Optimal collusion-resistant mechanisms with verification

We present the first general positive result on the construction of collusion-resistant mechanisms, that is, mechanisms that guarantee dominant strategies even when agents can form arbitrary coalitions and exchange compensations (sometimes referred to as transferable utilities or side payments). This is a much stronger solution concept as compared to truthful or even group strategyproof mechanisms, and only impossibility results were known for this type of mechanisms in the “classical” model.We describe collusion-resistant mechanisms with verification that return optimal solutions for a wide class of mechanism design problems (which includes utilitarian ones as a special case). Note that every collusion-resistant mechanism without verification must have an unbounded approximation factor and, in general, optimal solutions cannot be obtained even if we content ourselves with truthful (“non-collusion-resistant”) mechanisms. All these results apply to problems that have been extensively studied in the algorithmic mechanism design literature like, for instance, task scheduling and inter-domain routing.     

Assigning agents to a line

We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. Our focus is on aggregate gap minimizing methods, i.e., those that minimize the total gap between targets and assigned slots. We first consider deterministic assignment of agents to slots, and provide a direct method for testing if a given deterministic assignment is aggregate gap minimizing. We then consider probabilistic assignment of agents to slots, and make use of the previous method to propose an aggregate gap minimizing modification of the classic random priority method to solve this class of problems. We also provide some logical relations in our setting among standard axioms in the literature on assignment problems, and explore the robustness of our results to several extensions of our setting.     

An ordinal Shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for transferable utility (TU) games. We show a solution exists, and call it the ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous.     

Minimum cost arborescences

In this paper, we analyze the cost allocation problem when a group of agents or nodes have to be connected to a source, and where the cost matrix describing the cost of connecting each pair of agents is not necessarily symmetric, thus extending the well-studied problem of minimum cost spanning tree games, where the costs are assumed to be symmetric. The focus is on rules which satisfy axioms representing incentive and fairness properties. We show that while some results are similar, there are also significant differences between the frameworks corresponding to symmetric and asymmetric cost matrices.     

Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. Our main result is the characterization of the class of Pareto optimal and coalitionally strategy-proof allocation rules. Alternatively, this class of rules, which largely consists of serially dictatorial components, can be characterized by Pareto optimality, strategy-proofness, and weak non-bossiness (in terms of welfare). Furthermore, we study properties of fairness such as anonymity and no-envy. Journal of Economic Literature Classification Numbers: D63, D71.     

Implementation with partial provability

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agents? preferences or beliefs and agents need little information about each others? preferences. Our results are robust to evidence forgery at any strictly positive cost.     

When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds

We study the problem of rationing a divisible good among a group of people. Each person?s preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: any amount less than this threshold is just as good as receiving nothing at all. Any amount beyond his ideal quantity has no effect on his welfare.We search for Pareto-efficient, strategy-proof, and envy-free rules. The definitions of these axioms carry through from the more commonly studied problem without disposability or acceptance thresholds. However, these are not compatible in the model that we study. We adapt the equal-division lower bound axiom and propose another fairness axiom called awardee-envy-freeness. Unfortunately, these are also incompatible with strategy-proofness. We characterize all of the Pareto-efficient rules that satisfy these two properties. We also characterize all Pareto-efficient, strategy-proof, and non-bossy rules.     

Adoption externalities as public goods

A public good problem arises naturally in situations characterized by positive externalities or negative externalities. For positive externalities, agents furnish a public good by taking an action. Similarly, for negative externalities, agents furnish a public good by not taking an action. We examine these externalities in a binary choice problem, i.e. adoption externalities. In each case, there is a potential role for government intervention, even when equilibrium transfers are not allowed, since one equilibrium Pareto dominates all others. We analyze the positive and normative features of equilibria in these models, and we explore the possibility of useful government intervention.     

On the existence of lindahl equilibria in economies with a measure space of non-transitive consumers

We present a generalization of Roberts' theorem on the existence of Lindahl equilibria in economies with a measure space of agents. The principal contribution of this paper is methodological. We show that by formulating the problem in what we consider to be its natural infinite dimensional setting, the basic structure of Debreu's proof in the theory of value can be applied. Our proof makes use of functional analysis and relies, in particular, on Artstein's characterization of weak sequential convergence in L₁(μ).     

Problems of fair division and the Egalitarian solution

The problem of fair division is considered in situations where the number of agents among whom the division is to take place may vary. The approach is axiomatic. Along with four familiar axioms, Weak Pareto-optimality, Symmetry, Independence of Irrelevant Alternatives, and Continuity, a new axiom, named Monotonicity with Respect to Changes in the Number of Agents, is imposed, expressing a certain form of solidarity among the agents as their number varies but the resources at their disposal remain fixed. The only solution to satisfy these axioms is the Egalitarian solution, which selects the only feasible alternative that yields equal utilities to all agents and is undominated by any other feasible alternative.     

The nature of tournaments

This paper characterizes the optimal way for a principal to structure a rank-order tournament in a moral hazard setting (as in Lazear and Rosen in J Polit Econ 89:841?C864, 1981). We find that it is often optimal to give rewards to top performers that are smaller in magnitude than corresponding punishments to poor performers. The paper identifies four reasons why the principal might prefer to give larger rewards than punishments: (1) R is small relative to P (where R is risk aversion and P is absolute prudence); (2) the distribution of shocks to output is asymmetric and the asymmetry takes a particular form; (3) the principal faces a limited liability constraint; and (4) there is agent heterogeneity of a particular form.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

Organizational performance in hierarchies and communities of practice

In an earlier article we studied the Communities of Practice and their conditions of emergence using an Agent based model with a set of agents facing a continuous flow of problems. We now center our analysis on the performance of this organizational structure compared to a two-level hierarchical delegation structure. Our results show the crucial role played by the communication and the specialisation of agents; especially that community structures are efficient for competence building and learning in the long term. This paper backs the claim made by (Bowles, S., Gintis, H., 2002. Social capital and community governance. The Economic Journal 112, 419–437.) that hierarchy and communities are complementary modes of governance.     

Exploring group decision making in a power-to-take experiment

Most studies that compare individual and group behavior neglect the in-group decision making process. This paper explores the decision making process within groups in a strategic setting: a two player power-to-take experiment. Discussions preceding group decisions are video taped and analyzed. We find the following: (1) no impact of the group setting as such on individual behavior; (2) heterogeneity of individual types; (3) perceptions of fairness are hardly discussed and are prone to the self-serving bias; (4) groups ignore the decision rule of other groups and typically view them as if they were single agents. (5) We also show that to explain group outcomes two factors have to be taken into account that are often neglected: the distribution of individual types over groups and the decision rules that groups use to arrive at their decision. JEL Classification A12 · C72 · C91 · C92     

Influential listeners: An experiment on persuasion bias in social networks

This paper presents an experimental investigation of persuasion bias, a form of bounded rationality whereby agents communicating through a social network are unable to account for repetitions in the information they receive. We find that, after repeated communication within a social network, social influence depends not only on being listened to by many others, but also on listening to many others. We show that persuasion bias can be viewed as an extreme case of a generalized boundedly rational updating rule in which agents receive more or less attention depending on how many other agents they listen to. The results indicate that behavior in the experiment is consistent with an updating rule according to which agents' social influence is proportional to their indegree.     

Saddle point property and Hopf bifurcation in continuous optimal growth models: a Lagrangian approach

Conditions for saddle point property, and the loss of it, have been widely studied. Generally these properties are established by means of a Hamiltonian formalism; we propose here to work without reference to any Hamiltonian system, and to use only the Lagrangian.Our study is local; it may seem that no new result can be obtained in this setting; nevertheless we establish sufficient conditions for the loss of saddle point property and for the existence of periodic orbits which, to our knowledge, are not found in the literature.We take the standard assumption that the Lagrangian is concave. It is well known that the cross derivatives of the Hamiltonian (i.e. H_xp(x, p)) are important in these problems, but the concavity-convexity property of the Hamiltonian does not easily give any information on these derivatives. On the other hand, we obtain such information directly in the Lagrangian version, because the Lagrangian is concave on its two arguments.We give here a self-contained version of our results and we do not hesitate to re-establish some well-known results, because we believe it is interesting to underline the straightforward aspect of the Lagrangian approach.     

Preference submission timing in school choice matching: testing fairness and efficiency in the laboratory

We investigate the relative merits of the Boston and Serial Dictatorship mechanisms when the timing of students’ preference submission over schools varies within the structure of the mechanism. Despite the well-documented disadvantages of the Boston mechanism Abdulkadiroglu and Sonmez (American Economic Review 93:729–747 2003), we hypothesize that a Boston mechanism where students are required to submit their preferences before the realization of their exam scores, can in fact have fairness and efficiency advantages compared to the often favored Serial Dictatorship mechanism. We test these hypotheses in a series of laboratory experiments which vary by the class of mechanism implemented, and the preference submission timing by students, reflective of actual policy changes which have occurred in China. Our experimental findings confirm the efficiency hypothesis straightforwardly, and lend support to the fairness hypothesis when subjects have the chance to learn with experience. The results have important policy implications for school choice mechanism design when students’ relative rankings by schools are initially uncertain.     

Credibility and endogenous societal discounting

We consider a dynamic moral hazard economy inhabited by a planner and a population of privately informed agents. We assume that the planner and the agents share the same discount factor, but that the planner cannot commit. We show that optimal allocations in such settings solve the problems of committed planners who discount the future less heavily than agents. Thus, we provide micro-foundations for dynamic moral hazard models that assume a societal discount factor in excess of the private one. We extend the analysis to allocations that are reconsideration-proof in the sense of Kocherlakota [Kocherlakota, N., 1996. Reconsideration-proofness: A refinement for infinite horizon time inconsistency. Games and Economic Behavior 15, 33–54]. We show that these allocations solve the choice problem of a committed planner with a unit discount factor.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.