Motivation: Improving understanding of relationship between learning theory and game theory.
Topic: Study the behavior of learning algorithms in mortal population games, in the γ→1 limit. Specifically, consider the problem statements from the linked comment:
Are any/all of the fixed points attractors?
What can be said about the size of the attraction basins?
Do all Nash equilibria correspond to fixed points?
Do stronger game theoretic solution concepts (e.g. proper equilibria) have corresponding dynamical properties?
You can approach this theoretically (proving things) or experimentally (writing simulations). Specifically, it would be easiest to start from agents that follow fictitious play. You can then go on to more general Bayesian learners, other algorithms from the literature, or (on the experimental side) to using deep learning. Compare the convergence properties you get to those known in evolutionary game theory.
Notice that, due to the grain-of-truth problem, I intended to study this using non-Bayesian learning algorithms, but due to the ergodic-ish nature of the setting, Bayesian learning algorithms might perform well. But, if they perform poorly, this is still important to know.
Motivation: Improving understanding of relationship between learning theory and game theory.
Topic: Study the behavior of learning algorithms in mortal population games, in the γ→1 limit. Specifically, consider the problem statements from the linked comment:
Are any/all of the fixed points attractors?
What can be said about the size of the attraction basins?
Do all Nash equilibria correspond to fixed points?
Do stronger game theoretic solution concepts (e.g. proper equilibria) have corresponding dynamical properties?
You can approach this theoretically (proving things) or experimentally (writing simulations). Specifically, it would be easiest to start from agents that follow fictitious play. You can then go on to more general Bayesian learners, other algorithms from the literature, or (on the experimental side) to using deep learning. Compare the convergence properties you get to those known in evolutionary game theory.
Notice that, due to the grain-of-truth problem, I intended to study this using non-Bayesian learning algorithms, but due to the ergodic-ish nature of the setting, Bayesian learning algorithms might perform well. But, if they perform poorly, this is still important to know.
Strategies: See my other answer.