Learning and stability of the Bayesian–Walrasian equilibrium

Under the Bayesian–Walrasian Equilibrium (BWE) (see Balder and Yannelis, 2009), agents form price estimates based on their own private information, and in terms of those prices they can formulate estimated budget sets. Then, based on his/her own private information, each agent maximizes interim expected utility subject to his/her own estimated budget set. From the imprecision due to the price estimation it follows that the resulting equilibrium allocation may not clear the markets for every state of nature, i.e., exact feasibility of allocations may not occur. This paper shows that if the economy is repeated from period to period and agents refine their private information by observing the past BWE, then in the limit all agents will obtain the same information and market clearing will be reached. The converse is also true. The analysis provides a new way of looking at the asymmetric equilibrium which has a statistical foundation.     

A way of explaining unemployment through a wage-setting game

We investigate a duopsonistic wage-setting game in which the firms have a limited number of workplaces. We assume that the firms have heterogeneous productivity, that there are two types of workers with different reservation wages and that a worker's productivity is independent of his type. We show that equilibrium unemployment arises in the wage-setting game under certain conditions, although the efficient allocation of workers would result in full employment.     

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.     

Full or partial market coverage? A note on spatial competition with elastic demand

In this paper, a spatial model is used to endogenously determine product locations and prices when consumers have an elastic demand with a finite reservation price. I show under which condition a two‐stage Bertrand–Nash equilibrium yields maximal product differentiation with full market covering. Additionally, this paper highlights the effects of a change in the reservation price and in the utility loss rate on the equilibrium values of the model. The ambiguous effect of a change in the utility loss rate on prices constitutes a rather puzzling result. Copyright © 1999 John Wiley & Sons, Ltd.     

Stochastic costly state verification and dynamic contracts

I consider a dynamic costly state verification environment in which a risk-averse agent enters into a contract with a risk-neutral principal. The agent has random income which is unknown to the principal but can be verified at a cost. The principal can commit to executing random verifications.I extend the standard recursive methods to study the problem and show that it is optimal to set verification probabilities strictly less than 1. If the agent׳s absolute risk aversion declines sufficiently slowly, the principal will use verification regardless of its cost. If the agent's income is verified then he would get consumption and continuation utility strictly higher than if his income were not verified.     

A family production overlapping generations economy

This paper provides a theoretical analysis of an overlapping generations economy in which production decisions and input–output allocations are all carried out at the family level. I consider a single class of output allocation schemes and various degrees of knowledge about the production technology. Under complete knowledge, I show that a family organizational structure in which everyone receives his marginal contribution to output, invests less in physical capital than under a perfectly competitive equilibrium environment. Under incomplete knowledge, I analyze and compare how beliefs about the input–output relationship affect the physical capital accumulation dynamics and the long-run standards of living.     

Simple axioms for countably additive subjective probability

This paper refines Savage’s theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow’s (1970) Monotone Continuity. Second, I relax Savage’s primitives: in my framework, the class of events need not be a σ-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory’s unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.     

A mechanism implementing the proportional solution

We consider the problem of a commonly owned technology which transforms a single input into a single output. We are interested in implementing a social choice rule called theproportional solution. We introduce a mechanism which implements the proportional solution in Nash, strong (Nash) and undominated Nash equilibria. In the mechanism each agent announces only two numbers which can be interpreted as the total output and her share of the total input-output combination. This paper was originally titled "Doubly implementing the proportional solution." I would like to thank my advisor William Thomson for his detailed comments and suggestions. I would also like to thank Jeffrey Banks and Sung-Whee Shin for their comments. Two anonymous referees and an editor’s comments improved this paper substantially.     

The system of towns with spatial public goods

In this paper, we introduce a model of ‘spatial public goods’, whose provision costs depend on the size of the benefit area. It is assumed that there are many developers providing spatial public goods in their towns. Each developer chooses the area size of his/her town and the quality of its spatial public good so as to maximize profit, taking the market price system as given. Each consumer chooses the level of the public good, and hence the town that supplies it, so as to maximize his/her utility. We show that the competitive equilibrium allocation of this economy is efficient.     

An optimal-incentive contract for managers with exponential utility

This paper examines the manager–investor relationship in the case of exponential utility when the manager of investments in real or financial assets has an endowment which can be invested in the risky assets for which he has private information. We obtain a relationship showing trade-offs or hedging behavior among the investments the manager can choose for himself and the principal. Even with the hedging ability of the manager, the well-known first-best solution with ‘no moral hazard’ risk-sharing is obtained among these possible solutions to the manager's problem by specifying a ‘no conflict of interest’, zero investment by the manager of his own endowment in those risky assets for which he has private information. Thus, the agent imputes no disutility to the assignment of the principal's investments and the investor is assured of an investment strategy that he would make if he had access to the manager's private information.     

Resource-envy-free and efficient allocations: A new solution for production economies with dedicated factors

I consider the problem of determining an equitable and efficient allocation of resources in production economies with factors which must be dedicated to production and cannot be consumed directly. First, I show that in such economies envy-free and efficient allocations exist under standard assumptions. However, I argue this notion of fairness is unsuitable for the present context. I then introduce a new notion of fairness, which I call resource-envy-freeness. First, I associate with each consumption bundle its resource footprint consisting of the vector of factors used to produce it. I then show that preferences over consumption bundles can be extended to preferences over factor bundles. An allocation is resource-envy-free if no agent prefers another agent’s resource footprint to its own. The analysis of resource-envy-free allocations in production is exactly analogous to the analysis of envy-free allocations in exchange. I establish that resource-envy-free and efficient allocations exist under standard assumptions, and I demonstrate that such allocations are intuitively appealing.     

A simplified approach to subjective expected utility

I provide a novel simplified approach to Savage’s theory of subjective expected utility. Such an approach is based on abstract integral representation theorems in the space of measurable functions. The advantage of such an approach is that these results can be used to easily obtain variations on Savage’s theorem, such as representations with state-dependent utility or probability measures that can have atoms. Finally, I discuss how such an approach can be used in other settings such as decision making under ambiguity.     

Dissolving multi-partnerships efficiently

I study a market where agents with unit demand jointly own heterogeneous goods. In this market, the existence of an efficient, incentive compatible, individually rational, and budget balanced mechanism depends on the shares of the agents. I characterize the set of shares for which having such a mechanism is possible. This set includes the symmetric allocation and excludes the allocation in which every agent owns a separate good.     

供应商与制造商在订单分配方面的博弈行为

对于两类不同质供应商与单制造商组成的供应链在订单分配方面的博弈行为,通过综合考虑部件价格、质量、交货期等构造订单质量指标,建立制造商和两类供应商的斯塔克尔伯格效用模型。模型显示,当两类供应商送交的订单质量相等时,制造商的效用可以达到最大;同时两类供应商对订单数量的需求均受到竞争对手对订单偏好的影响,由此可能导致供应商出现虚报自身信息的情况。制造商引入惩罚机制,并通过对惩罚进行适当限制,可实现让供应商实报私人信息的目标。     

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.     

Utility functions on ordered convex sets

The work of Cantor in set theory near the end of the last century showed that a linearly ordered set need not be order isomorphic to a subset of the real numbers. To obtain order isomorphism, it is necessary and sufficient that some countable subset of the linearly ordered set be order- dense in the entire set. The present paper proves a negative result that is much stronger than Cantor's. It shows that a weakly ordered convex set whose order relation is ‘continuous’ and ‘totally convex’ need not be order homomorphic to a subset of the reals. To obtain order homomorphism, it is necessary and sufficient that the weakly ordered set be countably bounded, i.e., have countable coinitial and cofinal subsets. Countable boundedness is a significantly weaker condition than countable order-denseness. Connections between these results and economic utility theory are discussed.     

Reduction-consistency in collective choice problems

We consider the problem of choosing a subset of a feasible set over which each agent has a strict preference. We propose an invariance property, reduction-consistency, of choice rules and study its implications. The property is a natural expression for the problems of a general principle of consistency having been studied extensively in resource allocation problems. We show that no scoring rule satisfies reduction-consistency, and base a characterization of the top rule on the property. We also investigate the minimal extension of a rule needed to recover reduction-consistency, and identify the minimal extensions of several rules including the Borda and plurality rules.     

Existence of smooth utilities on Banach lattices

In this paper, we focus our attention on the representability of a preference relation by differentiable utility functions when the consumption sets belong to an infinite dimensional commodity space. We obtain sufficient conditions for the existence of a C^r function representing a preference relation defined on an open subset of a Banach lattice.     

Suburban Encroachment on the Old North 40: The Search for Effective Measures to Preserve Agricultural Land

A bstract . Since 1956, more than 40 states have passed some form of legislation to preserve agricultural land. These statutes or constitutional amendments invoke a variety of economic and/or legal strategies to obtain their objectives, but the most common strategy is that of the differential tax. None of the various strategies is entirely effective, however, although land resource allocation problems have prompted some economists to reexamine the merits of land value taxation. A survey of pertinent literature on land value taxation is examined in an effort to determine whether a system based on single tax principles might offer a simpler, more equitable, and therefore preferable solution to the problem of land resource allocation according to criteria believed to foster environmental conservation or social goals.     

Possibly-Final Offers

A price-setting seller faces a buyer with unknown reservation value. We show that if the buyer is sufficiently risk averse, the seller can benefit from employing a Possibly-Final Offer (PFO) strategy. In a PFO, if the buyer rejects the seller's initial offer the seller sometimes terminates the interaction. If the seller does not terminate, he follows up with a subsequent, more attractive offer. As the buyer's risk aversion increases, the seller's expected profit under the optimal PFO approaches the full-information profit. These results extend to contexts with endogenous commitment, multiple types of buyers, multidimensional objects, and nonseparable utility functions.