Rivalry, Exclusion, and Coalitions

This paper analyzes a model where groups can attain exclusive ownership of a resource by means of a contest. We show that more concave production technologies and more egalitarianism within groups induce higher levels of social conflict. We then study endogenous coalition formation. Under cooperative exploitation of the resource, the grand coalition is the efficient partition but there exists a strong tendency toward bipartisan conflicts. Under noncooperative exploitation, conflict can ex ante Pareto dominate peaceful access and it becomes more difficult to support the grand coalition as a stable structure.     

Dynamic group formation in the repeated prisoner?s dilemma

We consider dynamic group formation in repeated n-person prisoner?s dilemma. Agreements in coalitional bargaining are self-binding in that they are supported as subgame perfect equilibria of repeated games. Individuals are allowed to renegotiate the cooperating group agreement through a process of voluntary participation. We prove that a cooperating group forms as an absorbing state of a Markov perfect equilibrium after a finite number of renegotiations if and only if the group is Pareto efficient, provided that individuals are patient. The cooperating group can only expand.     

Exchange and optimality

Summary. A feasible social state is irreducible if and only if, for any non-trivial partition of individuals into two groups, there exists another feasible social state at which every individual in the first group is equally well-off and someone strictly better-off. Competitive equilibria decentralize irreducible Pareto optimal social states. Received: September 9, 1996; revised version: February 11, 1998     

The Design and Performance of Sharing Rules for a Partnership in Continuous Time

We study repeated partnerships with imperfect monitoring and risk neutrality. The interval between the partners' decisions, the delay, is given but can be arbitrarily small. Each stage-game's output is Gaussian, with mean and variance depending on the partners' actions, making the sequence of outcomes a discretization of a diffusion. A sharing rule is efficient if there is an equilibrium of the corresponding game whose outcomes are Pareto efficient; it is stable if these equilibria approach a limit as the delay approaches zero. We characterize partnerships for which there exist stable, efficient sharing rules, and describe the corresponding equilibria.Journal of Economic LiteratureClassification Numbers: C73, D2, D82.     

Self-selection and Pareto efficient taxation

This paper analyses the set of Pareto efficient tax structures. The formulation of the problem as one of self-selection not only shows more clearly the similarity between this problem and a number of other problems (such as the optimal pricing of a monopolist) which have recently been the subject of extensive research, but also allows the derivation of a number of new results. We establish (i) under fairly weak conditions, randomization of tax structures is desirable; (ii) if different individuals are not perfect substitutes for one another in production, then the general equilibrium effects—until now largely ignored in the literature—of changes in the tax structure may be dominant in determining the optimal tax structure; in particular if the relative wage of high ability and low ability individuals depends on the relative supplies of labor, the optimal tax structure entails a negative marginal tax rate on the high ability individuals, and a positive marginal tax rate on the low ability individuals (the marnitude of which depends on the elasticity of substitution); (iii) if individuals differ in their preferences, Pareto efficient taxation may entail negative marginal tax rates for high incomes; while (iv) if wage income is stochastic, the marginal tax rate at the upper end may be 100%.Our analysis thus makes clear that the main qualitative properties of the optimal tax structure to which earlier studies called attention are not robust to these attempts to make the theory more realistic.     

Private information,Coasian bargaining,and the second welfare theorem

Most of the debate about Coasian bargaining in the presence of externalities relates to the First Welfare Theorem: is the outcome under bargaining efficient? This debate has involved the definition and importance of transaction costs, the significance of private information, and the effect of entry. There has been little analysis of how Coasian bargaining relates to the Second Welfare Theorem: even if the bargaining outcome is efficient, does the process limit the set of Pareto optimal allocations which can be achieved?We consider a model in which individuals utilize a common resource and may affect each other's output. The individuals differ in their productivities or tastes and this information is private to each of them. The government can manage the common resource and use nonlinear taxes to correct for the externality or it can turn the common resource over to a private owner who can charge individuals to utilize it with a nonlinear fee schedule. The government and the owner have the same information about tastes and productivities of the individuals. Except for the private information, there are no bargaining or administrative costs for collecting the taxes or fees. Whether there is public or private ownership, the government desires to redistribute, but it faces self-selection constraints.We show that the outcome of Coasian bargaining is constrained Pareto efficient. That is, given the information constraints, no Pareto improvement is possible. However, private ownership may limit what Pareto optimal allocations the government can achieve. The private owner in seeking to maximize profits always proposes contracts which counteract the government's attempts to redistribute across individuals with different characteristics. Under public management, any Pareto optimum can be sustained. In this context, private ownership, while not inefficient, does limit the government's ability to redistribute.     

Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (in A Econ Rev, 95(4), 913–935, 2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable. Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence. In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.     

Near-efficient equilibria in contribution-based competitive grouping

We examine theoretically and experimentally how competitive contribution-based group formation affects incentives to free-ride. We introduce a new formal model of social production, called a “Group-based Meritocracy Mechanism” (GBM), which extends the single-group-level analysis of a Voluntary Contribution Mechanism (VCM) to multiple groups. In a GBM individuals are ranked according to their group contributions. Based on this ranking, participants are then partitioned into equal-sized groups. Members of each group share their collective output equally amongst themselves according to a VCM payoff function. The GBM has two pure-strategy Nash equilibria. One is non-contribution by all; this equilibrium thus coincides with the VCM's equilibrium. The second equilibrium is close to Pareto optimal. It is asymmetric and quite complex from the viewpoint of experimental subjects, yet subjects tacitly coordinate this equilibrium reliably and precisely. Extensions of the basic GBM model to incorporate various features of naturally occurring group formation are suggested in the conclusion.     

Evolutionary Game Theory with Two Groups of Individuals

Static stability conditions are developed for evolutionary games that involve two groups of individuals such as the evolution of frequencies in a two-species biological system. These conditions are related to a local version of the Pareto optimal solution concept. Solutions that satisfy these conditions are shown to be dynamically stable for the replicator dynamic. The theory is applied to a mate desertion model where the two groups (male and female) have two possible desertion times. In particular, for biologically reasonable fitness parameters, both sexes adopt mixed mean strategies where the sex that has the least to lose by deserting is the first, on average, to desert. Journal of Economic Literature Classification Numbers: C70, C72.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

The Fear of Exclusion: Individual Effort when Group Formation is Endogenous*

To secure their membership in a popular group, individuals may contribute more to the group's local public good than they would if group formation were exogenous. Those in the most unpopular group do not have this incentive to contribute. This may result in substantial differences in individual effort level between groups. Our model thus provides one explanation for the existence of group‐specific behavioral norms. A principal will prefer exogenous or endogenous group formation depending on whether he prefers high or low levels of the local public good. We analyze two stylized examples: social interaction in schools, and multiple‐task teamwork.     

Coalitional manipulation and the Pareto rule

This paper examines aggregation procedures that map profiles of individual preferences into choice sets. An aggregation procedure is said to be “manipulable by a coalition” if there is a group of individuals, and a preference profile, such that every member of the group prefers the choice set obtained when they are misrepresenting their preferences, to the one obtained when they are honest. We show that the Pareto rule, which is an aggregation procedure that maps profiles of individual preferences into corresponding sets of Pareto optima, is not manipulable by any coalition of individuals under various behavioural assumptions which relate preferences over choice sets to preferences over alternatives. The non-manipulability of the Pareto rule by a single individual follows as a special case under these behavioural assumptions.     

Correlated Equilibrium,Conformity, and Stereotyping in Social Groups

We argue that a social norm and the coordination of behavior within social groups can be expressed by a correlated equilibrium. Given a social group structure (a partition of individuals into social groups), we propose four conditions that one may expect of a correlated equilibrium consistent with social norms. These are: (1) within‐group anonymity (conformity within groups), (2) group independence (no conformity between groups), (3) homophily (individuals in the same group have similar attributes), and (4) predictable group behavior (ex post stability). We demonstrate that correlated equilibrium satisfying (1)–(3) exist very generally and equilibrium satisfying (1)–(4) exist in games with many players. We also consider stereotyped beliefs—beliefs that all individuals in a social group can be expected to behave in the same way—and show that stereotyping is not costly to the person who stereotypes but may or may not be beneficial to society.     

Stability of the cooperative equilibrium in N-person prisoners' dilemma with sequential moves

Summary. Nishihara [3] showed that N-person prisoners' dilemma has a cooperative Nash equilibrium, if the players decide their actions sequentially in the order determined by Nature under a certain information structure, and if each player's payoffs satisfy a certain inequality. This paper examines the stability of this cooperative equilibrium against two matters: players' slight mistakes and deviations by coalitions. The main results are as follows: (i) if the inequality on each player's payoffs strictly holds, then the cooperative equilibrium is a strictly proper equilibrium; (ii) if N≤3, and if full cooperation is Pareto efficient in N-person prisoners' dilemma, then the cooperative equilibrium is a strong Nash equilibrium; (iii) the cooperative equilibrium is in general a coalition-proof Nash equilibrium. Received: June 23, 1997; revised version: December 2, 1997     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

Efficiency and equilibrium when preferences are time-inconsistent

We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. If consumers have identical discount factors, then allocations that are Pareto efficient at the initial date are also renegotiation-proof. In an economy with a sequence of markets, competitive equilibria are Pareto efficient in this sense, and for generic endowments, only if preferences are locally homothetic.     

On the set of Pareto efficient allocations in economies with public goods

Summary We examine the set of Pareto-efficient allocations in economies with public goods. We show that even if preferences are continuous and strongly monotonic, it need not coincide with the set of weakly efficient allocations. We then study topological properties of the Pareto set. We show that it is neither connected nor closed in allocation space. Furthermore, if the public goods are local, the image of the Pareto set in utility space need not be closed or connected. We provide two independent sufficient conditions for the closedness of the Pareto set. The results are directly applicable to private goods economies with joint production. Our results should be of interest for general equilibrium and mechanism design theory; where for example, the properties of the efficient set are important for proving the existence of an equilibrium and for the study of the properties of monotone-path social choice correspondences.We thank Hideo Konishi, Tomoichi Shinotsuka, Nicholas Yannelis and an anonymous referee for valuable comments on previous drafts of this paper.     

VOTER PREFERENCES FOR TRADE POLICY INSTRUMENTS*

We analyze voter preferences for tariffs and production subsidies. The distribution of tax revenues argument shows that voters with high direct tax burdens prefer tariffs to subsidies. The uncertainty argument demonstrates that if actual tariff and subsidy rates are chosen from the set of individually optimal rates then the range of tariff rates is smaller than the range of subsidy rates. Thus, tariffs might be preferred even though they are less efficient. Finally, the large country argument shows that if a country is large then voters whose income shares decline with more protection prefer tariffs to subsidies.     

Voluntary formation of communities for the provision of public projects

In this paper we examine a group formation problem, where heterogeneous individuals partitioned themselves into communities, each choosing its own public project from the given space of feasible projects. The model is that of “horizontal product differentiation” where individuals display distinct preferences over the policy space. We consider the notion of “efficient” configuration that minimizes the total project-related costs and aggregate personalized costs of all individuals, and “sustainable” configurations, those are immune against breakaways by subgroups of individuals. Our main result is that, with a unidimensional project space and single-peaked personalized costs, every efficient partition is sustainable.     

Age‐related Optimal Income Taxation*

In most countries, average income varies with age. In this paper we investigate if and how it is possible to enhance the redistributive mechanism by relating tax payments to age. Using an OLG model where some individuals are low skilled all their life while others are low skilled when young but high skilled when old, we first show how an age dependent optimal income tax can Pareto improve upon an age independent income tax. We then characterize the optimal age dependent income tax. A tax on interest income is part of the optimal tax structure.