mobility and air quality in the New York metropolitan area