Core and equilibria in models of large household economy

Ekes, Maria

doi:10.4064/am30-4-5

Cited by 4 publications

(3 citation statements)

References 4 publications

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“…Subsequently, there is much literature on the convergences of the cores of different types of economies with different characteristics and infinitely or finitely many agents and on the convergence rate (Aumann, 1979; Debreu, 1975; Ekes, 2003; Lahiri, 2007; McLean & Postlewaite, 2005; Minelli & Polemarchakis, 2000; Rajan, 1997; Shapley & Shubik, 1969; Suzuki, 2013).…”

Section: Introductionmentioning

confidence: 99%

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

Chen

2022

Bulletin of Econ Res

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Debreu and Scarf (1963), Hildenbrand (1974), Aumann (1964, Dierker (1975), Bewley (1973), and others have shown that the core of an exchange economy with infinitely many or finitely many traders converges. However, an exchange economy does not always consist of infinitely many or finitely many traders. This note provides proof of the core convergence theorem on an exchange economy with limited traders by a bargaining game methodology. The main contribution of this note is to innovate the equilibrium solution to the bargaining game in the exchange economy. In this note, the concept of common payoff is introduced; in the bargaining game of a coalition on its common payoff, all coalition members will get the same distribution, thus the distribution scheme of the cooperation surplus of the exchange economy is determined.This note shows that the bargaining game among the traders on the distribution of the cooperation surplus will make the pure exchange economy with limited traders converge to the Walrasian equilibrium, all the allocations other than the Walrasian equilibrium will be eliminated from the core of this economy.

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Section: Introductionmentioning

confidence: 99%

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

Chen

2022

Bulletin of Econ Res

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“…Production-consumption models. A model of production and consumption, presented by Wieczorek in [2004] and also studied by Ekes (Roman) and Wieczorek [1999] and Ekes [2003], deals with infinitely many agents who first face the choice among k activities (the choice of the jth activity by an agent yields the production of a fixed amount of the jth good only) and then consume the goods jointly produced. The existence of a competitive equilibrium has been proven in Wieczorek [2004] by a reduction of the model to an LSF-game.…”

Section: Applications In Economics and Social Sciencesmentioning

confidence: 99%

Large games with only small players and strategy sets in Euclidean spaces

Wieczorek

2005

Appl. Math. (Warsaw)

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Abstract. The games of type considered in the present paper (LSEgames) extend the concept of LSF-games studied by Wieczorek in [2004], both types of games being related to games with a continuum of players. LSE-games can be seen as anonymous games with finitely many types of players, their action sets included in Euclidean spaces and payoffs depending on a player's own action and finitely many integral characteristics of distributions of the players' (of all types) actions. We prove the existence of equilibria and present a minimization problem and a complementarity problem (both nonlinear) whose solutions are exactly the same as equilibria in the given game. Examples of applications include a model of social adaptation and a model of economic efficiency enforced by taxation.1. The basic concepts. The object of our study, large games with only small players and strategy sets in Euclidean spaces (if necessary, we refer to them as LSE-games; L for large, S for small and E for Euclidean) is more general than that considered by Wieczorek in [2004] (referred to there as LSF-games), but the present paper offers results of different kind. The LSEgames deal with situations involving a large number of anonymous players who independently choose their actions in a set included in a Euclidean space and whose payoffs depend on finitely many integral characteristics of distributions of the players' actions. This concept generalizes that of LSEgames in Wieczorek [2004], where the sets of actions were assumed finite. Not

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“…However, unlike most models dealing with similar questions, we have not introduced a single entity aimed to reflect the influence of market clearing powers, but rather an infinity of small subjects who eventually elaborate a market clearing price system, but this is done in a decentralized manner as a result of actions performed independently and often with different targets in their range of vision. Efficiency in the presented model was studied by Roman (Ekes) and Wieczorek [1999], core and quasi-core by Ekes [2003], and general aspects by Wieczorek [2002].…”

Section: Theorem (Equal Treatment) At a Cournot-nash Equilibrium Thementioning

confidence: 99%

Large games with only small players and finite strategy sets

Wieczorek

2004

Appl. Math. (Warsaw)

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Abstract. Large games of kind considered in the present paper (LSFgames) directly generalize the usual concept of n-matrix games; the notion is related to games with a continuum of players and anonymous games with finitely many types of players, finitely many available actions and distribution dependent payoffs; however, there is no need to introduce a distribution on the set of types. Relevant features of equilibrium distributions are studied by means of fixed point, nonlinear complementarity and constrained optimization procedures in Euclidean spaces. The games are shown to fit well the voting procedures and evolutionary processes. As an example of application, we present a model of production and consumption by infinitely many households; a competitive equilibrium is obtained via a reduction to an LSF-game; the equilibrating market mechanism is modelled by actions of infinitely many small corrective powers.

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Core and equilibria in models of large household economy

Abstract: The paper deals with models of household economy with infinitely many agents classified into a finite number of types. The notions of competitive equilibrium, core and quasi-core are examined with special emphasis on their mutual relations.

Cited by 4 publications

References 4 publications

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

Large games with only small players and strategy sets in Euclidean spaces

Large games with only small players and finite strategy sets

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