Chaos, Extremism and Optimism: Volume Analysis of Learning in Games
Yun Kuen Cheung, Georgios Piliouras
Using these tools, we prove two novel, rather negative properties of MWU in zero-sum games. (1) Extremism: even in games with a unique fully-mixed Nash equilibrium, the system recurrently gets stuck near pure-strategy profiles, despite them being clearly unstable from game-theoretic perspective. (2) Unavoidability: given any set of good states (with a rather relaxed interpretation of “good” states), the system cannot avoid bad states indefinitely.
