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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.

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.

We show that even in very simple oligopolies with d ifferential 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 equilibri um in a certain class of industries. More general r esults arise when negative prices are allowed.

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.

We show that in a (finite) neoclassical pure exchange economy (with a weaker monotonicity condition than the usual one): if the number of traders of each type is the same and every type has a corner on one of the commodities, then the set of all symmetric Pareto-optimal allocations in the economy (i.e., Pareto-optimal allocations which assign indifferent commodity bundles to traders of the same type) is a von Neumann–Morgenstern stable set. Moreover, this is the unique stable set of symmetric allocations. A similar result holds in atomless economies with a finite number of types without the convexity assumption on the preference relations. It is also not necessary to assume (in the atomless case) that the members of the types' partition have the same measure.

Within the framework of (pure) exchange economies, we demonstrate that the von Neumann and Morgenstern stable set in the allocation space may differ from that in the corresponding utility space. Following Harsanyi (1974, Management Sci. 20 , 1472–1495), we then define the notion of the sophisticated stable set and establish an equivalence theorem: like the core, the sophisticated stable set in the allocation space coincides with that in the utility space. We also show that the sophisticated stable set has the desirable property of individual rationality. Journal of Economic Literature Classification Numbers: D51, C70, C71.

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.

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 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.

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 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 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.

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

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.

Consider a core allocation in a differentiable mixed market. It is shown that if this allocation can be derived by splitting the market [see Definition (1) below], then the monetary exploitation of the small traders disappears. We present examples of particular economies to which our theorem applies.

In this paper we investigate the number of coalitions that block a given non-competitive allocation. In an atomless economy with a finite number of types we identify coalition with its profile. Considering profiles π that represent coalitions with the same proportions of types as in the whole society, we prove that there is a ball B π with π as its center so that ‘almost half’ of the profiles in B π are blocking. This result is an analogous result to that of Mas-Colell (1978) who dealt with large finite markets.

Let ( R 1 ,…, R k ) be an arbitrary partition of the grand coalition in an atomless exchange economy with k “large enough.” We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the R i 's. K is “large enough” if k ⩾ r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x . Recall that it is always true that r ⩽ n , when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R , an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).

Considered are economies with a single output (a single consumption good) which is produced from l inputs by means of an increasing returns to scale production function f. We show that for quasi-concave and homogeneous functions f of degree r ⩾ 1, the Aumann-Shapley prices constitute a simple Scarf Social Equilibrium. Put differently, Shapley value of the associated atomless game is in the core of that game. Such is not the situation, however, in the more general case when f exhibits increasing returns to scale (but in homogeneous).

We study the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector. We show that under appropriate assumptions, the asymptotic nucleolus of the TU market game coincides with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite game belonging to its core and the Aumann Core Equivalence, which holds for this economy due to the cut-throat competition among the identical large players. A comparison with the Shapley value yields that in some cases, the asymptotic Shapley value is more favorable for the large traders than the asymptotic nucleolus. This may be interpreted by the `fairness property' of Shapley Value which does not reflect the intense competition among the large traders, accounting for the relative importance of their marginal contribution.