A Simple Selling and Buying Procedure

For the assignment game, we analyze the following mechanism. Sellers, simultaneously, fix their prices first. Then buyers, sequentially, decide which object to buy. Also, each buyer may report his or her indifferences (along with the previous buyers' indifferences) to the following buyer. The first phase determines the potential prices, while the second phase determines the actual matching. Reporting truthfully the indifferences is always a dominant strategy for the buyers. Moreover, when buyers state their true indifferences, the subgame perfect equilibria outcomes of the mechanism correspond to the maximum equilibrium price vector together with optimal matchings. Journal of Economic Literature Classification Numbers: C78, D78.     

Ordinal efficiency and dominated sets of assignments

Using lotteries is a common tool for allocating indivisible goods. Since obtaining preferences over lotteries is often difficult, real-life mechanisms usually rely on ordinal preferences over deterministic outcomes. Bogomolnaia and Moulin (J. Econom. Theory 19 (2002) 623) show that the outcome of an ex post efficient mechanism may be stochastically dominated. They define a random assignment to be ordinally efficient if and only if it is not stochastically dominated. In this paper we investigate the relation between ex post efficiency and ordinal efficiency. We introduce a new notion of domination defined over sets of assignments and show that a lottery induces an ordinally efficient random assignment if and only if each subset of the full support of the lottery is undominated.     

Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem

We study problems in which each of finitely many agents must be allocated a single object, based on the agents' rankings of pure outcomes. A random allocation is ordinally efficient if it is not ordinally dominated in the sense of there being another random assignment that gives each agent a first order stochastically dominant distribution of objects. We show that any ordinally efficient random assignment maximizes the sum of expected utilities for some vector of vNM utility functions that are consistent with the given ordinal preferences. One method of proof uses a new version of the separating hyperplane theorem for polyhedra. Journal of Economic Literature Classification Numbers: C78, D61.     

The roommates problem revisited

One of the oldest matching problems is Gale and Shapley's (1962) [8] “roommates problem”: is there a stable way to assign 2N students into N roommate pairs? Unlike the classic marriage problem or college admissions problem, there need not exist a stable solution to the roommates problem. However, stability ignores the key physical constraint that roommates require a room and is therefore too restrictive. This motivates a new matching problem: matching agents subject to an initial assignment. A particularly important example is kidney exchange where after an assignment has been made, subsequent tests may determine that a patient and donor are incompatible. This paper introduces an efficient algorithm for finding a Pareto improvement starting from any status quo roommates assignment.     

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.     

The most ordinally egalitarian of random voting rules

Aziz and Stursberg propose an “Egalitarian Simultaneous Reservation” rule (ESR), a generalization of Serial rule, one of the most discussed mechanisms in the random assignment problem, to the more general random social choice domain. This article provides an alternative definition, or characterization, of ESR as the unique most ordinally egalitarian one. Specifically, given a lottery p over alternatives, for each agent i the author considers the total probability share in p of objects from her first k indifference classes. ESR is shown to be the unique one which leximin maximizes the vector of all such shares (calculated for all i, k). Serial rule is known to be characterized by the same property. Thus, the author provides an alternative way to show that ESR, indeed, coincides with Serial rule on the assignment domain. Moreover, since both rules are defined as the unique most ordinally egalitarian ones, the result shows that ESR is “the right way” to think about generalizing Serial rule.     

The probabilistic serial mechanism with private endowments

A random assignment is ordinally efficient if it is not stochastically dominated with respect to individual preferences over sure objects. When there are no private endowments, the set of ordinally efficient random assignments is characterized by the eating algorithm (Bogomolnaia and Moulin, 2001). When there are private endowments, the main requirement is individual rationality; however, the eating algorithm fails to deliver this property. Our contribution is the natural generalization of the eating algorithm for this general class of problems. The family of this generalized eating algorithm characterizes the set of individually rational and ordinally efficient random assignments. A special solution in this family, the individually rational probabilistic serial (${\mathrm{PS}}^{\mathbf{IR}}$), also achieves a new fairness axiom, no justified-envy. However, it is not immune to strategic manipulation. We show that individual rationality, no justified-envy and strategy-proofness are incompatible.     

The rate of convergence to perfect competition of matching and bargaining mechanisms

We study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information. A friction parameter is τ, the length of the time period until the next meeting. We provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in τ, which is shown to be the fastest possible among all bargaining mechanisms. The condition requires that buyers and sellers always retain some bargaining power. The bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power (NBP) mechanisms. Simple random proposer take-it-or-leave-it protocols are NBP, while k-double auctions (k-DA) are not. We find that k-DAs have equilibria that converge to perfect competition at a linear rate, converge at a slower rate or even do not converge at all.     

Strategy-proof assignment on the full preference domain

We consider the problem of efficiently allocating several indivisible objects between agents who are to receive at most one object and whose preferences are private information. We examine this standard “assignment” problem from the perspective of mechanism design giving up the usual assumption of linear preferences and instead using a full preference domain (with indifferences permitted). We characterize two classes of mechanisms: (i) Bi-polar Serially Dictatorial Rules by Essential Single-Valuedness, Pareto Indifference, Strategy-Proofness and Non-Bossiness; and (ii) all selections from Bi-polar Serially Dictatorial Rules by Single-Valuedness, Efficiency, Strategy-Proofness and Weak Non-Bossiness. We compare the outcomes from the (Bi-polar) Serially Dictatorial Rules with the outcomes obtained using a market based approach, namely the “core” of the market. We show that all strongly efficient outcomes in the core can be generated using Serially Dictatorial Rules. Moreover, we argue that Serially Dictatorial Rules have an advantage over the market based approach in that they yield strongly efficient solutions for all preference profiles, making it possible to use randomization to restore equity. When preferences are private information, this type of ex ante equity cannot be implemented using the market based approach.     

Estimating VARs with long stationary heterogeneous panels: A comparison of the fixed effect and the mean group estimators

The most promising candidates for estimating vector autoregressive models with long, stationary, possibly heterogeneous panel data sets (panel-VARs) are the fixed effect (FE) and the mean group (MG) estimators. With a view to providing guidance to applied researchers on how to pool in a panel-VAR, this paper compares the performance of the FE and the MG estimators both asymptotically and in Monte Carlo simulations. The main results of the analysis suggest the use of both estimators in applied work. If FE and MG estimates give similar estimates, the FE estimator should be used because it is more efficient. If they differ, the MG estimator should be used only if the panel is sufficiently long — say, twice as long as usually recommended in the dynamic panel data literature. If FE and MG estimates differ and the panel is not long enough, neither is generally a desirable alternative and other estimation techniques are needed.     

Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

There is a wide range of economic problems that involve the exchange of indivisible goods with no monetary transfers, starting from the housing market model of the seminal paper by Shapley and Scarf (1974) to problems such as the kidney exchange or the school choice problem. The classical solution to many of these models is to apply a mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalize the Top Trading Cycles to the general case in which individuals are allowed to report indifferences, while preserving a maximal possible set of its desirable properties.     

Proper belief revision and equilibrium in dynamic games

We present a theory of rationality in dynamic games in which players, during the course of the game, may revise their beliefs about the opponents’ utility functions. The theory is based upon the following three principles: (1) the players’ initial beliefs about the opponents’ utilities should agree on some profile u of utility functions, (2) every player should believe, at each of his information sets, that his opponents are carrying out optimal strategies and (3) a player at information set h should not change his belief about an opponent's ranking of strategies a and b if both a and b could have led to h. Scenarios with these properties are called preference conjecture equilibria for the profile u of utility functions. We show that every normal form proper equilibrium for u induces a preference conjecture equilibrium for u, thus implying existence of preference conjecture equilibrium.     

A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game

It is well-known that a transferable utility game has a non-empty core if and only if it is balanced. In the class of non-transferable utility games balancedness or the more general π-balancedness due to Billera (SIAM J. Appl. Math. 18 (1970) 567) is a sufficient, but not a necessary condition for the core to be non-empty. This paper gives a natural extension of the π-balancedness condition that is both necessary and sufficient for non-emptiness of the core.     

Bargaining and network structure: An experiment

We consider bargaining in a bipartite network of buyers and sellers, who can only trade with the limited number of people with whom they are connected. We perform an experimental test of a graph-theoretic model that yields unique predictions about equilibrium prices for the networks in our sessions. The results diverge sharply depending on how a connection is made between two separate simple networks, typically conforming to the theoretical directional predictions. Payoffs can be systematically affected even for agents who are not connected by the new link, and we find evidence of a form of social learning.     

Rebate rules in threshold public good provision

This paper considers how six alternative rebate rules affect voluntary contributions in a threshold public-good experiment. The rules differ by (1) whether an individual can receive a proportional rebate of excess contributions, a winner-takes-all of any excess contributions, or a full rebate of one's contribution in the event the public good is provided and excess contributions exist, and (2) whether the probability of receiving a rebate is proportional to an individual's contribution relative to total contributions or is a simple uniform probability distribution set by the number of contributors. The paper adds to the existing experimental economics literature on threshold public goods by investigating both aggregate and individual demand revelation under the winner-take-all and random full-rebate rules. Half of the rules (proportional rebate, winner-take-all with uniform probability among all group members, and random full-rebate with uniform probability) provide total contributions that nearly equal total benefits, while the rest (winner-take-all with proportional probability, winner-take-all with uniform probability among contributors only, and random full-rebate with proportional probability) exceed benefits by over 30%. Only the proportional rebate rule is found to achieve both aggregate and individual demand revelation. Our experimental results have implications for both fundraisers and valuation practitioners.     

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.     

Risk-dominance and perfect foresight dynamics in N-player games

In perfect foresight dynamics, an action is linearly stable if expectation that people will always choose the action is self-fulfilling. A symmetric game is a PIM game if an opponent's particular action maximizes the incentive of an action, independently of the rest of the players. This class includes supermodular games, games with linear incentives and so forth. We show that, in PIM games, linear stability is equivalent to u-dominance, a generalization of risk-dominance, and that there is no path escaping a u-dominant equilibrium. Existing results on N-player coordination games, games with linear incentives and two-player games are obtained as corollaries.     

Cheap talk in games with incomplete information

The paper studies Bayesian games which are extended by adding pre-play communication. Let Γ be a Bayesian game with full support and with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e., involves probabilities that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of Γ, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in Γ such that for each type t_i of each player i the expected payoff of t_i in q is larger than the expected payoff of t_i in s.     

Equality of opportunity and luck: Definitions and testable conditions,with an application to income in France

We offer a model of equality of opportunity that encompasses different conceptions expressed in the public and philosophical debates. In addition to circumstances whose effect on outcome should be compensated and effort which represents a legitimate source of inequality, we introduce a third factor, luck, that captures the random factors whose impact on outcome should be even-handed for equality of opportunity to be satisfied. Then, we analyze how the various definitions of equality of opportunity can be empirically identified, given data limitations and provide testable conditions. Definitions and conditions resort to standard stochastic dominance tools. Lastly, we develop an empirical analysis of equality of opportunity for income acquisition in France over the period 1979–2000 which reveals that the degree of inequality of opportunity tends to decrease and that the degree of risk of income distributions, conditional on social origin, appears very similar across all groups of social origins.     

A simple sufficient condition for strong implementation

In an important step forward Maskin [E. Maskin, Nash equilibrium and welfare optimality, Rev. Econ. Stud. 66 (1999) 23–38] showed that two properties – monotonicity and no veto power – are together sufficient for Nash implementation. In contrast to the vast literature that followed, this characterization has two major advantages: First, it is often easy to verify, and second, it has an elegant and simple interpretation. However, there does not exist a similar condition for social choice correspondences that are implementable in strong equilibrium. All existing characterizations are either hard to verify or apply only to comprehensive preference domains. In this paper we improve the situation by giving one such condition. Moreover, using well-known examples we show that this is a practical tool.