Statement of Purpose

I have been interested in mathematics and recently won gold honour for securing a rank among the top 5 percentile in International Youth Math Challenge, 2019. In high school, however, I was more interested in making funny questions which used to make even my teachers smile once they figured out the answers. This innate urge towards mathematical thinking made me switch my major from Material Science and Engineering to Economic Sciences. This decision was a turning point of my life because it introduced me to game theory and eventually led me to become a finalist in NC Ray Paper Presentation Competition, 2019 for my work ‘Grammar Acquisition Game’. Thus my long term objective molded into researching behavioural and experimental game theory.

Game Theory has a tendency to slither into astronomically different fields, ranging from mathematics to biology, and also an immense potential to mark its significance. In economics, while game theory has had an impact in understanding and theoretically modelling behaviour, experimental studies on decision making and economic behaviour has also changed how game theory used to be perceived. The research at UCL has produced interesting propositions about game theory and its applicability. The works such as ‘Behavioral Economics and the Atheoretical Style’ and ‘Coordination under limited depth of reasoning’ deal with concepts which I find very intriguing. Also the workshops and seminars organised at UCL provide immense scope for learning. So considering the opportunities and exposures University College London provides the exact environment required for me to grow and pursue an exciting career in research.

The combination of a major in Economic Sciences and a minor in Cognitive Science enabled me to understand different perspectives of decision making and learning in strategic environment. This understanding has motivated me to work at the intersection of the two fields. In my undergraduate project, ‘Investigating Reinforcement learning through Evolutionary Game Theory’ I determined the evolutionarily stable strategy for learning the type of an opponent in a finitely repeated prisoner’s dilemma. The reinforcement learning strategies were Bush-Mosteller model and Temporal Difference Learning Model. I found that Temporal Difference Learning model was the evolutionarily stable strategy, primarily due to myopic nature of Bush-Mosteller model. This project taught me how to model situations through game theoretic perspective. Moreover, I noticed that the likelihood of choice of action learnt through reinforcement learning and the proportion of population opting an action subject to replicator dynamics, follow different perspectives of a similar idea.

In ‘The Game of Adjustment’ I determined a subjective optimal point between two extremes of a dimension of adjustment. In psychology, adjustment is the process by which one achieves harmony with oneself and the environment through changes in their behaviour and there are six dimensions of adjustment each with their extremes. The motivation was to show that an individual can display behaviour comprising of different extremes rather than strictly adhering to the one they have been characterised as, depending on their environment. I verified the same for tolerance using game theory. Tolerance, one of the dimensions of adjustment, has two extremes one being indiscriminate acceptance of self and others and the other extreme rejection. That is, in a game-theoretic setting with available actions being acceptance and rejection, subjectively a mixed strategy can be an optimal solution and the individual can display acceptance with some non zero probability in a given environment.

In ‘Grammar Acquisition Game’ I modeled grammar learning using game theory. The Universal Grammar hypothesis postulates that the set of structural features of speech and language is finite, thus there can be a finite number of grammars. A learner will receive greater communication success if it uses those features which are being used in its environment. So the grammars which are similar to the grammar being used in the environment should have a higher likelihood of being taught than a dissimilar grammar. Thus the grammar being used in the environment must have greatest fitness, so a learner must select the evolutionarily stable grammar. I accounted for limited memory and processing by limiting the number grammars processed at a time. Now since the number of grammars is finite and the learner selects the grammar with highest fitness it will reach at the correct grammar. This model accounts for the fact that children in early stages can use incorrect grammar but eventually learn the correct one. This work made me the finalist in NC Ray Paper Presentation Competition, a platform for undergraduate students to showcase and test their ideas. The prevalent trend among my peers is to opt for non academic jobs so I faced extreme social pressure against opting a research career but this accomplishment encouraged me to overcome this hurdle.

I volunteered to be the academic mentor for mathematics in my first year as an undergraduate. My responsibilities included taking remedial classes, doubt clearing sessions and one on one tutoring for the course ‘Linear Algebra Ordinary Differential Equation’ and some subtopics of the course ‘Calculus’. After my tenure as an academic mentor I took an internship as content developer with Xprep, for which I was required to write original mathematics questions for high school students. In the course of my dual degree I gained interdisciplinary experience and being from a technological institute I have a strong mathematical background. I also have hands on experience and theoretical background of econometrics.

I believe that a multidisciplinary perspective is currently much required for development of behavioural economics and will soon be imminent. I have cultivated my skills with this belief I hope that they align with the requirements of your department. And the opportunities offered by your department will help me in expanding my knowledge and experience. I am sure that my enthusiasm, sincerity and the excellence of your program can help me explore behavioural game theory. I would be deeply honored to study at University College London. Thank you for your time and consideration.