Research Projects

Every economy is identified on the basis of activities undertaken by individuals and organizations who are part of it. We analyze individuals and their decisions in a quantitative social science setting. Precisely, we posit certain mathematical economics frameworks and use various analytical tools and techniques from mathematics to solve this project. Arrow and Debreu \cite{Arrow} first established that an overall outcome or equilibrium does exist for an economy with a finite set of agents. The study of Arrow and Debreu highlighted one of the avenues of looking at the question: the market mechanism. The other outcome was the cooperative mechanism, namely the core. A more fitted adaptation of such frameworks to real-life scenarios is that of licenses. In an era where pollution levels are controlled, certain species of animals are being protected, individuals need permits for consumption or other related activities concerning such commodities. Although licenses are not a part of an individual's consumption directly, they influence their consumption by granting consumption rights to them. Herves-Beloso et al. consider markets with such tradable license rights and establish the existence of market equilibrium for a finite number of agents. A different kind of setup deals primarily with information possessed by individuals. For a measure space of agents, we define a coalition of agents to be any positive measurable subset of the entire set of agents. Now, given that each individual possesses some information, the question is how one aggregate information for coalitions. The core of such an economy has been characterized based on the governing information rule and the relationship between the various cores has been studied quite extensively. Since its inception, economics has been concerned with how wealth is created in an economy and how the social division of labor enhances wealth creation. Consumers who act as producers individually specialize in producing certain commodities. This further results in increasing returns to specialization, a notion parallel to increasing returns to scale. The adaptation of general equilibrium theory to such settings with collective goods is fairly new, and classical results like the existence of an equilibrium, welfare theorems, and the core-equivalence theorem have been studied by Giles and his co-authors. The main goal of this research project is to build up a general framework, which can be used to analyze some unsolved key problems in the area of economies involving tradable licenses, information sharing rules, and social division of labor. To do this, mathematical concepts and techniques from Functional Analysis, Measure Theory, and Set-valued Analysis will be employed. Upon completing this project we shall further extend the remarks by Schmeidler, Vind, Grodal, and the existence of equilibrium to further robust scenarios.