Ashoka University is a private university located in Sonipat, Haryana, India, focusing on liberal arts and sciences. It was established in 2014.&nbsp;It is guided by an academic council of academics and scholars from around the world. The council sets the university&#39;s academic standard, advising on matters of curriculum, faculty hiring and research.&nbsp;

Ashoka University offers a full-time 3 (+ 1) year undergraduate programme. The University comprises of&nbsp;2500 plus students, with a mix of both national and international students.&nbsp; &nbsp;

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Ashoka University

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Department of Economics

Journal of Dynamics and Games

TRIBUTES TO BILL SANDHOLM

Economic Theory

Evolutionary robustness of dominant strategy implementation

Due to externalities, the equilibrium behavior in aggregative games is not efficient in the sense of maximizing aggregate payoff. We characterize conditions such that efficiency can be globally implemented in such games under evolutionary dynamics. If payoffs satisfy certain important concavity conditions, then the aggregate payoff function of these games has a unique maximizer. Once the planner imposes a transfer equal to the externality generated by agents, we obtain a new externality adjusted game. This is a potential game with the aggregate payoff function of the original game being its potential function. Evolutionary dynamics converge globally to the maximizer of this potential function, thereby implementing efficiency in the original game. Our earlier paper on public goods (Lahkar and Mukherjee, 2019) emerges as an example of the present general analysis. Two new applications are public bads and the tragedy of the commons.

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Mathematical Social Sciences

Evolutionary implementation in aggregative games

We consider a generalization of perturbed best response dynamics in population games with a continuum of strategies. The previous literature has considered the logit dynamic generated through the Shannon entropy as a deterministic perturbation. We consider a wider class of deterministic perturbations satisfying lower semicontinuity and strong convexity. Apart from the Shannon entropy, Tsallis entropy and Burg entropy are other perturbations that satisfy these conditions. We thereby generate the generalized perturbed best response dynamic with a continuum of strategies. We establish fundamental properties of the dynamic and show convergence in potential games and negative semidefinite games.

Journal of Economic Theory

Generalized Perturbed Best Response Dynamics with a Continuum of Strategies

We consider a large population of firms in a market environment. The firms are divided into a finite set of types, with each type being characterized by a distinct private cost function. Moreover, the firms generate an external cost like pollution in the production process. As a result, the Nash equilibrium outcome is not socially optimal. We propose an evolutionary implementation mechanism to achieve the socially optimal outcome. In contrast to the classical VCG mechanism, evolutionary implementation does not require the planner to know or elicit any private information from firms. By imposing a tax equal to the current external damage being imposed by a firm, the planner can guide the evolution of the society toward the social optimum. The imposition of the tax generates a potential game whose potential function is the social welfare function of the model. Evolutionary dynamics converge to the maximizer of this function thereby evolutionarily implementing the social welfare maximizer.

Dynamic Games and Applications

An Evolutionary Approach to Pollution Control in Competitive Markets

We consider a supply chain where manufacturers can be differentiated along two dimensions—product quality and cost of social responsibility effort. There are two types of manufacturers: high and low. Under complete information, high-type manufacturers exert a greater level of social responsibility effort in comparison with the low-type manufacturers. We then show that under incomplete information, high-type manufacturers have an incentive to exert an even greater level of social responsibility effort. Surprisingly, the extent of effort put in by high-type firms cannot be lower and, in some cases, can be strictly higher under incomplete information.

Managerial and Decision Economics

Can incomplete information lead to better social outcomes?

We consider implementation of the efficient state in a large population public goods game. Agents are divided into a finite set of types. The planner asks agents to report types, which generates a reported type distribution. Based on reported types and distribution, the planner calculates the efficient strategy level and a Pigouvian transfer for each type of agent. We show that this direct mechanism satisfies incentive compatibility in strictly dominant strategies, strong budget balance and ex-post individual rationality.

Economics Letters

Dominant strategy implementation in a large population public goods game

We study evolution of preferences in large population aggregative games. In such games, all agents in society interact with each other. The material payoff or fitness of agents is entirely individualistic. Subjective payoffs, which represent preferences, depend upon a non-individualistic component which is adjusted through a type-dependent preference parameter. Using the indirect evolutionary approach, we show that the individualistic type enjoys fitness dominance under any type distribution in such games. Hence, under a class of evolutionary dynamics that satisfy monotone percentage growth, all non-individualistic types are eliminated. We apply this analysis to two classes of non-individualistic preferences-altruistic and Kantian. Altruistic preferences put a positive weight on the externality imposed on society while Kantian preferences incorporate the Kantian categorical imperative. In two important economic models, the tragedy of the commons and the public goods game, we show that both these classes of preferences are eliminated.

Journal of Mathematical Economics

Elimination of non-individualistic preferences in large population aggregative games

We consider the relationship between inequality and the business cycle. Empirical evidence suggests mutual causality between GDP and inequality over the business cycle and the countercyclical nature of inequality. We construct an evolutionary game-theoretic model with two types of workers to explain these observations. Cognitive workers produce capital of varying quality, which determines the productivity of physical workers who obtain the capital through an exogenous search process. We apply the logit dynamic to the model. The model satisfies positive definiteness due to which, both GDP and inequality converge to limit cycles and, therefore, fluctuate over time. These cyclical fluctuations have a common origin in the underlying evolutionary dynamic process, which explains the empirical observation of mutual causality between these variables. Further, simulations suggest an inverse relationship between GDP and inequality in our model, which accounts for the countercyclical nature of inequality.

Network Theory and Agent-Based Modeling in Economics and Finance

A limit cycle view of inequality

We consider population games in which payoff depends upon the aggregate strategy level and which admit a potential function. Examples of such aggregative potential games include the tragedy of the commons and the Cournot competition model. These games are technically simple as they can be analyzed using a one-dimensional variant of the potential function. We use such games to model the presence of externalities, both positive and negative. We characterize Nash equilibria in such games as socially inefficient. Evolutionary dynamics in such games converge to socially inefficient Nash equilibria.

Large Population Aggregative Potential Games

Using a survey dataset collected from Andhra Pradesh, India, we test if multiple borrowing is equivalent to over-borrowing. Results suggest that over-borrowing and multiple loans are not necessarily synonymous. As the number of credit agencies in a village increases, the average loan burden of villagers does not increase. We also find evidence of substitution of formal sources of credit for informal ones with increased presence of formal credit institutions. Such substitution is greater with addition of microcredit institutions than with other formal lending agencies. Our results indicate that joint liability setup seems to ensure that individuals at a greater risk of non-repayment are discouraged from obtaining microcredit.

Enterprise Development and Microfinance

Does multiple borrowing necessarily mean over-borrowing?

In this article, we discuss the possibility of economics as a discipline emulating the success of hard sciences. In our view, a fundamental obstacle arises from the fact that economics does not have (m)any stable and robust laws governing economic systems that hold true irrespective of the source of data. One possible but untested way to introduce some of the evolving features of large scale economic systems, e.g. out-of-equilibrium dynamics and finite rationality, is evolutionary game theory.

European Physical Journal: Special Topics

Absence of economic and social constants

The expansion of microfinance has triggered concerns of rising indebtedness and higher default and interest rates. Using a screening model, we show that even if interest and default rates increase due to expansion, borrower welfare may improve. This is because: (i) all borrowers previously denied credit can obtain loans and (ii) screening costs for pre-existing borrowers go down. Hence, policies that seek to regulate interest and screening levels can be counterproductive.

Economic Modelling

Expansion and welfare in microfinance: A screening model

We define the logit dynamic for games with continuous strategy sets and establish its fundamental properties, namely, the existence of a logit equilibrium, its convergence to a Nash equilibrium as the perturbation factor becomes small and existence, uniqueness and continuity of solution trajectories. We apply the dynamic to the analysis of potential games and negative semidefinite games. We show that in a restricted state space of probability measures with bounded density functions, solution trajectories of the logit dynamic converge to logit equilibria in these two classes of games.