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.     

Competitive equilibria in general choice spaces

This paper primarily demonstrates the existence of Arrow-Debreu equilibria in a general class of topological vector spaces of commodity bundles. Two conditions based on production possibilities, preferences, and the topological nature of bounded sets are shown to substitute, in any locally convex space, for the advantages of the Euclidean topology. Examples fulfilling these conditions are supplied. The approach is that of Bewley, demonstrating equilibria on finite dimensional sub-economies and establishing a net of these equilibria that converges to an equilibrium on the whole commodity space. An example of equilibrium with a storage technology is given. An auxiliary result concerns the price support of efficient allocations.     

Equilibrium asset pricing with Epstein-Zin and loss-averse investors

We study multi-period equilibrium asset pricing in an economy with Epstein-Zin (EZ-) agents whose preferences for consumption are represented by recursive utility and with loss averse (LA-) agents who derive additional utility of gains and losses and are averse to losses. We propose an equilibrium gain-loss ratio for stocks and show that the LA-agents are more (less) risk averse than the EZ-agents if their degree of loss aversion is higher (lower) than this ratio. When all the agents have unitary relative risk aversion degree and elasticity of intertemporal substitution, we prove the existence and uniqueness of the equilibrium and the market dominance of the EZ-agents in the long run. Finally, we extend our results to the case in which the LA-agents use probability weighting in their evaluation of gains and losses.     

The geometry of arbitrage and the existence of competitive equilibrium

We present the basic geometry of arbitrage, and use this basic geometry to shed new light on the relationships between various no-arbitrage conditions found in the literature. For example, under very mild conditions, we show that the no-arbitrage conditions of Hart [Journal of Economic Theory 9 (1974) 293] and Werner [Econometrica 55 (1987) 1403] are equivalent and imply the compactness of the set of utility possibilities. Moreover, we show that if agents’ sets of useless net trades are linearly independent, then the Hart–Werner conditions are equivalent to the stronger condition of no-unbounded-arbitrage due to Page [Journal of Economic theory 41 (1987) 392]—and, in turn, all are equivalent to compactness of the set of rational allocations. We also consider the problem of existence of equilibrium. We show, for example, that under a uniformity condition on preferences weaker than Werner’s uniformity condition, the Hart–Werner no-arbitrage conditions are sufficient for existence. With an additional condition of weak no-half-lines—a condition weaker than Werner’s no-half-lines condition—we show that the Hart–Werner conditions are both necessary and sufficient for existence.     

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.     

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.     

Prediction market prices under risk aversion and heterogeneous beliefs

In this paper, we examine the properties of prediction market prices when risk averse traders have heterogeneous beliefs in state probabilities. We show that the equilibrium state prices equal the mean beliefs of traders about that state if and only if the traders’ common utility function is logarithmic. We also provide a necessary and sufficient condition ensuring that the state prices are systematically below or above the mean beliefs of traders, thus providing a rational explanation to the favorite-longshot bias in prediction markets.     

Switching from complete to incomplete information

We construct an elementary mechanism [Dutta, B., Sen, A., Vohra, R., 1995. Nash implementation through elementary mechanisms in economic environments. Review of Economic Design 1, 173–203] that Nash implements the constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. In addition, measurability restrictions on allocations with respect to prices proper to constrained rational expectations equilibria are imposed in the outcome function. We show that by imposing such restrictions, the mechanism Bayesian implements the constrained rational expectations equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, these connections are obtained at the price of strong restrictions on the behavior of agents.     

Endowment redistribution and Pareto improvements in GEI economies

With incomplete markets and numeraire assets, there are open sets of economies such that their equilibrium allocations can be improved upon by a reallocation of period zero endowments. This strengthens the classical results on constrained Pareto inefficiency of equilibria in GEI.     

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.     

New conditions for the existence of Radner equilibrium with infinitely many states

In atomless differential information economies, equilibria are known not to exist prevalently even when agents are risk averse expected utility maximizers. The notion of prevalence involves essentially picking an economy at random. In this paper, however, we establish existence results with economically meaningful assumptions on the information structure. We obtain existence when agents have independent information, and also when the total endowment of the economy is common knowledge.     

Constrained suboptimality when prices are non-competitive

The paper addresses the following question: how efficient is the market system in allocating resources if trade takes place at prices that are not competitive? Even though there are many partial answers to this question, an answer that stands comparison to the rigor by which the first and second welfare theorems are derived is lacking. We first prove a “Folk Theorem” on the generic suboptimality of equilibria at non-competitive prices. The more interesting problem is whether equilibria are constrained optimal, i.e. efficient relative to all allocations that are consistent with prices at which trade takes place. We discuss an optimality notion due to Bénassy, and argue that this notion admits no general conclusions. We then turn to the notion of p-optimality and give a necessary condition, called the separating property, for constrained optimality: each constrained household should be constrained in each constrained market. If the number of commodities is less than or equal to two, the case usually treated in the textbook, then this necessary condition is also sufficient. In that case equilibria are constrained optimal. When there are three or more commodities, two or more constrained households, and two or more constrained markets, this necessary condition is typically not sufficient and equilibria are generically constrained suboptimal.     

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.     

Equilibrium with coordination

The obvious equilibrium concepts in the simplest institutions for transferring ownership of commodities—bilateral exchange—are neither Nash equilibria nor cooperative equilibria. To study such equilibria as special cases of equilibria of a social system it is necessary to introduce coordination. Two or more agents coordinate their actions, if, when they consider an alternative to a state, they take as given—for agents with whom they coordinate—the alternative state. If there is no coordination we obtain Nash equilibrium as a special case. If there is complete coordination we obtain optimality as a special case. The main result is an existence theorem for a social system with coordination. This theorem is then applied to prove existence of exchange equilibria in an economy with bilateral exchange.     

No unbounded arbitrage,weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions

Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162] prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page [Page, F.H., 1987. On equilibrium in Hart’s securities exchange model. Journal of Economic Theory 41, 392–404], is equivalent to the existence of a no arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. [Allouch, N., Le Van, C., Page F.H., 2002. The geometry of arbitrage and the existence of competitive equilibrium. Journal of Mathematical Economics 38, 373–391] extend the NAPS introduced by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418] and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart [Hart, O., 1974. On the existence of an equilibrium in a securities model. Journal of Economic Theory 9, 293–311]. They mention that this result implies the one given by Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162]. In this note, we show that all these conditions are equivalent.     

Asset prices in an exchange economy when agents have heterogeneous homothetic recursive preferences and no risk free bond is available

We study a pure exchange economy under incomplete markets where households have heterogeneous homothetic recursive preferences and lending and borrowing are precluded. We fully characterize the properties of the efficient allocations and the equilibrium asset price. The ownership distribution dynamics reveal the emergence of a dominant agent, who after some finite time, remains the only investor that increases asset holdings until asymptotically owning the entire wealth. Investors can be ranked according to a unique parameter that aggregates agents’ preference characteristics and we show how time discount rate, attitude towards risk and intertemporal substitution contribute to capital accumulation.     

Efficiency and truthfulness with Leontief preferences. A note on two-agent,two-good economies

In exchange economies where agents have private information about their preferences, strategy-proof and individually rational social choice functions are in general not efficient. We provide a restricted domain, namely the set of preferences representable by Leontief utility functions, where there exist mechanisms which are strategy-proof, efficient and individually rational. In two-agent, two-good economies we are able to provide an even stronger result. We characterize the class of efficient and individually rational social choice functions, which are fully implementable in truthful strategies.Received: 28 April 2003, Accepted: 23 June 2003, JEL Classification: D51, D71The author thanks Matthew Jackson, Jordi Massó and James Schummer for fruitful discussions, William Thomson for many valuable comments on an earlier version. A particular thank to Salvador Barberá for his fundamental help.     

Sales contests,promotion decisions and heterogeneous risk

This paper examines a general model of sales contests in which agents have heterogeneous attitudes toward risk. It shows that agents that are less risk averse have a higher probability of success. A corollary to this result shows that when absolute risk aversion is decreasing in wealth, wealthier agents have a higher probability of promotion. The same wealth effect makes it possible for more risk averse agents to take greater risks in a multi‐round promotion tournament. Next, a stability analysis shows that these equilibria are attractors under a best response dynamic. While it is well‐known that sales contests can be an effective incentive device for eliciting effort from employees, this research suggests the added benefit that when used as a basis for promotion decisions, sales contests act to filter the hardest working agents to the top of the corporate hierarchy. Copyright © 2008 John Wiley & Sons, Ltd.     

Risk aversion in a model of endogenous growth

Despite the evidence on incomplete financial markets and substantial risk being borne by innovators, current models of growth through creative destruction predominantly model innovators’ as risk neutral. Risk aversion is expected to reduce the incentive to innovate and we might fear that without insurance innovation completely disappears in the long run. The present paper introduces risk averse agents into an occupational choice model of endogenous growth in which insurance against failure to innovate is not available. We derive a clear negative relationship between the level of risk aversion and long run growth. Surprisingly, we show that in an equilibrium there exists a cut-off value of risk aversion below which the growth rate of the mass of innovators tends to a strictly positive constant. In this case, innovation persists on the long run and consumption per capita grows at a strictly positive rate. On the other hand, for levels of risk aversion above the cut-off value, the economy eventually stagnates.     

Equilibria in Banach lattices without ordered preferences

This paper establishes a very general result on the existence of competitive equilibria for exchange economies (with a finite number of agents) with an infinite-dimensional commodity space. The commodity spaces treated are Banach lattices, but no interiority assumptions on the positive cone are made; thus, the commodity spaces covered by this result include most of the spaces considered in economic analysis. Moreover, this result applies to preferences which may not be monotone, complete, or transitive; preferences may even be interdependent. Since preferences need not be monotone, the result allows for non-positive prices, and an exact equilibrium is obtained, rather than a free-disposal equilibrium.