Games with distorted information and self-verification of beliefs with applications to financial markets

• Authors: Agnieszka Wiszniewska-Matyszkiel
• Languages of publication: EN

Abstracts

EN

In the paper we examine discrete time dynamic games in which the global state variable changes in response to a certain function of the pro_le of layers' decisions, called statistic, while the players form some expectations about its future values based on the history. Besides, there are also players' private state variables. A general model is built, encompassing both games with _nitely many players as well as games with in_nitely many players. This model extends the class of games with distorted information considered by the author in [20], in which there were no private state variables and there were much stronger assumptions about the statistic of players' decisions considered. The notions of pre-belief distorted Nash equilibrium (pre-BDNE), self-veri_cation and belief distorted Nash equilibrium (BDNE), de_ned already in [20], are applied to our wider class of games. The relations between Nash equilibria, pre-BDNE and BDNE are examined as well as the existence and properties of pre-BDNE. A model of a _nancial market { a simpli_ed stock exchange { is presented as an example. Pre-BDNE using threshold prices are proposed. One of further results in this example is potential self-veri_cation of fundamental beliefs and beliefs in in_nite speculative bubbles.

Keywords

EN

games with continuum of players; n-player dynamic games; Nash equilibrium; pre-belief distorted Nash equilibrium; subjective equilibrium; self-verifcation of beliefs; financial markets.

• Publisher: Katedra Ekonometrii i Statystyki, Szkoła Główna Gospodarstwa Wiejskiego w Warszawie
• Journal: Metody Ilościowe w Badaniach Ekonomicznych
• Year: 2010
• Volume: 11
• Issue: 1
• Pages: 254-275

Dates

published

2010

Contributors

author

Agnieszka Wiszniewska-Matyszkiel

• Institute of Applied Mathematics and Mechanics University of Warsaw

References

• Aumann R. J., 1964, Markets with a Continuum of Traders, Econometrica 32, 39-50.
• Aumann R. J., 1974, Subjectivity and Correlation in Randomized Strategies, Journal of Mathematical Economics 1, 67-96.
• Aumann R. J., 1987, Correlated Equilibrium as an Expression of Bayesian Rationality, Econometrica 55, 1-19.
• Balder E., 1995, A Unifying Approach to Existence of Nash Equilibria, International Journal of Game Theory 24, 79-94.
• Battigalli P., Siniscalchi M., Rationalization and Incomplete Information, Advances in Theoretical Economics 3, no. 1.
• Blackwell D., 1965, Discounted Dynamic Programming, Annals of Mathematical Statistics 36, 226-235.
• Harsanyi J.C., 1967, Games with Incomplete Information Played by Bayesian Players, Part I, Management Science 14, 159-182.
• Kalai E., Lehrer E., 1993, Subjective Equilibrium in Repeated Games, Econometrica 61, 1231-1240.
• Kalai E., Lehrer E., 1995, Subjective Games and Equilibria, Games and Economic Behavior 8, 123-163.
• Mas-Colell A., 1984, On the Theorem of Schmeidler, Journal of Mathematical Economics 13, 201-206.
• Schmeidler D., 1973, Equilibrium Points of Nonatomic Games, Journal of Statistical Physics 17, 295-300.
• Stokey N.L., Lucas Jr. R.E., Prescott E.C., 1989, Recursive Methods in Economic Dynamics, Harvard University Press.
• Vind, 1964, Edgeworth-Allocations is an Exchange Economy with Many Traders, International Economic Review 5, 165-177.
• Wiszniewska-Matyszkiel A., 2000, Existence of Pure Equilibria in Games with Continuum of Players, Topological Methods in Nonlinear Analysis 16, 339-349.
• Wiszniewska-Matyszkiel A., 2002, Static and Dynamic Equilibria in Games with Continuum of Players, Positivity 6, 433-453.
• Wiszniewska-Matyszkiel A., 2003, Static and Dynamic Equilibria in Stochastic Games with Continuum of Players, Control and Cybernetics 32, 103-126.
• Wiszniewska-Matyszkiel A., 2005, A Dynamic Game with Continuum of Players and its Counterpart with Finitely Many Players, Annals of the International Society of Dynamic Games 7, A. S. Nowak, K. Szajowski (eds.), Birkhauser, 455-469.
• Wiszniewska-Matyszkiel A., 2008, Common Resources, Optimality and Taxes in Dynamic Games with Increasing Number of Players, Journal of Mathematical Analysis and Applications 337, 840-841.
• Wiszniewska-Matyszkiel A., 2008, Stock Exchange as a Game with Continuum of Players, Control and Cybernetics 37 No. 3, 617-647.
• Wiszniewska-Matyszkiel A., 2006, Games with Distorted Information and Self-Veri_cation of Beliefs with Applications to Exploitation of Common Resources and Minority Games, preprint 159/2006 Institute of
• Applied Mathematics and Mechanics, Warsaw University, available athttp://www.mimuw.edu.pl/english/research/reports/imsm/; changed and submitted as Belief Distorted Nash Equilibria { introduction of a new kind of equilibrium in dynamic games with distorted information.