Game theory and applications

Licentiate thesis, 2021

Individual-level interactions and decisions spread though populations and change the collective-level dynamics in an intricate way.
Nevertheless, game theory is well suited for the unification of these viewpoints.
This thesis introduces the works The strength of diversity and Decisions and disease: a mechanism for the evolution of cooperation, which show that games have broad applications in population dynamics modeling.

In The strength of diversity we calculate the equilibrium strategies of the so-called game of teams.
The game of teams is an individual-level competition between teams, and a team's strategy in this context is a distribution of strength over the team members.
It turns out that the equilibrium strategies are flat distributions or 'alternating' flat distributions whenever there exists equilibrium strategies.

In Decisions and disease: a mechanism for the evolution of cooperation we combine the classic SIR and SIS models from epidemiology with the prisoner's dilemma game.
The transmission rate is computed as the average over defecting and cooperating individuals, and the individuals are subjected to a replicator equation that takes into account the portion of infectious members of the population.
We compute the steady state solutions and interpret the results.