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EN
This paper contains the attempt to describe the phenomenon of shadow economy as a zero-sum non-cooperative, normal form game between households and the government. In the model government spending can be treated as a government consumption or as an expenses that contribute to increased social welfare and for the provision of public goods and services. We conduct sensitivity analysis of Nash equilibrium in models with two different types of government expenditure and examine whether proposed models indicate a various mechanisms and determinants of the undeclared economic activity.
EN
A class of two person nonzero-sum nonsymmetric stochastic games of capital accumulation/resource extraction is considered. It is shown that the Nash equilibrium in the discounted games has a limit when the discount factor tends to 1. Moreover, this limit is an epsilon-equilibrium in the discounted game with sufficiently large discount factor.
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Strategic option pricing

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EN
In this paper an extension of the well-known binomial approach to option pricing is presented. The classical question is: What is the price of an option on the risky asset? The traditional answer is obtained with the help of a replicating portfolio by ruling out arbitrage. Instead a two-person game from the Nash equilibrium of which the option price can be derived is formulated. Consequently both the underlying asset’s price at expiration and the price of the option on this asset are endogenously determined. The option price derived this way turns out, however, to be identical to the classical no-arbitrage option price of the binomial model if the expiration-date prices of the underlying asset and the corresponding risk-neutral probability are properly adjusted according to the Nash equilibrium data of the game.
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PL
Artykuł zawiera propozycje procedur kwantowania gier dobrze znanych w klasycznej teorii gier. Przedstawiono proste modele gier kwantowych. Jako pierwszy został omówiony dylemat więźnia zarówno w wersji klasycznej jak i kwantowej, który ma wiele praktycznych zastosowań w ekonomii, jednym z przykładów są oszustwa w porozumieniach kartelowych. Kolejnym modelem gry kwantowej jest kwantowa gra rynkowa opisana za pomocą kwantowego oscylatora harmonicznego. Jako ostatni został omówiony model kwantowej gry mniejszościowej.
EN
This paper builds up on proposed convincing procedures telling how to quantize well-known games from the classical game theory. The thesis introduces some simple models of quantum games. At first, the prisoners’ dilemma in classical and quantum version is described. This simple model has many practical applications in economics, one example being frauds in cartel agreements. The next model of quantum game is the quantum market game, described with the help of the quantum harmonic oscillator. It is known that quantum algorithms may be thought of as the games between classical and quantum agents; therefore, as the last example the quantum minority game is introduced.
EN
Decision-making by the two negotiating parties is simulated by a prisoner’s dilemma game. The game is formulated in a quantum manner, where players strategies are unitary transformations of qubits built over the basis of opposite decision options. Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the resulting transformed state. The range of strategies allowed for quantum players is richer than in case of a classical game and therefore the result of the game can be better optimized. On the other hand, the quantum game is save against eavesdropping and the players can be assured that this type of quantum arbitration is fair. We show that quantum prisoner’s dilemma has more favorable Nash equilibria than its classical analog and they are close to the Pareto optimal solutions. Some economical examples of utilizing quantum game Nash equilibria are proposed.
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The research performs an attempt to adapt accumulated approaches of the Institutional Economics to the application of the Coase theorem in public administration. Governance is mainly analyzed in the field of political science, while transactional costs definitely serve to the economic surveys. Solving the problem of social costs, Coase theorem revealed a conception of property rights as the outcome of mere contracting in independent exchanges. This conception is applicable for analyzing a wide range of issues, including externalities related to the use of assets and public goods. The article contains a brief characteristic of the self-governance in European states. The results of comparative analysis of the local governance in European region became a basis for proposing a series of transformation tools for Ukraine and neighboring states in this field. Obtained results of statistical modeling and payoff matrix of Nash equilibrium clearly confirm the validity of the Coase theorem for interpretation of the interaction between local self-governance and government institutions.
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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.
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The aim of this article is to examine how a businessman, who takes care about moral considerations should behave in some situations, in which some blameworthy common practices are present. There is a dilemma between efficiency (or even continuing existence) of business on one side and moral considerations on the other. The proposition formulated by R. M. Green is analyzed and criticized. The „everyone is doing it” argument is rejected., as well as the requirements coming from moral absolutism. In the end an argument based on writings of T. Carson, J. G. Dees and P. C. Crampton, which shows the proper way of moral behaviour where such dilemmas are met, is presented.
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Purpose: This article deals with the problem of forming Pareto non-optimal norms of mutual behavior of investors and government in the process of decision-making related to financing designed to reduce risks in investment activity. Methodology: Considering the interdependent type (nature) of interactions between related parties, game theory tools were used to model such interactions. Much attention was directed to search for� parameters of interaction leading to certain Nash equilibriums in pure strategies. The formal results obtained with the model were verified by statistical analysis. Findings: Analysis showed that the rational behavior of related parties can lead to unexpected results. Powerful investors will aim to work in socially-oriented economies, whereas primarily small investors will operate in most liberal economies with a�minimum tax burden but with a�higher level of risk. As for governments’ behaviors, the images are the same: small economies tend to liberalize their tax systems and to secure investment faster than powerful ones. Empirical verification based on statistical data of groups of countries generally confirmed the conclusions. These formal and logical conclusions were from statistical analysis of 124 countries divided into 5 groups: OECD countries, post-socialist countries, Latin American countries, APAC countries and ACP countries. Provided that the more powerful ones are covered economies, there was stronger interdependence between the size of economies and tax burden and also between total investment and tax burden, where this dependence is positive. Originality: The results obtained used Nash equilibriums in pure strategies as models of behavioral norms to define behaviors of related parties and also to explain assumptions concerning the behaviors of investors and government.
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In the FSS paper 157 (2005, p. 34-51) we presented a game approach for solving MADM problems with fuzzy decision matrix. The results of the paper essentially depend on the assumption that the entries of the fuzzy decision matrix are triangular fuzzy numbers and dependent via a real parameter \lambda. In this paper we present a more general game approach for solving fuzzy MADM problems free of these restrictions. The entries of the decision matrix are assumed to be not necessarily dependent fuzzy intervals with bounded support as defined by Dubois and Prade.
PL
Artykuł przedstawia wyniki analizy policy mix z wykorzystaniem niekooperacyjnej gry między władzami fiskalnymi i monetarnymi oraz modelu makroekonomicznego opartego na koncepcji nowej syntezy neoklasycznej. Dokonano estymacji modelu dla Polski w latach 2000-2014. Przeprowadzono szereg symulacji z wykorzystaniem modelu oraz systemu komputerowego wyznaczającego wypłaty gry. Przeanalizowano alternatywne policies mix w stosunku do realizowanych w przeszłości polityk: monetarnej i fiskalnej. Wyznaczono i przeanalizowano optymalne strategie odpowiedzi oraz strategie równowagi Nasha.
EN
Analysis of the policy mix is presented using a noncooperative game and a macroeconomic model formulated on the basis of the New Neoclassical Synthesis concept. The game describes interactions of the fiscal and monetary authorities. The model has been estimated for the Poland in 2000–2014. Simulations have been made using the model and the constructed computer based system calculating payoffs of the game. The fiscal and monetary policies alternative to the historical ones are shown and analyzed. The best response strategies and the Nash equilibria are derived and discussed.
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We present theoretical model of shadow economy. The model includes not only economic factors, such as tax burden or fines for unregistered activity, but also legal and organizational background factors, such as level of bureaucracy (corruption), quality of public sector services and institutions, or tax morale. In the proposed model shadow economy arises as a result of interactions between economic entities – government and households. The Nash Equilibrium level of shadow economy is derived and comparative statics analysis is presented.
PL
Przedstawiony zostanie model teoretyczny kształtowania się szarej strefy gospodarki. Uwzględnione w nim będą zarówno czynniki typowo ekonomiczne, takie jak obciążenia podatkowe i parapodatkowe czy wysokość kar za działalność nierejestrowaną, oraz czynniki kształtujące otoczenie prawno-organizacyjne działalności gospodarczej, takie jak poziom biurokracji (korupcji), jakość instytucji publicznych, czy moralność podatkowa społeczeństwa. W proponowanym modelu szara strefa powstaje jako wynik interakcji pomiędzy podmiotami gospodarczymi – rządem i gospodarstwami domowymi. Wyznaczony zostanie poziom szarej strefy będący równowagą Nasha, po czym przeprowadzona zostanie jego statyka porównawcza.
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