The inauguration of the biological interest in game theory unveiled a new horizon of thinking about the paradigm change regarding the level of aggregation. I am very curious about exploring the Evolutionary game theory (EGT), which is a fine development of evolutionary biology that combines game theory, evolution, and dynamical systems to interpret various biological situations. Individual or group-wise interaction in a population seems to be normal for survival in nature. These interactions are the key incident of our interest. Most biological games are generally a never-ending interaction to survive. Different kinds of phenotypes and behavioral characteristics of a population(or populations) are considered strategies for biological interaction (or game). The players who do not use a sufficient good strategy are invaded by the players who use a better strategy. Individuals who are better adapted to their environment will have more offspring than others, so their characteristics will spread. In a biological scenario, we try to find out such a trait or phenotype that can defend from invasion by other mutant phenotypes. That means a phenotype is the best response to the opponent phenotype executed in a biological game. The fitness (in function form called pay-off function) for each of the strategies is determined with the help of the pay-off matrix of the game. In the discrete case, we try to find out the Nash equilibria of the game, which leads us to our evolutionary stable strategy. For continuous cases, a dynamical system is proposed called the replicator equation (Taylor & Jonker 1978, Zeeman 1980), which is mainly a frequency dependent analysis of the evolutionary game.
My research focuses on the ecological aggregation of game theoretical analysis of evolutionary biology. We have noticed that too we have tried to create an extended model where replicator dynamics can combine both relative frequency and carrying capacity of the environment. From this new density dependent replicator dynamics, we can learn in detail about the simultaneous DDESS and overall population size changes.
Key research interests are
Mathematical Biology
Mathematical Ecology
Game dynamics
Evolutionary game theory
Fractional Calculus