Research

In this project, we studied behavioural games with myopic-rational and herding players, which commonly arise in online markets, transportation systems or financial markets. Below mentioned are the two aspects that we explored:

(1) alpha-rational Nash Equilibrium: Suppose that there is an alpha-fraction of perfectly rational players, while others are herding players, in an infinitely large population. For the corresponding mean-field game, we proposed and characterised the equilibrium outcomes. We investigated the impact of the presence of herding players on the outcome of the game to conclude that in many scenarios, all players benefit.

(2) Behavioral Dynamics in Games with Herding: Suppose that there is alpha-fraction of myopic-rational players, while others are herding players, in a infinitely large population. The players choose their actions one after the other, and can choose the action only once. For such a setting that can be seen in participation games (e.g., crowd-sourcing) or minority games, we derived the limiting analysis of the dynamics using stochastic approximation techniques. It is observed that the set of limits is a subset of the set of alpha-rational Nash equilibria. 

Branching process (BP) is a special stochastic process used to analyse the population dynamics (growth of population over time). During PhD, I worked on a novel class of BP where offspring distribution depends on both living and living+dead individuals. The thesis contributes on two main aspects:

(1) Limiting analysis: For the first time, we applied the stochastic approximation (SA) technique to derive the time-asymptotic proportion of the populations. Our analysis used a non-trivial, non-autonomous, measurable ODE to show that the proportion either converges to attractors or saddle points of the ODE, or hovers around saddle points with non-zero probability.  

Hovering around is a new, non-convergent behaviour where the proportion exhibits “nearness” to the saddle point. 

(2) Application to Online Social Networks: Using our theory, we explored various aspects of content propagation like (i) effect of competition and re-sharing, (ii) controlling fake-post propagation in the presence of adversaries, using users' responses.