Nash implementation with a private good

Summary. I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Received: February 19, 1998; revised version: January 30, 2002     

On Nash-Implementation in the Presence of Withholding

In this paper we construct a completely feasible and continuous mechanism whose Nash allocations coincide with Lindahl allocations when both preferences and initial endowments are unknown to the designer and unreported endowments are withheld. This mechanism extends the mechanism of Hong by allowing for semi-positivity of endowments for private goods economies and the mechanism of Tian by allowing for any number of private goods for public goods economies. Thus our mechanism improves all the existing mechanisms that implement Walrasian or Lindahl allocations. Journal of Economic Literature Classification Numbers: C72, D6l, D78, H41.     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

Ex ante contracting with endogenously determined communication plans

Summary. In this paper we introduce a new model of ex ante contracting for economies with asymmetric information to examine endogenously determined communication plans for information sharing in the interim stage. In contrast to the models used in previous research, in the present model agents negotiate not only on a contract of state contingent allocations but also on a communication plan, a set of rules describing how agents will reveal part of their private information at the interim stage to execute the trade contracts. We prove a result about the nested structure of the set of allocations implementable by various communication plans and establish the existence of core strategies for this cooperative game under various regularity conditions. Received: 4 March 1998; revised version: 17 September 1999     

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.     

Core concepts in economies where information is almost complete

Summary. The paper analyzes the properties of cores with differential information, as economies converge to complete information. Two core concepts are investigated: the private core, in which agents' net trades are measurable with respect to agents' private information, and the incentive compatible core, in which coalitions of agents are restricted to incentive compatible allocations. Received: March 15, 2000; revised version: August 24, 2000     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

Efficiency, monotonicity and rationality in public goods economies

Summary. In economies with public goods, we identify a necessary and sufficient condition for the existence of cost monotonic, Pareto optimal and individually rational mechanisms. These exist if and only if the preferences of the agents satisfy what we call the equal ordering property. We also show that when this condition holds the egalitarian equivalent correspondence is the only cost monotonic selection from the core of the economy. Furthermore, it is unambiguous in the sense that the agents are indifferent among all the allocations in it. Received: February 26, 1996; revised version: January 31, 1997     

A family of supermodular Nash mechanisms implementing Lindahl allocations

Summary. We present a family of mechanisms which implement Lindahl allocations in Nash equilibrium. With quasilinear utility functions this family of mechanisms are supermodular games, which implies that they converge to Nash equilibrium under a wide class of learning dynamics. Received: April 27, 2000; revised version: January 16, 2001     

A dual characterization of incentive efficiency

We show that incentive efficient allocations in economies with adverse selection and moral hazard problems can be determined as optimal solutions to a linear programming problem and we use duality theory to obtain a complete characterization of the optima. Our dual analysis identifies welfare effects associated with the incentives of the agents to truthfully reveal their private information. Because these welfare effects may generate non-convexities, incentive efficient allocations may involve randomization. Other properties of incentive efficient allocations are also derived.     

Intertemporal equilibria with Knightian uncertainty

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents? multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.     

Idiosyncratic risk and financial policy

In economies subject to uninsurable idiosyncratic risks, competitive equilibrium allocations are constrained inefficient: reallocations of assets support Pareto superior allocations. This is the case even if the asset market for the allocation of aggregate risks is complete.     

Incentive Mechanism Design for Production Economies with Both Private and Public Ownerships

In this paper we deal with the problem of incentive mechanism design which yields efficient allocations for general mixed ownership economies when preferences, individual endowments, and coalition patterns among individuals are unknown to the planner. We do so by doubly implementing the proportional solution for economies with any number of private sector and public sector commodities and any number of individuals as well as the coexistence of privately and publicly owned firms with general convex production possibility sets. Furthermore, the mechanisms work not only for three or more agents, but also for two-agent economies. Journal of Economic Literature Classification Numbers: C72, D61, D71, D82.     

A reconsideration of the problem of social cost: Free riders and monopolists

Summary. One version of the Coase Theorem is, If property rights are fully allocated, competition leads to efficient allocations. This version implies that the public goods problem can be solved by allocating property rights fully. We show that this mechanism is not likely to work well in economies with global externalities because the privatized economy is highly susceptible to strategic behavior: The free-rider problem manifests itself as a complementary monopoly problem in an associated private goods economy. Thus, our work relates the validity of the Coase Theorem to the literature on the incentives for strategic behavior in economies with complementarities. Received: 12 May 1999; revised version: 9 July 1999     

Outside versus inside bonds: A Modigliani–Miller type result for liquidity constrained economies

When agents are liquidity constrained, two options exist – sell assets or borrow. We compare the allocations arising in two economies: in one, agents can sell government (outside) bonds and in the other they can borrow by issuing (inside) bonds. All transactions are voluntary, implying no taxation or forced redemption of private debt. We show that any allocation in the economy with inside bonds can be replicated in the economy with outside bonds but that the converse is not true. However, the optimal policy in each economy makes the allocations equivalent.     

Fair allocations in large economies

The purpose of this paper is the study of problems of equity in an economy with many agents. Conditions are given under which every equitable and Pareto optimal allocation is a competitive equilibrium with equal incomes for all agents. The results are also of potential relevance for the literature on incentive compatibility since the allocations that are obained through incentive mechanisms in large economies turn out to be equitable.     

On the optimality of optimal income taxation

The Mirrleesian model of income taxation restricts attention to simple allocation mechanism with no strategic interdependence, i.e., the optimal labor supply of any one individual does not depend on the labor supply of others. It has been argued by Piketty (2009) [12] that this restriction is substantial because more sophisticated mechanisms can reach first-best allocations that are out of reach with simple mechanisms. In this paper, we assess the validity of Piketty?s critique in an independent private values model. As a main result, we show that the optimal sophisticated mechanism is a simple mechanism, or, equivalently, a Mirrleesian income tax system.     

Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Strategy-proofness versus efficiency for small domains of preferences over public goods

Summary. It has long been known that when agents have von Neumann-Morgenstern preferences over lotteries, there is an incompatibility between strategy-proofness and efficiency (Gibbard, [9]; Hylland, [12]) – a solution satisfying those properties must be dictatorial. We strengthen this result by showing that it follows from the same incompatibility on a series of much smaller domains of preferences. Specifically, we first show the incompatibility to hold on our smallest domain, in which two agents are restricted to have linear preferences over one private good and one public good produced from the private good (Kolm triangle economies). This result then implies the same incompatibility on increasingly larger domains of preferences, ending finally with the class of von Neumann-Morgenstern preferences over lotteries. Received: February 6, 1997; revised version: January 29, 1998     

Regulator flexibility and the administrative allocation licensing of 3G spectrum

Globally, most nations assign radio spectrum to provide 3G mobile services during the period 1999–2007. While there is consensus among most economists that auctions are the preferred assignment mechanism, the assignment mode is split, more or less, equally (in terms of the number of licences issued) between administrative allocations and auctions. With auction procedures tending to raise more revenue for governments (Cartelier, 2003) the question that naturally arises is: why are administrative allocations so popular a method to assign spectrum? McMillan (1995) conjectures that administrative allocations provide additional ‘flexibility’. Accordingly, this study examines the performance of 3G assignments in terms of an econometric analysis of a unique sample of national 3G spectrum administrative allocations. These outcomes are modelled as depending on spectrum package attributes, and post-award network deployment requirements.