Simple Adaptive Strategies: From Regret-Matching To Uncoupled Dynamics, 1st Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 9814390704
  • ISBN-13: 9789814390705
  • DDC: 519.3
  • Grade Level Range: College Freshman - College Senior
  • 336 Pages | eBook
  • Original Copyright 2013 | Published/Released December 2014
  • This publication's content originally published in print form: 2013

  • Price:  Sign in for price



This volume collects almost two decades of joint work of Sergiu Hart and Andreu Mas-Colell on game dynamics and equilibria. The starting point was the introduction of the adaptive strategy called regret-matching, which on the one hand is simple and natural, and on the other is shown to lead to correlated equilibria. This initial finding - boundedly rational behavior that yields fully rational outcomes in the long run - generated a large body of work on the dynamics of simple adaptive strategies. In particular, a natural condition on dynamics was identified: uncoupledness, whereby decision-makers do not know each others payoffs and utilities (so, while chosen actions may be observable, the motivations are not). This condition turns out to severely limit the equilibria that can be reached. Interestingly, there are connections to the behavioral and neurobiological sciences and also to computer science and engineering (e.g., via notions of regret).Simple Adaptive Strategies is self-contained and unified in its presentation. Together with the formal treatment of concepts, theorems, and proofs, significant space is devoted to informal explanations and illuminating examples. It may be used for advanced graduate courses - in game theory, economics, mathematics, computer science, engineering - and for further research.

Table of Contents

Front Cover.
Half Title Page.
Other Frontmatter.
Title Page.
Copyright Page.
1: Correlated Equilibria.
2: Existence of Correlated Equilibria.
3: Regret Matching.
4: A Simple Adaptive Procedure Leading to Correlated Equilibrium.
5: A General Class of Adaptive Strategies.
6: A Reinforcement Procedure Leading to Correlated Equilibrium.
7: Regret-Based Continuous-Time Dynamics.
8: General Procedures Leading to Correlated Equilibria.
9: Uncoupled Dynamics.
10: Uncoupled Dynamics Do Not Lead to Nash Equilibrium.
11: Stochastic Uncoupled Dynamics and Nash Equilibrium.
12: Uncoupled Automata and Pure Nash Equilibria.
13: How Long to Equilibrium? The Communication Complexity of Uncoupled Equilibrium Procedures.
14: Dynamics and Equilibria.
15: Adaptive Heuristics.
16: Nash Equilibrium and Dynamics.