Walrasian analysis via two-player games

We associate to any pure exchange economy a game with only two players, regardless of the number of consumers. In this two-player game, each player represents a different role of the society, formed by all the individuals in the economy. Player 1 selects feasible allocations trying to make Pareto improvements. Player 2 chooses an alternative from the wider range of allocations that are feasible in the sense of Aubin. The set of Nash equilibria of our game is non-empty and our main result provides a characterization of Walrasian equilibria allocations as strong Nash equilibria of the associated society game.     

The bargaining set of a large economy with differential information

Summary. We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy. Received: February 15, 1999; revised version: August 9, 1999     

Robustness of sunspot equilibria

Summary. A sunspot equilibrium (SSE) is based on some extrinsic randomizing device (RD). We analyze the robustness of SSE. (1) We say that an SSE allocation is robust to refinements if it is also an SSE allocation based on any refinement of its RD. (2) We introduce two core concepts for analyzing the robustness of SSE in the face of cooperative-coalition formation. In the first, the blocking allocations are based on the RD that defines the SSE. In the second (stronger) core concept, coalitions select their own RDs. For the convex economy with restricted market participation, SSE allocations are robust under each of the definitions and the cores converge on replication of the economy to the set of SSE allocations. For the economy with an indivisible good, SSE allocations are not always robust. We provide examples of each of the following: (i) an SSE allocation that is not robust to refinement, (ii) an SSE allocation that is in neither core, (iii) an SSE allocation that is in the first core, but not in the second, and (iv) a core that does not converge upon replication to the set of SSE allocations. Received: July 31, 1995; revised version August 30, 1996     

Existence and fairness of value allocation without convex preferences

Shafer (Econometrica, 48 (1980), 467–476) proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations by introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations may discriminate in favor of or against a coalition of agents.     

Fair allocations of a renewable resource

In an economy with finitely many agents, one renewable resource, and an infinite horizon, it is shown that there is exactly one maximal allocation corresponding to given limiting shares of consumption and this allocation converges monotonically. Therefore, if there is no discounting, at most one fair maximal program exists—that which gives an equal amount to each individual in the limit. In this allocation, envy is always finite. However, only in special cases is it envyfree. This is in contrast to the case of finite economies where envy-free and Pareto efficient allocations may not exist or, if they exist, may not be unique.     

Pareto optima and equilibria when preferences are incompletely known

An exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is considered. Sufficient conditions for the set of efficient allocations and equilibria to coincide with the set of efficient allocations and equilibria that result when each agent has a utility in her family are provided. Welfare theorems in an incomplete preferences framework therefore hold under these conditions and efficient allocations and equilibria are characterized by first order conditions.     

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.     

Pension,possible phaseout,and endogenous fertility in general equilibrium

The rich literature on Pay-As-You-Go (PAYG)-type pensions provides a notion that when pension return is dominated by the market return, generally it is impossible to phase pension out without hurting any generation. We show that PAYG pensions can indeed be phased out in a much richer framework where fertility is endogenous and general equilibrium effects are present. Interestingly, the factor that helps us to phase the pension out in a Pareto way is hidden in the structure of PAYG pension itself. Individualistic agents fail to recognize the benefits of their fertility decision on these programs and, therefore, end up in an allocation that is strictly dominated by the allocations that internalize this externality. Exploiting this positive externality, competitive economy can improve its allocations and can reach the planner's steady-state in finite time where each generation secures as much utility as in the competitive equilibrium. Clearly, it is possible to transition in a Pareto way to an economy either with no pension or with pensions whose return is not dominated by market return.     

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.     

关于社会主义与市场经济相结合的若干思考

对社会主义制度与市场经济能不能结合、如何结合的问题,学术界一直议论纷纷.邓小平提出,市场经济是发展生产的方法、调节经济的手段,资本主义可以用,社会主义也可以用.这才使人们从思想上把市场经济等同于资本主义的观点束缚下解放了出来,从而为我们建立社会主义市场经济体制奠定了理论基础.当人们谈到社会主义市场经济与资本主义市场经济的区别时,往往只是指出社会主义制度与资本主义制度的区别,而没有指出社会主义条件下的市场经济与资本主义条件下的市场经济有什么区别,仿佛不管在什么社会制度下,市场经济都没有什么区别,也不会有区别.笔者认为,社会主义基本制度和市场经济机制在结合过程中,它们的具体实现形式都会发生一定的变化,从而相互渗透、相互影响、相互融合成为一个整体.社会主义制度和市场经济机制各自在坚持自身的本质特征的情况下,在具体实现形式方面相互适应对方的需要做出调整,才能形成作为一个有机整体的社会主义市场经济体制.     

Non-myopic learning in differential information economies: the core

Summary. We study the process of learning in a differential information economy, with a continuum of states of nature that follow a Markov process. The economy extends over an infinite number of periods and we assume that the agents behave non-myopically, i.e., they discount the future. We adopt a new equilibrium concept, the non-myopic core. A realized agreement in each period generates information that changes the underlying structure in the economy. The results we obtain serve as an extension to the results in Koutsougeras and Yannelis (1999) in a setting where agents behave non-myopically. In particular, we examine the following two questions: 1) If we have a sequence of allocations that are in an approximate non-myopic core (we allow for bounded rationality), is it possible to find a subsequence that converges to a non-myopic core allocation in a limit full information economy? 2) Given a non-myopic core allocation in a limit full information economy can we find a sequence of approximate non-myopic core allocations that converges to that allocation? Received: May 25, 1999; revised version: August 9, 1999     

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.     

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.     

Competitive equilibria with limited enforcement

We show how to decentralize constrained efficient allocations that arise from enforcement constraints between sovereign nations. In a pure exchange economy these allocations can be decentralized with private agents acting competitively and taking as given government default decisions on foreign debt. In an economy with capital these allocations can be decentralized if the government can tax capital income as well as default on foreign debt. The tax on capital income is needed to make private agents internalize a subtle externality. The decisions of the government can arise as an equilibrium of a dynamic game between governments.     

On mixed markets with asymmetric information

In asymmetric information exchange economies involving both non-negligible and negligible agents, one should expect the failure of the private Core-Walras Equivalence Theorem. This paper shows that if “large” traders are similar to each other, then they lose their market power and hence the Equivalence Theorem can be restored. We also investigate on weaker equivalences among Walrasian expectations allocations, Aubin private core and private core allocations of the original mixed economy and the atomless one associated to it, without the assumption that all atoms are of the same type. Furthermore, extensions of Hervés-Moreno-Yannelis and Schmeidler Theorems (compare Hervés et al. in J Math Econ 41:844–856, 2005a; Schemidler in Econometrica 40:579–580, 1972) are given for differential information economies in which the feasibility constraints are imposed with an equality (exact feasibility).     

Correlated equilibrium and sunspot equilibrium

Summary We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.     

A revised concept of distributional equity

Recent studies have shown that in a private goods economy with production, allocations which are considered to be distributionally fair may not exist. As a solution for such cases, just allocations are introduced and examined in some detail. Such allocations are shown, by rigorous proof, to exist in general.     

A Core‐Equilibrium Convergence in a Public Goods Economy

This paper shows a core‐equilibrium convergence in a public goods economy where consumers' preferences display warm glow effects. We demonstrate that if each consumer becomes satiated to other consumers' provision, then as the economy grows large the core shrinks to the set of Edgeworth allocations. Moreover, we show that an Edgeworth allocation can be decentralized as a warm glow equilibrium.     

Endogenous property rights regimes, common-pool resources and trade

A model is developed where opening to trade affects a dynamic common-pool resource stock and welfare through a community's voting decision to institute a property rights regime regulating the stock. The model finds that resource stock levels can decline even when a Markov perfect equilibrium path for labor and property rights regimes are chosen to maximize welfare. Thus, opening to trade can be welfare maximizing even when resource stock declines. Experimental results show that under certain conditions, subjects briefly follow a Markov perfect equilibrium path for property rights regime choice but labor allocations are myopically chosen indicating that some resource dynamics may be considered by subjects.     

Short run core equivalence in an overlapping generations model

This essay establishes the equality between the set of competitive equilibrium allocations and the set of allocations which belong to the cores of a sequence of short run economies for an overlapping generations model. A short run economy is a finite period economy obtained by truncating the original economy so that the truncated economy is irreducible.