Recent research reveals that while analysing complex market mechanisms, one can notice certain quantum effects. On the other hand, the current mass-scale involvement in financial market investment activities leads to the conclusion that – when studying the operation of financial markets – the models of minority games, based on static physics, should be applied. Consequently, both quantum games and minority games have become focus of considerable interest. The financial market model, otherwise known as a minority game, postulates that the process of securities and money allocation is conditional upon price fluctuation, as well as information available in the market. Whenever a vast majority of investors intend to purchase goods and services on a massive scale, sale proves to be the more profitable option, and vice versa. The players who end up on the minority side win. Furthermore, the models based on quantum games have a certain advantage over the others, since they extend the theory of Nash equilibrium to the so-called quantum response equilibrium. The aim of this paper is to present two models of market mechanisms – of which one uses minority games as its basis, while the other – quantum games. The author begins with a discussion of the minority games model, which is followed by an analysis of the mechanism of dynamic English auction by means of the quantum theory.
It is a self-evident truth that nowadays a growing number of economic phenomena is described by means of physics methods. The most frequent theories derived from physics and applied to economy are: (1) the universal gravitation law and (2) the first as well as the second law of thermodynamics. The methods of static physics are applicable also to the theory of financial markets. In this case it is assumed that the financial market is composed of single participants interacting as a system of particles. Such approach is associated with a model of financial market otherwise known as a minority game. It is postulated that the process of securities and money allocation is performed on the basis of prices fluctuation, where - if a vast majority of investors tend to purchase goods or services - the sale constitutes a more profitable option, and vice versa. The players who end up on minority side win. At the end of the XX century the economy commenced to apply the laws of quantum mechanics. These laws proved to be useful, in particular when attempting to generalize game theory, which resulted in quantum games. The aim of the paper is to compare the rules and auction mechanisms with selected laws of quantum mechanics. This paper aims also to introduce the basic concepts of quantum mechanics to the process of economic phenomena modeling. Quantum mechanics is a theory describing a behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found at a given position and at a given time, as well as (2) the Heisenberg uncertainty principle stating that a certain pair of physical properties may not be simultaneously measured to arbitrarily high precision.
Certain type of perfect information games (PI-games), the so-called Banach-Mazur games, so far have not been applied in economy. The perfect information positional game is defined as the game during which at any time the choice is made by one of the players who is acquainted with the previous decision of his opponent. The game is run on the sequential basis. The aim of this paper is to discuss selected Banach-Mazur games and to present some applications of positional game
The Polish energy market gained its competitive character in late 1990s. At that time in majority of European countries a new law was enacted (in Poland – in 1987), which enabled the creation of internal energy markets. The Polish Power Exchange has been functioning since the end of 1999. However, from the very onset it has constituted a vital component of under grounding liberalization of electricity market. Since it was created the Polish Power Exchange has served as a market mechanism for setting objective energy market price. Support and control of the Polish Financial Supervision Authority guarantee the security of concluded transactions. The spot energy market was created as the first one and has functioned according to the rule of the double auction. The model of Sadrieh will be used for the description of the auction rules applied to the spot energy trade on the Polish Power Exchange. Furthermore, an algorithm on the basis of which it is possible to forecast transaction prices is presented. The effectiveness of this algorithm will be compared with other traditional methods of forecasting transaction prices.
A growing number of economic phenomena are nowadays described with methods known in physics. The most frequently applied physical theories by economists are: (1) the universal gravitation law and (2) the first and second law of thermodynamics. Physical principles can also be applied to the theory of financial markets. Financial markets are composed of individual participants who may be seen to interact as particles in a physical system. This approach proposes a financial market model known as a minority game model in which securities and money are allocated on the basis of price fluctuations, and where selling is best option when the vast majority of investors tend to purchase goods or services, and vice versa. The players who end up being on the minority side win.The above applications of physical methods in economics are deeply rooted in classical physics. However, this paper aims to introduce the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found in a given position and at a given time, and as (2) the Heisenberg uncertainty principle stating that certain pairs of physical properties cannot be economic applications of the Schrödinger equation as well as the Heisenberg uncertainty principle. We also try to describe the English auction by means the quantum mechanics methods.
Many important economic decisions involve an element of risk. Risk aversion is a concept in economic, game theory, finance and psychology related to the behavior of consumers, players and investors under uncertainty. Loss aversion is an important component of a phenomenon that has been discussed a lot in recent years. Loss aversion is a tendency to feel the pain of a loss more acutely than pleasure of the equal – sized gain. Many scientists have analyzed the problem of profitability in the game. Some authors presented certain features, by which “safe” games played once should be characterized. Kahneman and Tversky (1991) showed that loss – aversion – to – gain – attraction ratio should amount to 1:2. The aim of this paper is to show an asymptotically effective strategy which enables the risk – aversive player to establish boundary variables loss and gain at each stage of the repeated game.
PL
Wiele decyzji ekonomicznych podejmowanych w warunkach niepewności zawiera w sobie element ryzyka, a uczestnicy rynku mogą mieć zróżnicowany do niego stosunek, przy czym przez wiele lat obowiązywało założenie, że mają oni awersję do ryzyka. Awersja do ryzyka jest koncepcją znaną nie tylko z ekonomii, ale również teorii gier, finansów i psychologii, a dotyczy ona zachowań konsumentów, graczy, inwestorów działających w warunkach niepewności. Również awersja do strat jest koncepcją szeroko dyskutowaną w ostatnich latach. Zauważono bowiem, że uczestnicy rynku o wiele intensywniej odczuwają stratę niż czerpią radość z takiego samego co do wartości bezwzględnej zysku. Wielu autorów analizowało problem opłacalności uczestnictwa w grach z określoną wartością zysku lub straty. Kahneman i Tversky (1991) ustalili nawet, że warto brać udział w grach, w których stosunek ewentualnego zysku do ewentualnej straty ma się tak jak 2:1. Inni autorzy prezentowali cechy tzw. bezpiecznych gier. Celem pracy jest zaprezentowanie asymtotycznie efektywnej strategii stosowanej w grach wieloetapowych, która umożliwia interaktywne wyznaczanie granicznych wartości straty i zysku przy jakich warto kontynuować grę.
The Polish energy market gained its competitive character in late 1990s. At that time in majority of European countries a new law was enacted (in Poland – in 1987), which enabled the creation of internal energy markets. The Polish Power Exchange has been functioning since the end of 1999. However, from the very onset it has constituted a vital component of under grounding liberalization of electricity market. Since it was created the Polish Power Exchange has served as a market mechanism for setting objective energy market price. Support and control of the Polish Financial Supervision Authority guarantee the security of concluded transactions. The spot energy market was created as the first one and has functioned according to the rule of the double auction. Double auction are a form of money and goods exchange, during which the bids are made by purchases as well as by sellers. Besides the price, each bid discloses the amount of ware which is to be purchased by contracting parties. The rules of the double auctions, as well as of other auction types, are comparable to the rules of a game. The double auction is one of the most common exchange institution, used extensively in stock markets, commodity markets an in markets for financial instruments, including options and futures. Searches and simulation experiments pertaining to the functioning of the double auctions have been conducted on a wide scale. They were initiated in 60s in twenties centuries by the Vernon L. Smith. Many authors such as: Wilson (1987), Friedman (1991), Gode and Sunder (1993), Gjerstad and Dickhaut (1998), Sadrieh (1998), Xia, Stallaert, Whinston (2004) attempted to construe models of behavior of double auction participants. Although these models have furthered understanding of the interaction of individual behavior and institution in the double auction. The model of Sadrieh will be used for description of the auction rules applied to the spot energy trade on the Polish Power Exchange. Furthermore, an algorithm on the basis of which it is possible to forecast transaction prices is presented. The effectiveness of this algorithm will be compared with other traditional methods of forecasting transaction prices.
PL
Rynek energii w Polsce nabrał charakteru konkurencyjnego w końcu lat 90. XX wieku. Wówczas to w większości krajów europejskich uchwalono nowe prawo (w Polsce w 1997 r.), które umożliwiło tworzenie wewnętrznych rynków energii elektrycznej. Pod koniec 1999 r. powstała w Polsce Towarowa Giełda Energii Elektrycznej (TGE), która niemalże od początku swego istnienia spełniała m.in. rolę mechanizmu rynkowego służącego do wyznaczania obiektywnej ceny energii. Jako pierwszy na TGE uruchomiony został rynek „spot” (kasowy) energii elektrycznej, na którym ceny ustalane są na zasadzie reguł aukcji dwustronnej. Aukcja dwustronna jest taką formą wymiany towarów i pieniędzy, podczas której oferty składane są zarówno przez kupujących, jak i sprzedających. W każdej ofercie oprócz ceny podawana jest ilość towaru, którą kontrahenci zamierzają nabyć lub sprzedać. Badania oraz eksperymenty symulacyjne dotyczące funkcjonowania aukcji dwustronnych prowadzone są na szeroka skalę. Zapoczątkował je w latach 60. XX wieku, późniejszy laureat Nagrody Nobla, Vernon L. Smith. Próby modelowania mechanizmów aukcji dwustronnej oraz zachowań jej uczestników podejmowało wielu autorów, takich jak: Wilson (1987), Friedman (1991), Easley i Ledyard (1993), Gjestad i Dichaut (1998), Sadierih (1998) oraz Xia, Stallaert, Whinston (2004). Celem pracy jest dopasowanie jednego z istniejących modeli aukcji dwustronnej do opisu funkcjonowania TGE. Do tego celu zostanie wykorzystany model Sadieriha, który dobrze oddaje reguły aukcyjne. Zostanie również zaprezentowany algorytm wyznaczania ceny transakcji dla aukcji dwustronnych (Drabik 1999), przy czym wyniki działania tego algorytmu zostaną porównane z rzeczywistymi cenami transakcji, które zostały odnotowane na TGE.
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