Stock market as a dynamic game with continuum of players

This paper contains a game-theoretic model describing the behaviour of investors at a stock exchange. The model presented is developed to reect the actual market microstructure. The players constitute a non-uniform continuum, differing, among others, by the planning horizon, the external ow of money which can be invested, formation of expectations about future prices, which, briey, divides the investors into the following groups: fundamental analysts, chartist, users of various econometric models, users of Capital Asset Pricing Model, and players observing a random exogenous signal. Prices are determined by orders and the equilibrating mechanism of the stock exchange. The mechanism presented is the actual single-price auction system used, among others, at Warsaw Stock Exchange. One of the main issues are self-verifying beliefs. Results of numerical simulations of stock exchange based on the model are also included

The operation of ecosystems, and game theory. I. Deterministic non-cooperative games

Artykuł nie zawiera streszczeniaThe article contains no abstrac

Existence of pure equilibria in games with nonatomic space of players

In this paper known results on the existence of pure Nash equilibria in games with nonatomic measure space of players are generalized and also a simple proof is offered. The relaxed assumptions include metrizability of the space of actions, measurability of payoff functions and available strategy correspondences

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

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

Conferences in Applied Mathematics

XLVI Ogólnopolska Konferencja Zastosowań Matematyki, 5--12 września 2017,  Zakopane-Kościelisko (Ł. Stettner)Krótka historia Seminarium Zastosowań Matematyki. XLVII Seminarium Zastosowań Matematyki w Kobylej Górze(M. Chalfen)XXIII Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie (Urszula Foryś).Jedenaste Warsztaty ISDG W Warszawie (Agnieszka Wiszniewska-Matyszkiel)XLIII Konferencja ,,Statystyka Matematyczna'' (P. Grzegorzewski)Semestr Simonsa z Biologii Matematycznej (J. Miękisz)XLVI Nationalwide Conference on Applications of Mathematics, 5 - 12 September 2017, Zakopane-Kościelisko (Ł. Stettner)    A brief history of Mathematics Applications Seminar. XLVII Seminar on Applications of Mathematics in Kobyla Góra (Chalfen)XXIII Nationalwide Conference on Applications of Mathematics in Biology and Medicine (Urszula Foryś). Eleventh ISDG Workshops in Warsaw (Agnieszka Wiszniewska-Matyszkiel)XLIII Conference "Mathematical Statistics" (P. Grzegorzewski)Simons Semester at Banach Center. Mathematical Biology (J. Miekisz