The efficiency of training and hiring with intrafirm bargaining

This paper demonstrates that firms hire and train workers efficiently in a matching and intrafirm bargaining economy when the Hosios condition holds and returns to scale are constant. This conclusion stands in contrast to the prevailing view that training costs are a source of inefficiency in imperfect labor markets. The efficiency of the competitive economy relies on the ability of large firms to take into account the negative impact of the training rate on the wages negotiated inside the firm through intrafirm bargaining: untrained workers accept a wage reduction in compensation for potential training that is accessible only following employment. This intrafirm bargaining process solves efficiency problems associated with training costs that would otherwise lead to inefficient hiring and training decisions. This conclusion holds true for both specific and general human capital.     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

Stable and efficient bargaining networks

Abstract. We examine a bargaining game among players connected by a network, where successively potential partners negotiate over terms of a project. For any network structure and ordering of selection of bargaining partners, there is a unique subgame perfect equilibrium outcome which coincides with the standard Rubinstein split. Based on this, we derive expected payoffs for players as a function of the network. We the characterize the pairwise stable and efficient bargaining networks. These two sets do not always coincide and in many situations pairwise stable networks are over-connected. Received: 10 April 2001 / Accepted: 17 January 2002 I am indebted to Matthew Jackson for suggesting this paper. I also thank Bernard Caillaud, Sanjeev Goyal, and the seminar participants at Universidad de Alicante, Universidad Carlos III de Madrid, CEMFI (Madrid), Universitat Autònoma de Barcelona, Erasmus University of Rotterdam, Universitat Pompeu Fabra (Barcelona) and CERAS (Paris) for helpful comments. This paper was written while at Universitat Pompeu Fabra and CERAS. Financial support from the Spanish Ministry of Education through research grant DGESIC PB96-0302, and from the Ecole Nationale des Ponts et Chaussées, Paris is gratefully acknowledged. All errors are of course mine.     

Competition among mechanism designers in a common value environment

A competitive economy is studied in which sellers offer alternative direct mechanisms to buyers who have private information about their own private use value for the commodity being traded. In addition the commodity has a common value to all buyers, perhaps represented by the future resale value of the commodity. A competitive equilibrium in mechanisms is described. In every such equilibrium it is shown that sellers must offer mechanisms that are allocationally equivalent to English ascending price auctions. The reservation prices that sellers set are shown to be below their ex post cost of trading the commodity. Received: 24 April 1998 / Accepted: 8 March 1999     

Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation

We characterize full implementation of social choice sets in mixed-strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu–Matsushima’s measurability, thereby implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.     

Learning in a multilateral bargaining experiment

This paper analyzes data from an investigation of a majoritarian bargaining experiment. A learning model is proposed to account for the evolution of play in this experiment. It is also suggested that an adjustment must be made to account for the panel structure of the data. Such adjustments have been used in other fields and are known to be important as unadjusted standard errors may be severely biased downward. These results indicate that this adjustment also has an important effect in this application. Furthermore, an efficient estimator that takes into account heterogeneity across players is proposed. A unique learning model to account for the paths of play under two different amendment rules cannot be rejected with the standard estimator with adjusted standard errors, however it can be rejected using the efficient estimator. The data and the estimated learning model suggest that after proposing “fair” divisions, subjects adapt and their proposals change rapidly in the treatment where uneven proposals are almost always accepted. Their beliefs in the estimated learning model are influenced by more than just the most recent outcomes.     

What restrictions do Bayesian games impose on the value of information?

In a Bayesian game players play an unknown game. Before the game starts some players may receive a signal regarding the specific game actually played. Typically, information structures that determine different signals, induce different equilibrium payoffs. In two-person zero-sum games the equilibrium payoff measures the value of the particular information structure which induces it. We pose a question as to what restrictions Bayesian games impose on the value of information. We provide answers for two kinds of information structures: symmetric, where both players are equally informed, and one-sided, where only one player is informed.     

Achieving the first best in sequencing problems

Abstract. In a sequencing problem with linear time cost, Suijs (1996) proved that it is possible to achieve first best. By first best we mean that one can find mechanisms that satisfy efficiency of decision, dominant strategy incentive compatibility and budget balancedness. In this paper we show that among a more general and natural class of sequencing problems, sequencing problems with linear cost is the only class for which first best can be achieved. Received: 2 December 1999/Accepted: 9 May 2001     

A non-cooperative interpretation of bargaining sets

This paper provides a non-cooperative interpretation for bargaining sets concepts in economic environments. We investigate the implementability of the Aumann-Maschler and Mas-Colell bargaining sets, and provide mechanisms whose subgame perfect equilibrium outcomes realize these sets. These mechanisms, in contrast to general mechanisms suggested in the implementation literature, have a natural structure closely related to that of the rationale underlying the bargaining sets. Furthermore, the strategy sets consist mainly of allocations and coalitions (thus avoiding any reference to preference parameters) and are finite dimensional. Received: 17 February 1997 / Accepted: 2 February 1999     

Empirical implementation of nonparametric first-price auction models

Nonparametric estimators provide a flexible means of uncovering salient features of auction data. Although these estimators are popular in the literature, many key features necessary for proper implementation have yet to be uncovered. Here we provide several suggestions for nonparametric estimation of first-price auction models. Specifically, we show how to impose monotonicity of the equilibrium bidding strategy; a key property of structural auction models not guaranteed in standard nonparametric estimation. We further develop methods for automatic bandwidth selection. Finally, we discuss how to impose monotonicity in auctions with differing numbers of bidders, reserve prices, and auction-specific characteristics. Finite sample performance is examined using simulated data as well as experimental auction data.     

Estimation of collective household models with Engel curves

The structural consumer demand methods used to estimate the parameters of collective household models are typically either very restrictive and easy to implement or very general and difficult to estimate. In this paper, we provide a middle ground. We adapt the very general framework of [Browning, M., Chiappori, P.A., Lewbel, A., 2004. Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power, Boston College Working Papers in Economics 588] by adding a simple restriction that recasts the empirical model from a highly nonlinear demand system with price variation to a slightly nonlinear Engel curve system. Our restriction has an interpretation in terms of the behaviour of household scale economies and is testable. Our method identifies the levels of (not just changes in) household resource shares, and a variant of equivalence scales called indifference scales. We apply our methodology to Canadian expenditure data.     

Timing of information in agency problems with hidden actions

This paper endogenizes in a standard hidden action model the point in time when a risk neutral and wealth constrained agent and the principal observe the realization of an additional signal: before the agent’s effort choice (ex ante information) or after (ex post information). In a decision problem, ex ante information does (weakly) better than ex post information because the decision maker can tailor efforts to the information. We show that this is not the case for incentive problems: a negative incentive effect arises under ex ante information that prevails even though the principal tailors the agent’s effort to the information.     

A note on the multiple partners assignment game

In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International Journal of Game Theory 1, 11–130] agents are allowed to form one partnership at most. That paper proves that, in the context of firms and workers, given two stable payoffs for the firms there is a stable payoff which gives each firm the larger of the two amounts and also one which gives each of them the smaller amount. Analogous result applies to the workers. Sotomayor [Sotomayor, M., 1992. The multiple partners game. In: Majumdar, M. (Ed.), Dynamics and Equilibrium: Essays in Honor to D. Gale. Mcmillian, pp. 322–336] extends this analysis to the case where both types of agents may form more than one partnership and an agent's payoff is multi-dimensional. Instead, this note concentrates in the total payoff of the agents. It is then proved the rather unexpected result that again the maximum of any pair of stable payoffs for the firms is stable but the minimum need not be, even if we restrict the multiplicity of partnerships to one of the sides.     

Efficient trading with nonlinear utility

In an environment in which agents have nonlinear utility and sufficiently asymmetric initial endowments, we show that efficient trading is achievable. This result is in contrast with Myerson and Satterthwaite (1983), which shows efficient trading is not possible if agents have linear utility and asymmetric initial endowments. Our result is also different from Cramton et al. (1987), in which they maintain the linear utility assumption as in Myerson and Satterthwaite but assume that traders’ initial endowments are relatively symmetric.     

National Estimates of Gross Employment and Job Flows from the Quarterly Workforce Indicators with Demographic and Industry Detail

The Quarterly Workforce Indicators (QWI) are local labor market data produced and released every quarter by the United States Census Bureau. Unlike any other local labor market series produced in the US or the rest of the world, QWI measure employment flows for workers (accession and separations), jobs (creations and destructions) and earnings for demographic subgroups (age and gender), economic industry (NAICS industry groups), detailed geography (block (experimental), county, Core-Based Statistical Area, and Workforce Investment Area), and ownership (private, all) with fully interacted publication tables. The current QWI data cover 47 states, about 98% of the private workforce in those states, and about 92% of all private employment in the entire economy. State participation is sufficiently extensive to permit us to present the first national estimates constructed from these data. We focus on worker, job, and excess (churning) reallocation rates, rather than on levels of the basic variables. This permits a comparison to existing series from the Job Openings and Labor Turnover Survey and the Business Employment Dynamics Series from the Bureau of Labor Statistics (BLS). The national estimates from the QWI are an important enhancement to existing series because they include demographic and industry detail for both worker and job flow data compiled from underlying micro-data that have been integrated at the job and establishment levels by the Longitudinal Employer-Household Dynamics Program at the Census Bureau. The estimates presented herein were compiled exclusively from public-use data series and are available for download.     

Corruption and auctions

We investigate how corruption affects the outcome of a first-price auction (bidding behavior, efficiency and the seller’s expected revenue). The auctioneer approaches the winner to offer the possibility of a reduction in his bid in exchange for a bribe. The bribe can be a percentage of the difference between the winning and the second-highest bid or a fixed amount. We show that there exists a symmetric bidding strategy equilibrium that is monotone, i.e., higher valuation buyers bid higher. Corruption does not affect efficiency but both the auctioneer’s expected bribe and the seller’s expected revenue depend on the format of the bribe payments. We also find the optimal bribe scheme.     

The Blocking Lemma for a many-to-one matching model

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.     

Strategy-proofness in many-to-one matching problems

We search forstrategy-proof solutions in the context of (many-to-one) matching problems (Gale and Shapley, 1962). In this model, whenever the firms can hire as many workers as they want (the capacities are unlimited) the stable set is a singleton. There exists aPareto efficient, individually rational, andstrategy-proof matching rule if and only if the capacities are unlimited. Furthermore, whenever the capacities unlimited, the matching rule which selects the unique stable matching is the only matching rule that isPareto efficient, individually rational, andstrategy-proof.     

Implementation of stable solutions in a restricted matching market

I analyze the admission mechanism used in Spanish universities. The system is open to strategic manipulation. This is because students are not allowed to express the whole list of available options. However, the mechanism implements the set of stable matchings in Nash equilibrium and the student's optimum in strong equilibrium. The mechanism also implements the students' optimum, in Nash equilibrium, under the class of “non-reverse” preferences. All these properties come from the fact that colleges do not have the opportunity to misrepresent their preferences. Received: 30 June 1995 / Accepted: 31 January 1997     

Fairness and implementability in allocation of indivisible objects with monetary compensations

This paper introduces a general framework for the fair allocation of indivisible objects when each agent can consume at most one (e.g., houses, jobs, queuing positions) and monetary compensations are possible. This framework enables us to deal with identical objects and monotonicity of preferences in ranking objects. We show that the no-envy solution is the only solution satisfying equal treatment of equals, Maskin monotonicity, and a mild continuity property. The same axiomatization holds if the continuity property is replaced by a neutrality property.