An Evolutionary Model of Subgame Perfect Equilibrium

Classical game theory begins with the assumption that its agents are rational, and proceeds to find various solution concepts from these premises. These solution concepts are often interpreted as the rational way to behave in games. However, this method often faces normative (and empirical) concerns on the validity of its rationality assumptions. This is particularly the case in games with complex structures (e.g. dynamic games or games involving uncertainty), where the rationality assumptions become increasingly strong. 

One useful tool for evaluating these rationality assumptions is evolutionary game theory. Unlike classical game theory, evolutionary game theory makes no such assumptions of rationality, but instead begins with specifying a rule or dynamic by which the system (e.g. a population or an individual’s strategies/beliefs) evolve over time. However, most evolutionary dynamics currently treat dynamic games in their normal form - this makes them unable to properly represent the backward induction and subgame perfect equilibrium, an important solution concept specifically for dynamic games. 

In this thesis, I discuss some of the connections between these two theories, including examples of when they agree and disagree. I then present a modified version of a popular evolutionary dynamic (the replicator equation) that is capable of selecting for subgame perfect equilibrium. This model has two different settings that can be used to model situations of evolution (not rational) and situations of learning (rational), and is also potentially useful for modeling evolutionlearning hybrid scenarios. In addition, the new model is computationally much simpler than the original, as it breaks down the strategy space in this way.