Reflexion in mathematical models of decision-making

References

• Novikov DA, Ckhartishvili AG. Reflexion and control: mathematical models. Leiden: CRC Press; 2014.
   Google Scholar
• Novikov DA, Chkhartishvili AG. Mathematical models of informational and strategic reflexion: a survey. Adv Syst Sci Appl. 2014;14(3):254–278.
   Google Scholar
• Pacuit E, Roy O. Epistemic Foundations of Game Theory: the Stanford Encyclopedia of Philosophy. In: Edward N. Zalta, editor. 2017 (Summer Edition). Available from: https://plato.stanford.edu/archives/sum2017/entries/epistemic-game/
   Google Scholar
• Schumann A. Payoff cellular automata and reflexive games. J Cell Autom. 2014;9(4):287–313.
   Google Scholar
• Abramsky S, Winschel V. Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting. Math Struct Comput Sci. 2017;27(5):751–761. doi:10.1017/S0960129515000365.
   Google Scholar
• Germeier Y. Non-antagonistic games, 1976. Russian – Dordrecht: D. Reidel Publishing Company; 1986.
   Google Scholar
• Myerson R. Game theory: analysis of conflict. London: Harvard University Press; 1991.
   Google Scholar
• Geanakoplos J. Handbook of game theory. Vol. 2. Amsterdam: Elsevier; 1994. Chapter 40, Common knowledge; p. 1438–1496.
   Google Scholar
• Morris S, Shin SS. Approximate common knowledge and coordination: recent lessons from game theory. J Log Lang Inf. 1997;6:171–190.10.1023/A:1008270519000
   Google Scholar
• Lewis D. Convention: a philosophical study. Cambridge (MA): Harvard University Press; 1969.
   Google Scholar
• Mertens JF, Zamir S. Formulation of bayesian analysis for games with incomplete information. Int J Game Theor. 1985;14:1–29.10.1007/BF01770224
   Google Scholar
• Novikov DA, Chkhartishvili AG. Reflexivniye igry [reflexive games]. Moscow: Sinteg; 2003.
   Google Scholar
• Chkhartishvili AG, Novikov DA. Models of reflexive decision-making. Syst Sci. 2004;30(2):45–59.
   Google Scholar
• Chkhartishvili AG. Bayes-nash equilibrium: infinite-depth point information structures. Autom Remote Control. 2003;64(12):1922–1927.10.1023/B:AURC.0000008430.60568.b0
   Google Scholar
• Costa-Gomes M, Crawford V. Cognition and behavior in two-person guessing games: an experimental study. AER. 2006;96:1737–1768.
   Google Scholar
• Nagel R. Unraveling in guessing games: an experimental study. AER. 1995;85:1313–1326.
   Google Scholar
• Stahl D, Wilson P. On players models of other players: theory and experimental evidence. Games Econ Behav. 1995;10:213–254.
   Google Scholar
• Camerer CF, Ho TH, Chong J. A cognitive hierarchy model of games. Q J Econ. 2004;8:861–898.10.1162/0033553041502225
   Google Scholar
• Camerer CF, Ho TH, Chong JK. A cognitive hierarchy theory of one-shot games: some preliminary results; 2002. Available from: http://people.hss.caltech.edu/~camerer/camerer.html
   Google Scholar
• Chong JK, Ho TH, Camerer CF. A generalized cognitive hierarchy model of games. Games Econ Behav. 2016;99:257–274.10.1016/j.geb.2016.08.007
   Google Scholar
• McKelvey RD, Palfrey TR. Quantal response equilibria for normal form games. Games Econ Behav. 1995;10(1):6–38.10.1006/game.1995.1023
   Google Scholar
• Wright JR, Leyton-Brown K. Behavioral game theoretic models: a Bayesian framework for parameter analysis. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems. Vol. 2; 2012 June 4–8; Valencia, Spain: International Foundation for Autonomous Agents and Multiagent Systems; 2012. p. 921–930.
   Google Scholar
• Wright JR, Leyton-Brown K. Predicting human behavior in unrepeated, simultaneous-move games. arXiv preprint arXiv:1306.0918; 2013.
   Google Scholar
• Korepanov VO, Novikov DA. The reflexive partitions method in models of collective behavior and control. Autom Remote Control. 2012;73(8):1424–1441.10.1134/S0005117912080152
   Google Scholar
• Wright JR, Leyton-Brown K. Level-0 meta-models for predicting human behavior in games. Proceedings of the fifteenth ACM conference on Economics and computation; 2014 June 08–12; Stanford,CA,USA: ACM; 2014. p. 857–874.
   Google Scholar
• Ho TH, Camerer CF, Weigelt K. Iterated dominance and iterated best response in experimental ‘p-beauty contests’. Am Econ Rev. 1998;88(4):947–969.
   Google Scholar
• Novikov DA. Models of strategic behavior. Autom Remote Control. 2012;73(1):1–19.10.1134/S0005117912010018
   Google Scholar
• Chkhartishvili AG, Korepanov VO. Adding informational beliefs to the players strategic thinking model. IFAC-PapersOnLine. 2016;49(32):19–23.10.1016/j.ifacol.2016.12.183
   Google Scholar
• Kagel J, Roth A, Editors. The handbook of experimental economics. Princeton (NJ): Princeton University Press; 1995.
   Google Scholar
• Wright JR, Leyton-Brown K. Beyond equilibrium: predicting human behavior in normal form games. Proceedings of the Conference Association for the Advancement of Artificial Intelligence (AAAI-10); 2010 Jule 11–15; 2010. p. 461–473.
   Google Scholar
• Kahneman D, Slovic O, Tversky A. Judgment under uncertainty: heuristics and biases. Cambridge: Cambridge University Press; 1982.10.1017/CBO9780511809477
   Google Scholar
• Nisan N, Roughgarden T, Tardos E, et al. Algorithmic game theory. Cambridge: Cambridge University Press; 2007.10.1017/CBO9780511800481
   Google Scholar
• Bernheim D. Rationalizable strategic behavior. Econometrica. 1984;5:1007–1028.10.2307/1911196
   Google Scholar
• Weibull J. Evol Game Theor. Cambridge (MA): MIT Press; 1995.
   Google Scholar
• Sutton RS, Barto AG. Reinforcement learning: an introduction. Cambridge (MA): MIT Press; 1998.
   Google Scholar
• Roth AE, Erev I. Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Games Econ Behav. 1995;8(1):164–212.10.1016/S0899-8256(05)80020-X
   Google Scholar
• Camerer CF, Ho TH. Experience-weighted attraction learning in normal form games. Econometrica. 1999;67(4):827–874.10.1111/ecta.1999.67.issue-4
   Google Scholar
• Cournot AA. Recherches sur les Principes Mathematiques de la Theorie de Richesses. Translated by Bacon NT, [Researches into the mathematical principles of the theory of wealth]. London: Hafner; 1838. p. 1960.
   Google Scholar
• Robinson J. An iterative method of solving a game. Ann Math. 1951;54(2):296–301.10.2307/1969530
   Google Scholar
• Brown GW. Iterative solution of games by fictitious play. Act Anal Prod Allocation. 1951;13(1):374–376.
   Google Scholar
• Fudenberg D, Levine DK. Theory of learning in games. Cambridge (MA): MIT Press; 1998.
   Google Scholar
• Healy PJ. Learning dynamics for mechanism design: an experimental comparison of public goods mechanisms. J Econ Theor. 2006;129(1):114–149.10.1016/j.jet.2005.03.002
   Google Scholar
• Cheung YW, Friedman D. Individual learning in normal form games: some laboratory results. Games Econ Behav. 1997;19(1):46–76.10.1006/game.1997.0544
   Google Scholar
• Chen Y, Tang FF. Learning and incentive‐compatible mechanisms for public goods provision: an experimental study. J Political Econ. 1998;106(3):633–662.10.1086/250024
   Google Scholar
• Ho TH, Camerer CF, Chong JK. Self-tuning experience weighted attraction learning in games. J Econ Theor. 2007;133(1):177–198.10.1016/j.jet.2005.12.008
   Google Scholar
• Arifovic J, Ledyard J. A behavioral model for mechanism design: Individual evolutionary learning. J Econ Behav Organ. 2011;78(3):374–395.10.1016/j.jebo.2011.01.021
   Google Scholar
• Camerer CF, Ho TH, Chong JK. Sophisticated experience-weighted attraction learningand strategic teaching in repeated games. J Econ Theor. 2002;104(1):137–188.10.1006/jeth.2002.2927
   Google Scholar
• Camerer CF, Ho TH, Chong JK. Advances in understanding strategic behaviour. Basingstoke: Palgrave Macmillan; 2004. Chapter 8, Behavioral game theory:thinking, learning, and teaching; p. 120–180.10.1057/9780230523371
   Google Scholar
• Chkhartishvili AG. Reflexive games: transformation of awareness structure. Autom Remote Control. 2010;71(6):1208–1216.10.1134/S0005117910060214
   Google Scholar
• Korepanov VO, Novikov DA. The diffuse bomb problem. Autom Remote Control. 2013;74(5):863–874.10.1134/S000511791305010X
   Google Scholar
• Korepanov VO, Novikov DA. Models of strategic behavior in the diffuse bomb problem. Autom Remote Control. 2016;77(10):1838–1848.10.1134/S0005117916100106
   Google Scholar