## Learning in Games

*18 Jul 2023 08:34*

That is, learning in game *theory*, or at least contexts pretty
close to it.

- See also
- Collective Cognition
- Economics
- Evolutionary Economics
- Evolutionary Game Theory
- Learning Theory
- Low-Regret Learning
- Machine Learning, Statistical Inference and Induction
- Mean-Field Games the Minority Game
- Sequential Decisions Under Uncertainty
- Universal Prediction Algorithms

- Recommended, big picture:
- Nicolo Cesa-Bianchi and Gabor Lugosi, Prediction, Learning, and Games
- Herbert Gintis, Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction
- Larry Samuelson, Evolutionary Games and Equilibrium Selection
- William Sandholm, Population Games and Evolutionary Dynamics

- Recommended, close-ups:
- Jenna Bednar and Scott Page, "Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior Within Multiple Games",
Rationality and Society
**19**(2007): 65--97 [PDF preprint via Prof. Bednar] - Lawrence E. Blume and David Easley
- "If You're So Smart, Why Aren't You Rich? Belief Selection
in Complete and Incomplete Markets", Econometrica
**74**(2006): 929--966, SFI Working Paper 01-06-031 - "Optimality and Natural Selection in Markets," SFI Working Paper 98-09-0 82

- "If You're So Smart, Why Aren't You Rich? Belief Selection
in Complete and Incomplete Markets", Econometrica
- Tilman Börgers and Rajiv Sarin, "Learning Through Reinforcement and Replicator Dynamics", Journal of Economic Theory
**77**(1997): 1--14 - Vivek S. Borkar, "Reinforcement Learning in Markovian Evolutionary Games", Advances in Complex Systems
**5**(2002): 55--72 - William A. Brock and Cars H. Hommes, "A Rational Route to Randomness", Econometrica
**65**(1997): 1059--1095 - Christophe Chamley, Rational Herds: Economic Models of Social Learning
- Ido Erev and Alvin E. Roth, "Simple Reinforcement Learning Models and Reciprocation in the Prisoner's Dilemma Game", pp. 215--232 in Gigerenzer and selten (eds.), Bounded Rationality
- Ignacio Esponda, Demian Pouzo, Yuichi Yamamoto, "Asymptotic Behavior of Bayesian Learners with Misspecified Models", arxiv:1904.08551
- Dean P. Foster and H. Peyton Young, "Learning, hypothesis testing,
and Nash equilibrium," Games and Economic
Behavior
**45**(2003): 73--96 [pdf] - Joseph Y. Halpern, Rafael Pass, "Iterated Regret Minimization: A More Realistic Solution Concept", arxiv:0810.3023 [Somewhat astonishingly, does mention the huge literature on low-regret learning]
- Ariel Rubinstein, Modeling Bounded Rationality [Review:
*O docta simplicitas!*] - Timothy C. Salmon, "An Evaluation of Econometric Models of Adaptive Learning", Econometrica
**69**(2001): 1597--1628 - José M. Vidal and Edmund H. Durfee, "Predicting the Expected Behavior of Agents That Learn About Agents: The CLRI Framework," cs.MA/0001008
- H. Peyton Young, Individual Strategy and Social Structure: An Evolutionary Theory of Institutions [Review: A Myopic (and Sometimes Blind) Eye on the Main Chance, or, the Origins of Custom]

- To read:
- Jacob Abernethy, Alekh Agarwal, Peter L. Bartlett, Alexander Rakhlin, "A Stochastic View of Optimal Regret through Minimax Duality", arxiv:0903.5328
- James Bergin and Barton L. Lipman, "Evolution with State-Dependent
Mutations," Econometrica
**64**(1996): 943--956 - Andreas Blume, "A Learning-Efficiency Explanation of Structure in
Language", Theory
and Decision
**57**(2004): 265--285 - Oliver Board, "Dynamic interactive epistemology", Games and
Economic Behavior
**49**(2004): 49--80 - Jacob W. Crandall and Michael A. Goodrich, "Learning to compete, coordinate, and cooperate in repeated games using reinforcement learning",
Machine Learning
**82**(2011): 281--314 - Vincent P. Crawford, Miguel A. Costa-Gomes, and Nagore Iriberri,
"Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications", Journal of Economic Literature
**51**(2013): 5--62 - Emilio De Santis and Carlo Marinelli, "Stochastic games with infinitely many interacting agents", math.PR/0505608 [Sounds very cool: "study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics.... in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions ... as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved ... ergodicity [implies] ``fixation'', i.e. that players will adopt a constant strategy after a finite time. ... related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume."]
- Pradeep Dubey and Ori Haimanko, "Learning with Perfect
Information", Games and Economic
Behavior
**46**(2004): 304--324 - Jim Engle-Warnick, William J. McCausland and John H. Miller, "The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior" [i.e., inferring stochastic transducers from data; hence the inclusion here]
- Ido Erev and Alvin F. Roth, "Maximization, learning, and economic behavior", Proceedings of the National
Academy of Sciences (USA)
**111**: 10818--10825 - Anders Eriksson and Kristian Lindgren, "A simple model of cognitive processing in repeated games", q-bio.PE/0608015
- Ignacio Esponda and Demian Pouzo, ""Berk-Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models", Econometrica 84 (2016): 1093--1130
- Drew Fudenberg and David K. Levine
- The Theory of Learning in Games
- "Recency, consistent learning, and Nash equilibrium",
Proceedings of the
National Academy of Sciences (USA)
**111**(2014): 10826--10829

- Douglas Gale and Hamid Sabourian, "Complexity and Competition",
Econometrica
**73**(2005): 739--769 - Val E. Lambson and Daniel A. Probst, "Learning by Matching
Patterns", Games and Economic
Behavior
**46**(2004): 398--409 - Panayotis Mertikopoulos and Aris L. Moustakas, "The emergence of rational behavior in the presence of stochastic perturbations", Annals of Applied Probability
**20**(2010): 1359--1388 - Liviu Panait, Karl Tuyls, Sean Luke, "Theoretical Advantages of
Lenient Learners: An Evolutionary Game Theoretic Perspective",
Journal of
Machine Learning Research
**9**(2008): 423--457 - Alessandro Panella and Piotr Gmytrasiewicz, "Interactive POMDPs with finite-state models of other agents", Autonomous Agents and Multi-Agent Systems
**31**(2017): 861--904 [These seem, from the abstract, like Bayesian parallels to the Foster and Young (2003) results on learning by hypothesis-testing (not cited)] - Mark Stegeman and Paul Rhode, "Stochastic Darwinian equilibria in
small and large populations", Games and Economic
Behavior
**49**(2004): 171--214 - Arne Traulsen, Dirk Semmann, Ralf D. Sommerfeld, Hans-Juergen Krambeck, Manfred Milinski, "Human strategy updating in evolutionary games", arxiv:1001.3768
- Finbarr Timbers, Nolan Bard, Edward Lockhart, Marc Lanctot, Martin Schmid, Neil Burch, Julian Schrittwieser, Thomas Hubert, Michael Bowling, "Approximate exploitability: Learning a best response in large games", arxiv:2004.09677
- Yevgeniy Vorobeychik, Michael P. Wellman and Satinder Singh, "Learning payoff functions in infinite games", Machine Learning
**67**(2007): 145--168