Pareto-optimal Nash equilibria are competitive in a repeated economy

Consider a finite exchange economy first as a static, 1 period, economy and then as a repeated economy over T periods when the utility of each agent is the mean utility over T. A family of strategic games is defined via a set of six general properties the most distinct of which is the ability of agents to move commodities forward in time. Now consider Pareto optimal allocations in the T period economy which are also Nash equilibria in this family of strategic games. We prove that as T becomes large this set converges to the set of competitive utility allocations in the one period economy. The key idea is that a repetition of the economy when agents can move commodities forward in the time acts as a convexification of the set of individually feasible outcomes for player i holding all other strategies fixed.     

Efficient Allocations in Club Economies

We explore the characteristics of Pareto‐optimal allocations in the context of local public goods or clubs. A set of first‐order conditions for Pareto optimality is provided. Classical treatments apparently neglect an important term related to migrant compensation, and thus are incorrect. A Pareto optimum is shown to exist.     

Serial dictatorship and Pareto optimality

In a deterministic allocation problem in which each agent is entitled to receive exactly one object, an allocation is Pareto optimal if and only if it is the outcome of a serial dictatorship. We extend the definition of serial dictatorship to settings in which some agents may be entitled to receive more than one object, and study the efficiency and uniqueness properties of the equilibrium allocations. We prove that subgame perfect equilibrium allocations of serial dictatorship games are not necessarily Pareto optimal; and generally not all Pareto optima can be implemented as subgame perfect equilibrium allocations of serial dictatorship games, except in the 2-agent separable preference case. Moreover, serial dictatorship games do not necessarily have unique subgame perfect equilibrium allocations, except in the 2-agent case, hence their outcomes are indeterminate and manipulable.     

Collective Organizations versus Relative Performance Contracts: Inequality, Risk Sharing, and Moral Hazard

This paper studies collective economic organizations that share risk and mitigate moral hazard and compares them with relative performance contracts. Information-constrained optimal distributions of organizations and contracts are shown to be functions of the underlying primitives, in particular, the distribution of Pareto weights, and hence degree of inequality. Internal inequality of a potential, local group is a force for collective organization. That is, multi-agent organizations exist in order to extract wealth from some but not necessarily all members. The group organization is also shown to be information-constrained Pareto optimal at extremes of local wealth relative to an outsider. But the group organization is susceptible to both agents simultaneously deviating, colluding against the outsider, and this distortion makes an individualistic, relative performance contract an attractive alternative. More generally, organizations, contracts, and allocations are jointly determined. These implications could be distinguished in cross-sectional, time series data. Journal of Economic Literature Classification Numbers: D70, D82.     

An Allocation Rule with Wealth-Regressive Tax Rates

We introduce a public good allocation rule whose direct implementation by asking agents their endowments leads to Nash equilibrium outcomes—always Pareto dominating voluntary contributions outcomes. Although the Nash equilibrium allocations induced by this rule are not Pareto optimal in general, they are so in two-person economies.     

Local envy-freeness and equal-income Walrasian allocations

This paper introduces a local version of envy-freeness and investigates its implications in a continuum agent economy with connected preferences. We show that the set of locally envy-free and Pareto efficient allocations coincides with the set of equal-income Walrasian allocations.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

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.     

On the interaction between risk sharing and capital accumulation in a stochastic OLG model with production

We analyze the interaction between risk sharing and capital accumulation in a stochastic OLG model with production. We give a complete characterization of interim Pareto optimal competitive equilibrium allocations. Furthermore, we provide tests of Pareto optimality/suboptimality based on (risky) rates of return only.     

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.     

A Characterization of Robust Sunspot Equilibria

In nonconvex environments, a sunspot equilibrium can sometimes be destroyed by the introduction of new extrinsic information. We provide a simple test for determining whether or not a particular equilibrium survives, or is robust to, all possible refinements of the state space. We use this test to provide a characterization of the set of robust sunspot-equilibrium allocations of a given economy; it is equivalent to the set of equilibrium allocations of the associated lottery economy. Journal of Economic Literature Classification Numbers: D51, D84, E32.     

Judicial review and the power of the executive and legislative branches

The legal system can affect what policies a government can implement. In particular, when there is separation of powers, the strength of the judiciary to review and overturn actions of the executive and legislative branches can affect such things as how much redistribution these policy-making branches can do. Surprisingly, having judicial review helps the policy-making branches—the stronger is the judiciary, the more redistribution they are able to do. This occurs because the policy-making branches must make promises on and off the equilibrium path to individuals in order to make redistribution possible. However, in many circumstances, the government wants to renege on these promises, either to do more redistribution than promised or to not carry out severe threats against any individuals who lied. Judicial review can prevent reneging on these promises, thus making them credible.We develop this in the context of an optimal income tax model with a finite number of individuals where the government knows the exact distribution of types but not which individual is of which type. In this finite model, the government can detect misrevelation by even a single individual so that an individual׳s taxes can depend not just on one׳s own actions but also on others’ actions. Piketty (JET, 1993) showed that the government could implement any full-information Pareto optimal allocation if the government could commit to its announcements, even to infeasible allocations in circumstances after some individuals misreveal. We derive the sequential equilibrium allocations when individuals reveal their types by simple announcements when feasibility on and off the equilibrium path is imposed. Increasing the degree of judicial review expands the set of achievable allocations on the full-information utility possibility frontier. We also relate the different possible legal rules to different solution concepts in game theory.     

Retrading in market games

When agents are not price takers, they typically cannot obtain an efficient real location of resources in one round of trade. This paper presents a non-cooperative model of imperfect competition where agents can retrade allocations, consistent with Edgeworth's idea of recontracting. We show (a) there are Pareto optimal allocations, including competitive equilibrium allocations, that can be approximated arbitrarily closely when trade is myopic, i.e., when agents play a static Nash equilibrium at every round of retrading; (b) any converging sequence of allocations generated by myopic retrading can be supported along some retrade-proof subgame perfect equilibrium path when traders anticipate future rounds of trading.     

Policy Discrimination with and without Interpersonal Comparisons of Utility

Can the Pareto criterion guide policymakers who do not know the true model of the economy? If policymakers specify ex ante preferences for agents, then Pareto improvements from a distorted status quo are usually possible, and with more commodities than states, one can implement almost every Pareto optimum. Unlike the standard second welfare theorem, planners cannot dictate allocations: agents must trade. Unfortunately ex ante preferences impose interpersonal comparisons. If policymakers merely aim to maximize some social welfare function then optimal policies form an open set; hence small changes in the environment do not necessitate any policy response. Planners with symmetric information about agents can sometimes intervene without making interpersonal comparisons.     

Equilibrium Prices When the Sunspot Variable Is Continuous

We analyze sunspot-equilibrium prices in nonconvex economies with perfect markets and a continuous sunspot variable. Our primary result is that every sunspot equilibrium allocation can be supported by prices that, when adjusted for probabilities, are constant across states. This result extends to the case of a finite number of equally-probable states under a nonsatiation condition, but does not extend to general discrete state spaces. We use our primary result to establish the equivalence of the set of sunspot equilibrium allocations based on a continuous sunspot variable and the set of lottery equilibrium allocations. Journal of Economic Literature Classification Numbers: D51, D84, E32.     

An iterative allocation mechanism in the edgeworth box

This paper considers an iterative allocation mechanism which resolves the problem of multiplicity of allocations given by a mechanism in commodity space. At each stage, the average of the extreme allocations is taken and used as the starting point of the next stage. As long as the mechanism is individually rational and Pareto optimal, this iterative procedure yields a unique final allocation which is also individually rational and Pareto optimal. (JEL C63, C71)This paper was written while both authors were at the State University of New York at Buffalo.     

The overprovision anomaly of private public good supply

It is well known that private provision of a public good may lead to a higher supply than that in some Pareto optimal allocation. The traditional view attributes this overprovision anomaly to a specific kind of preferences. The present paper, however, shows that preferences do not play a decisive role. Assuming normality, overprovision will occur only if the distribution of income is extremely skewed and Pareto optimal allocations are not within the set of cost-share equilibria.     

The Identification of Preferences from Equilibrium Prices under Uncertainty

The competitive equilibrium correspondence, which associates equilibrium prices of commodities and assets with allocations of endowments, identifies the preferences and beliefs of individuals under uncertainty; this is the case even if the asset market is incomplete. Journal of Economic Literature Classification Numbers: D52, D80.     

The existence of budget-constrained pareto-efficient allocations

The existence of a budget constrained Pareto efficient allocation is proved. Preferences are assumed to be strongly monotonic and continuous pre-orderings. In addition, it is assumed that the set of Pareto efficient allocations, corresponding to a utility distribution, is a convex set. The mathematical tool is Brouwer's (or Kakutani's) fixed point theorem.     

Optimal non-linear income taxation for reduction of envy

This paper examines the optimal non-linear income taxation problem based on λ-equitability. An allocation is λ-equitable if no agent envies a proportion λ of the bundle of any other agent. We examine the properties of Pareto undominated allocations for various λ-equitability requirements. When there is one output, the marginal income tax rate can increase only if leisure is a luxury. In a multi-commodity model with commodity taxes, the goods preferred by the low skilled agent and/or those with high Hicksian elasticities are taxed more heavily. When preferences exhibit quasi-linearity, we can show that the introduction of the λ-equitability constraint increases the marginal income tax rates of the entire population.