Manipulation of the Walrasian mechanism in production economies with unbounded short-selling

Hurwicz (1979) and Otani and Sicilian (1982, 1990) characterized the Nash equilibrium allocations of the Walrasian demand manipulation game in successively more general exchange environments. In this paper, I extend the analysis to production economies with short-selling. First, I generalize Hurwicz’s and Otani and Sicilian’s theorem that any allocation at which each agent’s consumption bundle lies above her true offer curve can be supported in Nash equilibrium. I then show that for finite economies of any size the set of such allocations is often topologically large.Received: 17 January 2003, Accepted: 4 April 2005, JEL Classification: D51, D82For comments on this and earlier versions of the paper, I wish to thank Rick Bond, Bhaskar Chakravorti, Tom Gresik, Costas Syropoulos and William Thomson. I would especially like to thank Mike Jerison for helping to overcome a difficulty with a previous version. Also, the comments of the anonymous referees are gratefully acknowledged.     

Implementation of marginal cost pricing equilibrium allocations with transfers in economies with increasing returns to scale

This paper considers implementation of marginal cost pricing equilibrium allocations with transfers for production economies with increasing returns to scale. We present a mechanism whose Nash equilibrium allocations coincide with the set of marginal cost pricing equilibrium allocations with transfers that characterizes Pareto efficient allocations for economies with non-convex production technologies. We allow production sets and preferences to be unknown to the planner. The mechanism has some nice properties such as feasibility, continuity, and finite-dimension of message space. Furthermore, it works not only for three or more agents, but also for two-agent economies.     

Implementation of Pareto efficient allocations

This paper considers Nash implementation and double implementation of Pareto efficient allocations for production economies. We allow production sets and preferences are unknown to the planner. We present a well-behaved mechanism that fully implements Pareto efficient allocations in Nash equilibrium. The mechanism then is modified to fully doubly implement Pareto efficient allocations in Nash and strong Nash equilibria. The mechanisms constructed in the paper have many nice properties such as feasibility and continuity. In addition, they use finite-dimensional message spaces. Furthermore, the mechanism works not only for three or more agents, but also for two-agent economies.     

Existence of equilibria with infinitely many commodities: Banach lattices reconsidered

The purpose of this paper is twofold. The first aim is to present an extension of the results on the existence of Walrasian equilibrium to the infinite dimensional setting. The result depends on two crucial assumptions. These are the compactness of the collection of feasible allocations and the non-emptiness of the interior of the production set. The proof is a direct generalization of Bewley's (1972) proof for the L_∞ case. The second purpose of this paper is to show that the recent result of Mas-Colell (1986) on the existence of equilibrium for exchange economies on Banach lattices can be obtained through an argument based on the result outlined above. That is, exchange economies on Banach lattices with ‘uniformly proper’ preferences behave as though they were production economies in which the production sets have non-empty interior.     

Efficient allocations and equilibria with short-selling and incomplete preferences

This paper reconsiders the theory of existence of efficient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. Our model is motivated by an example in the theory of assets with short-selling where there is risk and ambiguity. Agents have Bewley’s incomplete preferences. As an inertia principle is assumed in markets, equilibria are individually rational. It is shown that a necessary and sufficient condition for the existence of an individually rational efficient allocation or of an equilibrium is that the relative interiors of the risk adjusted sets of probabilities intersect. The more risk averse, the more ambiguity averse the agents, the more likely is an equilibrium to exist. The paper then turns to incomplete preferences represented by a family of concave utility functions. Several definitions of efficiency and of equilibrium with inertia are considered. Sufficient conditions and necessary and sufficient conditions are given for the existence of efficient allocations and equilibria with inertia.     

Strategy-proof allocation when preferences are single-plateaued

Abstract. We consider private good economies with single-plateaued preferences. A solution selects for each preference profile a non-empty set of allocations. An agent strictly prefers a set of allocations to another set of allocations if and only if he strictly prefers any allocation in the first set to any in the second set according to his single-plateaued preference relation. We characterize the class of sequential-allotment solutions by essentially single-valuedness, Pareto-indifference, and coalitional stragety-proofness. These solutions are the Pareto-indifferent extensions of the solutions studied by Barberà et al. 1997. Received: 9 May 2000 / Accepted: 1 May 2001     

Weakly fair allocations and strategy-proofness

This paper investigates the problem of allocating two types of indivisible objects among a group of agents when a priority-order must be respected and only restricted monetary transfers are allowed. Since the existence of a fair (as in envy-free) allocation is not generally guaranteed, due to the restrictions on the money transfers, the concept of fairness is weakened, and a new concept of fairness is introduced. This concept is called weak fairness. This paper defines an allocation rule that implements weakly fair allocations and demonstrates that it is coalitionally strategy-proof. In fact, under a mild regulatory condition and quasi-linear utility functions, it is demonstrated that this is the only coalitionally strategy-proof allocation rule that implements a weakly fair allocation. We would like to thank two anonymous referees, the participants at the Society for the Advancement of Economic Theory Conference (Greece, 2007) and the participants at the Association for Public Economic Theory Meeting (Nashville, USA, 2007) for valuable comments. The authors would also like to acknowledge financial support from The Jan Wallander and Tom Hedelius Foundation.     

Pareto efficiency in the jungle

We revisit the jungle economy of Piccione and Rubinstein (Econ J 117(July):883–896, 2007) in which the allocation of resources is driven by coercion. In this economy the unique equilibrium satisfies lexicographic maximization. We show that relaxing the assumptions on consumption sets and preferences slightly, allocations other than lexicographic maximizers can be jungle equilibria. We attribute this result to single unilateral taking where a stronger agent takes goods from only one weaker agent. Once multiple unilateral takings are introduced, we show that jungle equilibria coincide with lexicographic maximization under weak assumptions. However, we also present examples of equilibria that are Pareto inefficient, where voluntary gift giving by stronger agents is needed to achieve Pareto efficiency and even voluntary trade has a role in the jungle.     

Stable cost sharing in production allocation games

Suppose that a group of agents have demands for some good. Every agent owns a technology which allows them to produce the good, with these technologies varying in their effectiveness. If all technologies exhibit increasing returns to scale (IRS) then it is always efficient to centralize production of the good, whereas efficiency in the case of decreasing returns to scale (DRS) typically requires to spread production. We search for stable cost allocations while differentiating allocations with homogeneous prices, in which all units produced are traded at the same price, from allocations with heterogeneous prices. For the respective cases of IRS or DRS, it is shown that there always exist stable cost sharing rules with homogeneous prices. Finally, in the general framework (under which there may exist no stable allocation at all) we provide a sufficient condition for the existence of stable allocations with homogeneous prices. This condition is shown to be both necessary and sufficient in problems with unitary demands.     

A decentralized and informationally efficient mechanism realizing fair outcomes in economies with public goods

We present a decentralized mechanism (called Lindahl Egalitarian), which yields Pareto efficient and envy free allocations (i.e. fair outcomes). We show that the mechanism is informationally efficient in general production economies with an arbitrary, but finite, number of private and public goods, and a finite number of agents. The mechanism reduces to the Walrasian mechanism starting from equal wealth when no agent cares about public goods. We also prove that the set of Public Competitive equilibrium allocations (from equal endowments and proportional taxation), and the set of the Lindahl Egalitarian equilibrium allocations are the same. We are grateful to Xavier Calsamiglia and Albert Marcet for helpful conversations, and to A. de la Fuente, I. Macho, and an anonimous referee for useful suggestions. A. Manresa’s research has been supported by the grant CICYT PB90-0172. J. Aizpurua acknowledges financial support from the Government of Navarra.     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Existence of marginal pricing equilibria in economies with externalities and non-convexities

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect.We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.     

Generalized coalitions and bargaining sets

We introduce new notions of bargaining set for mixed economies which rest on the idea of generalized coalitions (Aubin, 1979) to define objections and counter-objections. We show that the bargaining set defined through generalized coalitions coincides with competitive allocations under assumptions which are weak and natural in the mixed market literature. As a further result, we identify some additional properties that a generalized coalition must satisfy to object an allocation.     

Swap-flexibility in the assignment of houses

A house allocation rule should be flexible in its response to changes in agents’ preferences. We propose a specific notion of this flexibility. An agent is said to be swap-sovereign over a pair of houses at a profile of preferences if the rule assigns her one of the houses at that profile and assigns her the other house when she instead reports preferences that simply swap the positions of the two houses. A pair of agents is said to be mutually swap-sovereign over their assignments at a profile if the rule exchanges their assignments when they together report such ‘swap preferences’. An allocation rule is individually swap-flexible if any pair of houses has a swap-sovereign agent, and is mutually swap-flexible if any pair of houses has either a swap-sovereign agent or mutually swap-sovereign agents. We show for housing markets that the top-trading-cycles rule is the unique strategy-proof, individually rational and mutually swap-flexible rule. In house allocation problems, we show that queue-based priority rules are uniquely strategy-proof, individually swap-flexible and envy non-bossy. Varying the strength of non-bossiness, we characterise the important subclasses of sequential priority rules (additionally non-bossy) and serial priority rules (additionally pair-non-bossy and pair-sovereign).     

Equilibrium participation in public goods allocations

We consider a notion of voluntary participation for mechanism design in public goods economies in which mechanisms select public goods allocations and individuals then choose whether or not to submit their requested transfer to the central planner. The set of allocations that are robust to non-participation is shown to be sub-optimal in a wide variety of environments and may shrink to the endowment as the economy is replicated. When agents become small as the economy becomes large, any non-trivial mechanism suffers from non-participation when agents cannot be coerced to contribute.     

Uniform allocation and reallocation revisited

Thomson (1995a) proved that the uniform allocation rule is the only allocation rule for allocation economies with single-peaked preferences that satisfies Pareto efficiency, no-envy,one-sided population-monotonicity, and replication-invariance on a restricted domain of single-peaked preferences. We prove that this result also holds on the unrestricted domain of single-peaked preferences. Next, replacing one-sided population-monotonicity by one-sided replacement-domination yields another characterization of the uniform allocation rule, Thomson (1997a). We show how this result can be extended to the more general framework of reallocation economies with individual endowments and single-peaked preferences. Following Thomson (1995b) we present allocation and reallocation economies in a unified framework of open economies. Received: 20 February 1999 / Accepted: 15 February 2000     

Equilibrium theory with unbounded consumption sets and non-ordered preferences : Part I. Non-satiation

A new condition is introduced for the existence of equilibrium for an economy where preferences need not be transitive or complete and the consumption set of each agent need not be bounded from below. The new condition allows us to extend the literature in two ways. First, the result of the paper can cover the case where the utility set for individually rational allocations may not be compact. As illustrated in Page et al. [Page Jr., F.H., Wooders, M.H., Monteiro, P.K., 2000. Inconsequential arbitrage. Journal of Mathematical Economics 34, 439–469], the no arbitrage conditions do not apply to an economy with a non-compact utility set. Second, we generalize the arbitrage-based equilibrium theory to the case of non-transitive preferences.     

Randomization under ambiguity: Efficiency and incentive compatibility

We generalize de Castro and Yannelis (2018) by taking into account the use of randomization. We answer the following questions: Is each efficient allocation of de Castro and Yannelis (2018) still Pareto optimal? Are all efficient allocations still incentive compatible under the Wald’s maxmin preferences? We provide positive answers and give applications.     

Eliciting the socially optimal allocation from responsible agents

We consider designing a mechanism to allocate objects among agents without monetary transfers. There is a socially optimal allocation, which is commonly known by the agents but not observable by the designer. The designer possibly has information about the existence of responsible agents. A responsible agent, when indifferent between his objects at two different allocations, prefers the first allocation to the second if the first allocation is closer to the optimal allocation than the second, in the sense that all the agents who are allocated their optimal objects in the second allocation are allocated their optimal objects also in the first allocation, and there is at least one more agent in the first allocation receiving his optimal object. We show that, if the designer knows that there are at least three responsible agents, even if the identities of the responsible agents are not known, the optimal allocation can be elicited.     

The Aubin private core of differential information economies

Abstract We establish characterizations of Radner equilibrium allocations via private core notions in the framework of differential information economies with a finite number of states of nature and a measure space of agents that may have atoms. The commodity space is an ordered separable Banach space whose positive cone admits an interior point. We introduce the notion of Aubin private core and prove that it provides a characterization of Radner equilibrium allocations. We show that the Aubin private core is equivalent to Edgeworth private equilibria and to privately non-dominated allocations of suitable associated economies. Mathematics Subject Classification (2000): 91B50, 91B44 Journal of Economic Literature Classification: D51, D82, D11