Matching soulmates

We study iterated matching of soulmates (IMS), a recursive process of forming coalitions that are mutually preferred by members to any other coalition containing individuals as yet unmatched by this process. If all players can be matched this way, preferences are IMS-complete. A mechanism is a soulmate mechanism if it allows the formation of all soulmate coalitions. Our model follows Banerjee, Konishi, and Sönmez, except reported preferences are strategic variables. We investigate the incentive and stability properties of soulmate mechanisms. In contrast to prior literature, we do not impose conditions that ensure IMS-completeness. A fundamental result is that, (1) any group of players who could change their reported preferences and mutually benefit does not contain any players who were matched as soulmates and reported their preferences truthfully. As corollaries, (2) for any IMS-complete profile, soulmate mechanisms have a truthful strong Nash equilibrium, and (3) as long as all players matched as soulmates report their preferences truthfully, there is no incentive for any to deviate. Moreover, (4) soulmate coalitions are invariant core coalitions—that is, any soulmate coalition will be a coalition in every outcome in the core. To accompany our theoretical results, we present real-world data analysis and simulations that highlight the prevalence of situations in which many, but not all, players can be matched as soulmates. In the Appendix we relate IMS to other well-known coalition formation processes.     

Regulated Competition under Increasing Returns to Scale

In the classical models of regulation economics, a mechanism that secures truthful revelation involves paying a subsidy to the firm. In this paper, we investigate whether it is possible to create a regulatory mechanism under a no‐subsidy constraint that induces the firm to report its private information truthfully. We consider a number of firms operating under regulated competition and with increasing returns to scale technology. It is shown that in equilibrium each firm chooses to report truthfully without receiving any subsidy. The use of competition may give rise to an efficiency loss due to the increasing returns to scale. However, we show that our mechanism may still be better, from a social welfare point of view, than the case of monopoly regulation that involves no subsidy.     

The communication cost of selfishness

We consider how many bits need to be exchanged to implement a given decision rule when the mechanism must be ex post or Bayesian incentive compatible. For ex post incentive compatibility, the communication protocol must reveal enough information to calculate monetary transfers to the agents to motivate them to be truthful (agents' payoffs are assumed to be quasilinear in such transfers). For Bayesian incentive compatibility, the protocol may need to hide some information from the agents to prevent deviations contingent on the information. In both settings with selfish agents, the communication cost can be higher than in the case in which the agents are honest and can be relied upon to report truthfully. The increase is the “communication cost of selfishness.” We provide an exponential upper bound on the increase. We show that the bound is tight in the Bayesian setting, but we do not know this in the ex post setting. We describe some cases where the communication cost of selfishness proves to be very low.     

A solution to the random assignment problem on the full preference domain

We consider the problem of allocating a set of indivisible objects to agents in a fair and efficient manner. In a recent paper, Bogomolnaia and Moulin consider the case in which all agents have strict preferences, and propose the probabilistic serial (PS) mechanism; they define a new notion of efficiency, called ordinal efficiency, and prove that the probabilistic serial mechanism finds an envy-free ordinally efficient assignment. However, the restrictive assumption of strict preferences is critical to their algorithm. Our main contribution is an analogous algorithm for the full preference domain in which agents are allowed to be indifferent between objects. Our algorithm is based on a reinterpretation of the PS mechanism as an iterative algorithm to compute a “flow” in an associated network. In addition we show that on the full preference domain it is impossible for even a weak strategyproof mechanism to find a random assignment that is both ordinally efficient and envy-free.     

Incentives in the probabilistic serial mechanism

The probabilistic serial mechanism (Bogomolnaia and Moulin, 2001 [9]) is ordinally efficient but not strategy-proof. We study incentives in the probabilistic serial mechanism for large assignment problems. We establish that for a fixed set of object types and an agent with a given expected utility function, if there are sufficiently many copies of each object type, then reporting ordinal preferences truthfully is a weakly dominant strategy for the agent (regardless of the number of other agents and their preferences). The non-manipulability and the ordinal efficiency of the probabilistic serial mechanism support its implementation instead of random serial dictatorship in large assignment problems.     

Eliciting Subjective Beliefs about Mortality Risk Orderings

We develop an experimental method to elicit subjective beliefs about the ordering of mortality risk over different causes of death. The experimental procedure emphasizes incentive-compatibility, so that the individual has a positive financial incentive to respond truthfully. We also consider the extent to which individuals have subjective beliefs for sub-segments of the population that are more accurate than their beliefs about the risks for the population as a whole. We propose several hypotheses concerning the degree of familiarity of the risks, and find that the evidence supports those hypotheses. The evidence also suggests that there is no discernible difference between beliefs elicited using hypothetical or real financial rewards in the elicitation format we use. Our findings restore some confidence in the ability to elicit beliefs about mortality risks, and therefore to get reliable estimates of the monetary value of a statistical life. We dedicate this paper to the memory of J. Clay Lesley, who assisted us in the design and execution of the experiments and was a valued student, colleague and friend.     

Group robust stability in matching markets

We introduce the notion of group robust stability which requires robustness against a combined manipulation, first misreporting preferences and then rematching, by any group of students in the school choice type of matching markets. Our first result shows that there is no group robustly stable mechanism even under acyclic priority structures. Next, we define a weak version of group robust stability, called weak group robust stability. Our main theorem, then, proves that there is a weakly group robustly stable mechanism if and only if the priority structure of schools is acyclic, and in that case, it coincides with the student-optimal stable mechanism.     

Cheating to win: Dishonesty and the intensity of competition

We argue that the intensity of competition within a group or organization can have an important influence on whether or not people cheat. To make this point we first work through a simple model of strategic misreporting in the workplace. For low and high levels of competition we show that, in equilibrium, few are predicted to misreport. It is for medium levels of competition that misreporting is predicted to be highest. We test this prediction experimentally and find good support for it. This finding has implications for the design of incentive structures within groups and organizations.     

Robustness of simple menus of contracts in cost-based procurement

We consider a model of cost-based procurement in which the principal faces Knightian uncertainty about the agent's preferences for cost reduction. We show that a particularly simple incentive scheme—a menu comprising a fixed-price contract and a cost-reimbursement contract—minimizes the maximum expected payment, where this maximum is taken over the set of possible agent preferences. For some parameters of the problem, a range of alternative incentive schemes also satisfy this criterion. We show that the simple incentive scheme is not weakly dominated by any of the alternatives: there does not exist an alternative mechanism for which the expected payment is no higher for all realizations of the agent's preferences and strictly lower for some realization.     

Equity vs. efficiency vs. self-interest: on the use of dictator games to measure distributional preferences

We conduct modified dictator games in which price of giving varies across choice situations, and examine responses to price changes in two contexts—one where dictators divide their own earnings, and another where they divide the earnings of others. Varying the price of giving allows us to decompose social preferences into two components: the level of altruism when the price of giving is one, and the willingness to reduce aggregate payoffs to enhance equity. Changing the source of a dictator’s budget impacts her decisions because it affects the weight that she places on others’ payoffs. However, we find no impacts on the willingness to trade off equity and efficiency.     

GRANTING AN EXIT OPTION TO CONDUCT AN AUDIT

We study a principal–agent relationship with auditing in which information from an audit is ‘soft’– by conducting an audit, the principal observes the agent's private information, but cannot obtain verifiable evidence on the information. Moreover, the principal's auditing effort is unverifiable in our model. Therefore, besides the agent's misreporting incentive, there is the principal's incentive to accuse the truthful agent even without auditing. If the principal's auditing effort is verifiable, granting no exit option to the agent is optimal although the principal can still accuse a truthful agent after the audit. We show that when the principal's auditing effort is unverifiable, granting an exit option to the agent and auditing are complementary. Without granting an exit option to the agent, no auditing is optimal, and the principal grants an exit option to conduct a sincere audit, which in turn mitigates the agent's misreporting incentive. Our analysis also reveals that, when the cost of auditing is sufficiently large, the principal conducts more sincere audits with a smaller amount of penalty.     

Group incentive compatibility for matching with contracts

Hatfield and Milgrom [Hatfield, John William, Milgrom, Paul R., 2005. Matching with contracts. Amer. Econ. Rev. 95, 913–935] present a unified model of matching with contracts, which includes the standard two-sided matching and some package auction models as special cases. They show that the doctor-optimal stable mechanism is strategy-proof for doctors if hospitals' preferences satisfy substitutes and the law of aggregate demand. We show that the doctor-optimal stable mechanism is group strategy-proof for doctors under these same conditions. That is, no group of doctors can make each of its members strictly better off by jointly misreporting their preferences. We derive as a corollary of this result that no individually rational allocation is preferred by all the doctors to the doctor-optimal stable allocation.     

Group incentive compatibility for matching with contracts

Hatfield and Milgrom [Hatfield, John William, Milgrom, Paul R., 2005. Matching with contracts. Amer. Econ. Rev. 95, 913–935] present a unified model of matching with contracts, which includes the standard two-sided matching and some package auction models as special cases. They show that the doctor-optimal stable mechanism is strategy-proof for doctors if hospitals' preferences satisfy substitutes and the law of aggregate demand. We show that the doctor-optimal stable mechanism is group strategy-proof for doctors under these same conditions. That is, no group of doctors can make each of its members strictly better off by jointly misreporting their preferences. We derive as a corollary of this result that no individually rational allocation is preferred by all the doctors to the doctor-optimal stable allocation.     

Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare.We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium.We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small.     

A dual characterization of incentive efficiency

We show that incentive efficient allocations in economies with adverse selection and moral hazard problems can be determined as optimal solutions to a linear programming problem and we use duality theory to obtain a complete characterization of the optima. Our dual analysis identifies welfare effects associated with the incentives of the agents to truthfully reveal their private information. Because these welfare effects may generate non-convexities, incentive efficient allocations may involve randomization. Other properties of incentive efficient allocations are also derived.     

A contest with the taxman - the impact of tax rates on tax evasion and wastefully invested resources

We develop a moral hazard model with auditing where both the principal and the agent can influence the probability that the true state of nature is verified. This setting is widely applicable for situations where fraudulent reporting with costly state verification takes place. However, we use the framework to investigate tax evasion. We model tax evasion as a concealment-detection contest between the taxpayer and the authority. We show that higher tax rates cause more evasion and increase the resources wasted in the contest. Additionally, we find conditions under which a government should enforce incentive compatible auditing in order to reduce wasted resources.     

Demand Revelation,Hypothetical Bias,and Threshold Public Goods Provision

We examine the issues of hypothetical bias, demand revelation, and gender differences in a threshold public goods experiment with heterogeneous induced-values. First, we find no evidence of hypothetical bias in our threshold provision public goods experiments, despite the fact this is an open-ended type mechanism. Our results support recent experimental findings that use induced-values to investigate hypothetical bias. Second, we investigate the demand revealing performance of real and hypothetical payments and find no evidence that real payment performs better than hypothetical payment in our experiments. Third, we examine whether payments, real and hypothetical, are positively related to induced-values. Our results suggest there is statistical evidence that payments are positively related to true values. Finally, we examine the effect of gender on real and hypothetical payments in our experiment. The results show that gender matters for contributions through both real and hypothetical payments, after controlling for true values as well as socio-economic variables. Results also indicate that females are more likely to truthfully reveal their value than males through hypothetical payments, but gender is not significant for truthfully revealing their value through real payments.     

The role of private benefits in information acquisition

In many cases, the cost of hiring an agent to acquire information is lower than the cost for the principal to perform that task. However, because of a difference in preferences between the principal and the agent, the principal often cannot fully utilize the agent’s expertise. This paper considers the cost of motivating the agent to acquire information and inducing him to report truthfully. The larger the private benefit, the greater is the cost of eliciting true information. At the same time, a private benefit may reduce the cost of motivating information acquisition. Thus, there are cases in which an agent with a different preference is desirable.     

The dynamics of environmentalism and the environment

We study the relationship between environmental preferences and the environment. Preferences are transmitted intergenerationally and through social interactions, where we assume that agents are more likely to adopt environmental preferences the larger the amount of pollution. In the basic setting we find that both converge non-monotonically towards an interior steady state. When including technical change we notice that there will be no change in the steady state level of the environment unless technical change is sufficiently strong, which stands in stark contrast to the literature. Upon introducing environmental laws we find that these may lead to a virtually pollution-free environment. This happens if environmental laws are implemented when public support is strong enough.     

Collusive dominant-strategy truthfulness

We show that collusion and wrong beliefs may cause a dramatic efficiency loss in the Vickrey mechanism for auctioning a single good in limited supply. We thus put forward a new mechanism guaranteeing efficiency in a very adversarial collusion model, where the players can partition themselves into arbitrarily many coalitions, exchange money with each other, and perfectly coordinate their actions. Our mechanism bypasses classic impossibility results (such as those of Green and Laffont, and of Schummer) by providing the players with a richer set of strategies, making it dominant for every coalition C to instruct each of its members to report truthfully not only his own valuation, but also his belonging to C. Our mechanism is coalitionally rational, which implies being individually rational for independent players.