Search

We apply the mixed measure space model of players to the analysis of smooth oligopolies with two types of players. Following Kannai (1966) and others, we use the asymptotic approach to obtain the structure of the asymptotic kernel for smooth Transferable Utility production market games with symmetric big players and a uniform ocean of small players. We show that in the case of a duopoly, the asymptotic kernel is a nondegenerate interval that strictly contains the asymptotic nucleolus, which in turn coincides with the unique Transferable Utility Competitive Equilibrium being the upper end-point of the interval (from the point of view of the uniform ocean).

In this paper, we apply the framework of a public bad economy with a finite set of economic agents and a finite set of consumption commodities. The pollution of an agent is emitted into the air while consuming his consumption goods. A linear public bad economy model with a single private good had been introduced in Shitovitz and Spiegel (Econ Theory 22(1):17–31, 2003) and here we reconsider its extension to finite number of private goods and prove existence of a core ‘trading’ allocation (Perets et al. J Math Econ 48(3):163–169, 2012) that Pareto dominates the Nash allocation. This mathematical model embodies the restriction of consumption by all polluting agents, to decrease the amount of the public bad, affecting the whole economy, worldwide. Note specifically that the Lindahl allocation may not Pareto dominate the Nash allocation in some finite economy, in contrast to well-known asymptotic results.

In Tullock contests in which the common value of the prize is uncertain, information advantages are rewarded: if a player i has better information about the value than some other player j, then the payoff of i is greater or equal to the payoff of j, regardless of the information of the other players. (C) 2018 Elsevier B.V. All rights reserved. Acknowledgments of financial support. Einy: Israel Science Foundation, Israel, grant 648/2. Moreno: Ministerio Economía (Spain), grants ECO2014-55953-P and MDM2014-0431, and Comunidad de Madrid, Spain , grant S2015/HUM-3444.

Consider a symmetric common-value Tullock contest with incomplete information in which the players' cost of effort is the product of a random variable and a deterministic real function of effort, d. We show that the Arrow&-Pratt curvature of d, Rd,Rd, determines the effect on equilibrium efforts and payoffs of the increased flexibility/reduced commitment that more information introduces into the contest: If RdRd is increasing, then effort decreases (increases) with the level of information when the cost of effort (value) is independent of the state of nature. Moreover, if RdRd is increasing (decreasing), then the value of public information is nonnegative (nonpositive). Einy acknowledges financial support of the Israel Science Foundation, grant 648/2. Moreno acknowledges financial support from the Ministerio de Ciencia e Innovación, grant ECO2011-29762

Interactions strategiques et pouvoir des atomes dans des economies avec biens publicsDans cet article, nous etudions l’equilibre de Nash dans une economie d’echange avec biens publics. Cette economie decrit un jeu avec un espace mesure mixte d’agents. Il est suppose un nombre fini de biens prives. Nous montrons qu’il existe, sous certaines conditions, un unique equilibre de Nash pour cette economie dans laquelle les biens publics sont produits avec une technologie lineaire. De plus, nous discutons de la difference en termes de pouvoir de marche qu’il existe entre une situation dans laquelle le secteur non atomique et un atome ont la meme fonction d’utilite, et une situation ou l’atome devient negligeable.Classification JEL : C72, H41.

This paper extends results on information advantage in Cournot oligopoly to a public good economy with uncertainty and private information where the state-dependent utilities have a multiplicative structure. We show that in a Bayesian–Nash equilibrium where consumers’ contributions are positive in all states of nature, a consumer with superior information is rewarded with a higher ex ante expected utility. Our counter example shows that in the case where one consumer does not contribute, information disadvantage might emerge. Thus, the interiority assumption is essential to obtain our results.

Lindahl and Nash equilibria are often used in the theory of public good. Shitovitz and Spiegel (1998) present an example of 2-person economy with one private good and one pure public good, where the core efficient Lindahl allocation does not Pareto dominate the (inefficient) Nash allocation. In this paper we introduce the new concept of Trading equilibrium for a general public good economy with smooth preferences and a mixed measure space of consumers. We obtain that this economy admits a unique Trading equilibrium. Moreover, the Trading equilibrium induces a core allocation that strictly Pareto dominates the Nash allocation.

This paper studies the provision of a public good via voluntary contributions in an economy with uncertainty and differential information. Consumers differ in their private information regarding their future endowment as well as in their preferences. Each consumer selects her consumption exante, i.e., before knowing the state of nature. Contributions to the provision of the public good are determined ex-post, i.e., when the state of nature is realized. Assuming that some normality conditions hold, a Bayesian equilibrium exists. Further, equilibrium is unique, regardless of the number of consumers, when either (a) the information partitions of consumers can be ranked from the finnest to the coarsest, or (b) there are only two types of consumers.

We focus on a class of linear Cournot duopolies with differentiated products and prove that whether there is an information advantage or disadvantage depends on firms' information setup. Specifically, we show that when the cross-effects are common value, the uninformed firm that commits to quantity will not have lower ex ante profits than a firm that has complete information about its cross-effects. This result contrasts to the information advantage that holds in the same duopolies with independent cross-effects.

This paper analyzes the voluntary provision of the pure public good in a sequence of finite economies. The boundedness of this provision is established under very weak conditions. The Cournot–Nash provision of the public good is bounded. In contrast, the Lindahl provision is unbounded but the proportion of private good devoted to its production may be infinitesimal. Several examples are provided to relate this paper to the literature.

Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities.

Shitovitz and Spiegel (1998, Journal of Economic Theory83, pp. 1–18) demonstrated that in pure public good economies, for some consumers the Lindahl consumption bundles can be inferior (utility-wise) to their Cournot–Nash allocation. In this paper, we prove that in any finite pure public good economy there exists a core allocation that is unanimously preferred, utility-wise, by all consumers over their Cournot–Nash consumption bundles.

We study the asymptotic nucleolus of differentiable monopolistic market games in continuum economies with a finite number of traders' types, and show that, under appropriate assumptions, it is the center of symmetry of the subset of the core in which all the monopolists receive the same payoff. Thus, the nucleolus discriminates the traders in the atomless sector, whereas the competitive equilibrium does not. Moreover, if there is a single syndicated atom and a finite number of atomless sectors, the syndicate is treated more favorably under the asymptotic nucleolus than under the Shapley value associated with the pure monopolistic market. Journal of Economic Literature Classification Numbers: C71, D40.

In this paper, we derive qualitative and asymptotic results on Cournot–Nash and Lindahl equilibria in pure public good economies. In a discrete finite economy with similar consumers (e.g., sharing the same Cobb–Douglas utility), we show that the consumer with the biggest initial endowment prefers the proportional Lindahl over his Cournot–Nash bundle. The asymptotic results are derived using a model of a mixed economy with an atomless sector of consumers as an idealization for economies with few influential players and many very small consumers. Conditions which ensure that all consumers prefer the Pareto-efficient Lindahl allocation over the non-cooperative Cournot–Nash allocation were specified.Journal of Economic LiteratureClassification Numbers: C72, D50, D60, H41.

Using a mixed market model for analyzing imperfectly competitive economies, we maximize the oligopolists' Welfare Function, given individual rationality and feasibility constraints. We prove that solutions belong to the core for a large class of economies. This class includes, in particular, every monopoly having a single type of small traders. Note that all such solutions yield the large trader, utility-wise, strictly more than at any monopoly solution, where the monopolist plays strategically, and the ocean of small traders act as being as price-takers.

We show that the core of a continuous convex game on a measurable space of players is a von Neumann–Morgenstern stable set. We also extend the definition of the Mas–Colell bargaining set to games with a measurable space of players and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measures in the bargaining set. We provide examples which show that the continuity assumption is essential to our results.Journal of Economic LiteratureClassification Number: C71.

In this paper, we consider a continuum economy ℰ with a finite number of types of agent, and several private and public goods. The main result of the paper is that the graph of the equal-treatment Lindahl equilibria mapping is the unique abstract stable set with respect to the dominance relation in economies with crowding effects introduced by Vasil'ev et al. in 1995. The external stability of this mapping implies that, for any equal-treatment allocation x in ℰ, that is not a Lindahl equilibrium, there exists a subeconomy ℰ of ℰ such that one of its equal-treatment Lindahl allocations blocks x . This result is a counterpart of the theorem of Mas-Colell for Aumann's atomless market with private goods.

Greenberg (1990) and Ray (1989) showed that in coalitional games with a finite set of players the core consists of those and only those payoffs that cannot be dominated using payoffs in the core of a subgame. We extend the definition of the dominance relation to coalitional games with an infinite set of players and show that this result may not hold in games with a countable set of players (even in convex games). But if a coalitional game with a countable set of players satisfies a mild continuity property, its core consists of those and only those payoff vectors which cannot be dominated using payoffs in the core of a subgame.

It is well known that the core of a convex coalitional game with a finite set of players is the unique von Neumann–Morgenstern stable set of the game. We extend the definition of a stable set to coalitional games with an infinite set of players and give an example of a convex simple game with a countable set of players which does not have a stable set. But if a convex game with a countable set of players is continuous at the grand coalition, we prove that its core is the unique von Neumann–Morgenstern stable set. We also show that a game with a countable (possibly finite) set of players which is inner continuous is convex iff the core of each of its subgames is a stable set.Journal of Economic LiteratureClassification Numbers: C70, C71.

It is shown that the core of a non-atomic glove-market game which is defined as the minimum of finitely many non-atomic probability measures is a von Neumann–Morgenstern stable set. This result is used to characterize some stable sets of large games which have a decreasing returns to scale property. We also study exact non-atomic glove-market games. In particular we show that in a glove-market game which consists of the minimum of finitely many mutually singular non-atomic measures, the core is a von Neumann-Morgenstern stable set iff the game is exact.Journal of Economic LiteratureClassification Numbers: C70, C71, D24.

We show that in a production economy with public goods and a measure space of agents an allocation belongs to the core of the economy if and only if there exists no allocation in the core of a subeconomy that blocks it.

I apply the ‘Theory of Social Situations’ (Greenberg, 1990) to a special class of extensive form games of perfect information and without chance moves. I prove the existence of an ‘Optimistic Stable Standard of Behavior’ (OSSB) which is associated with such games. This class includes all n -person discounted sequential bargaining games where a finite set of strictly positive offers can be made at each stage. The derived OSSB yields an appealing selection from among the subgame perfect paths. As is always the case, OSSB is strongly related to the von Neumann and Morgenstern abstract stable sets.

We show that the core mapping of a mixed market is the unique optimistic stable standard of behavior for the core situation. That is, an allocation belongs to the core of a market if and only if there exists no allocation in the core of a submarket that blocks it.

We prove here that duopolistic market's core coincides with the associated split (atomless) market's core even when these sets are not guaranteed to coincide with the competitive allocations. In a small way, this result makes the counter intuitive Theorem B of Shitovitz (1973) easier to understand.

We characterize convex vNM-Stable Sets according to von Neumann and Morgenstern for orthogonal linear production games with a continuum of players. The results of Rosenmüller & Shitovitz [International journal of game theory 29 (2000), pp. 39-61] are thereby substantially improved. Simultaneously, this is a corrigendum concerning the proof of a lemma in our first paper.

We establish uniform continuity of the value for zero-sum games with differential information, when the distance between changing information fields of each player is measured by the Boylan pseudometric. We also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change (even with the weak topology on players' strategy sets), and is approximately lower semicontinuous.

We show that even in very simple oligopolies with differential information a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. However, we find sufficient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries. More general results arise when negative prices are allowed.

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy.

We study upper semi-continuity of the private and coarse core and the Walrasian expectations equilibrium correspondences for economies with differential information, with Boylan (1971) topology on agents information fields. Publicado

We derive alternative sufficient conditions for the value of public information to be either positive or negative in a Cournot duopoly where firms technology exhibits constant returns to scale. Publicado

Consider an oligopolistic industry where firms have access to the same technology but are asymmetrically informed about the environment. Even though it is commonplace to think that in this context superior information leads to higher profits, we find that under Cournot competition this is not generally the case: It holds when firms' technology exhibits constant returns to scale, but it does not necessarily hold otherwise. Journal of Economic Literature Classification Numbers: C72, D43, L13.

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. Publicado

We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Publicado

We study the relationship between the set of rational expectations equilibrium allocations and the ex-post core of exchange economies with asymmetric information.

Publisher Summary This chapter discusses the core in imperfectly competitive economies, and presents the study of mixed markets that includes in particular the study of alternative cooperative game-theoretic solution concepts in the framework of mixed markets and the problem of approximating mixed markets by finite exchange economies. The chapter begins with a brief comment about some surprising features of the core's behavior in such markets. The model of mixed markets has also been used to examine the behavior of other cooperative concepts, like the von Neumann and Morgenstern (v-N.M.) solutions, the bargaining set, and the transferable Shapley value. This survey is mainly concerned with the concept of the core. The problem of approximating mixed markets via large, but finite, economies, in the tradition for the approximation of atomless economies is discussed in the chapter.

The existence of a competitive equilibrium for an economy with a measure space of agents is proved by reducing the economy to a three-person game and then applying Debreu's lemma (1952). In addition to the relative simplicity and shortness of the proof, we generalize known results [Aumann (1966), Hildenbrand (1970), Schmeidler (1969)] by allowing both price dependent preferences and satiation.

In a rather long and complicated way Shitovitz proved that in mixed markets with at least two large traders all of the same ‘type’, all core allocations are competitive. We provide a simple and short proof for this important result. Unlike Shitovitz, we do not prove directly this equivalence. Rather, we first show that the core of an oligopolistic market coincides with the core of the atomless market derived by splitting the atoms into a continuum of traders. We then apply Aumann's Equivalence Theorem to this atomless market, whose set of competitive equilibria coincides with that of the original mixed market.