arXiv subjects

Anuj Bhowmik

Publications and source records attributed to Anuj Bhowmik.

6 recordsLinked to original sources

arXiv2025

Characterizations of equilibrium allocations in an economy with public goods and infinitely many commodities

This paper examines the characterizations of equilibrium in economies with public projects. Public goods, as discussed by Mas-Colell (1980), are modeled as elements of an abstract set lacking a unified ordering structure. We introduce the concepts of cost share equilibrium for such economies, where the private commodity space is a (possibly nonseparable) Banach lattice. Within this framework, we present two distinct characterizations of cost share equilibria via the veto power of the grand coalition in economies featuring finitely many agents. The first characterization involves allocations that are Aubin non-dominated, while the second establishes that an allocation is a cost share equilibrium if and only if it cannot be dominated by the grand coalition, where domination is considered under specific perturbations of initial endowments.

econ.TH↗

arXiv2025

Carath\'eodory-type selection and random fixed point theorems for discontinuous correspondences

Research in Economics and Game theory has necessitated results on Carath\'eodory-type selections. In particular, one has to obtain Carath\'eodory type-selections from correspondences that need not be continuous (neither lower-semicontinuous nor upper-semicontinuous). We provide new theorems on Carath\'eodory type-selections that include as corollaries the results in Kim-Prikry-Yannelis \cite{KPY:87}. We also, obtain new random fixed-point theorems, random maximal elements, random (Nash) equilibrium and Bayesian equilibrium extending and generalizing theorems of Browder \cite{Browder:68}, Fan \cite{Fan:52} and Nash \cite{Nash}, among others.

math.GN↗

arXiv2017

Ex-post core, fine core and rational expectations equilibrium allocations

This paper investigates the ex-post core and its relationships to the fine core and the set of rational expectations equilibrium allocations in an oligopolistic economy with asymmetric information, in which the set of agents consists of some large agents and a continuum of small agents and the space of states of nature is a general probability space. We show that under appropriate assumptions, the ex-post core is not empty and contains the set of rational expectations equilibrium allocations. We provide an example of a pure exchange continuum economy with asymmetric information and infinitely many states of nature, in which the ex-post core does not coincide with the set of rational expectations equilibrium allocations. We also show that when our economic model contains either no large agents or at least two large agents with the same characteristics, the fine core is contained in the ex-post core.

econ.GN↗

arXiv2012

Aggregate Preferred Correspondence and the Existence of a MREE

In this paper, a general model of a pure exchange differential information economy is studied. In this economic model, the space of states of nature is a complete probability measure space, the space of agents is a measure space with a finite measure, and the commodity space is the Euclidean space. Under appropriate and standard assumptions on agents' characteristics, results on continuity and measurability of the aggregate preferred correspondence in the sense of Aumann in [4] are established. These results together with other techniques are then employed to prove the existence of a maximin rational expectations equilibrium (maximin REE) of the economic model.

math.FA↗

arXiv2011

Infinite dimensional mixed economies with asymmetric information

In this paper, we study asymmetric information economies consisting of both non-negligible and negligible agents and having ordered Banach spaces as their commodity spaces. In answering a question of Hervés-Beloso and Moreno-García, we establish a characterization of Walrasian expectations allocations by the veto power of the grand coalition. It is also shown that when an economy contains only negligible agents a Vind's type theorem on the private core with the exact feasibility can be restored. This solves a problem of Pesce.

math.FA↗

arXiv2011

On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces

In this paper, we establish two different characterizations of Walrasian expectations allocations by the veto power of the grand coalition in an asymmetric information economy having finite numbers of agents and states of nature and whose commodity space is a Banach lattice. The first one deals with Aubin non-dominated allocations, and the other claims that an allocation is a Walrasian expectations allocation if and only if it is not privately dominated by the grand coalition, by considering perturbations of the original initial endowments in precise directions.

math.FA↗