Sequential Equilibria in Infinite Extensive Form Games

Explore a comprehensive lecture on sequential equilibria in infinite extensive form games presented by Michael Greinecker at the One World Mathematical Game Theory Seminar. Delve into the complexities of games with uncountable action spaces, focusing on multistage games and the challenges posed by informational discontinuities. Learn about the characterization of sequential equilibrium strategy profiles, the importance of continuous signal functions, and the concept of strategic measures. Examine how probability zero events impact game dynamics and why sequential rationality is tested only at observable events. Gain insights into the limitations of completely mixed strategies and the alternative approach of using strategic measures that reach all observable events.

Intro
There is no sequential equilibrium when players can choose from a continuum of actions
We start from a characterization of sequential equilibrium strategy profiles
Completely mixed strategies only guarantee that all information sets are reached
We focus on multistage games
The pathologies of games with uncountable action spaces come from informational discontinuities
Our main assumption says that signal functions are continuous
Strategies tell more than what players would do
Strategies induce strategic measures
Strategic measures behave well
Probability zero events matter because which events have probability zero is endogenous
Information sets contain all past signals and all past own actions of a player
It is not that bad if a player conditions on their previous actions imperfectly
We use strategic measures that reach all observable events instead of completely mixed strategies
Sequential rationality is only tested at observable events