An Optimization Landscape of Dynamics in Economies

Stability is one of the most sought properties in games and markets. Indeed, stability notions like Nash equilibrium and competitive (market) equilibrium have underpinned the developments of game theory and general equilibrium theory over the past few decades. However, if we view games and markets as distributed, myopic, noisy and/or random computers, there remain many interesting questions on how such "limited computers" can possibly reach an equilibrium. In this talk, I will survey some of the recent developments in applying convex optimization to achieve stability in limited computers via adaptive update rules (e.g., tâtonnement and proportional response). I will also discuss how amortized analysis and stochastic approximation can be applied to deal with asynchrony and randomness.

The talk is partly based on the joint works with Richard Cole, Nikhil Devanur, Stefanos Leonardos, Georgios Piliouras, Yixin Tao, Lexing Xie and Haiqing Zhu.