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EN
Scholars making economic policy recommendations to resolve corruption problem use several approaches, the most dominant of which are the principal-agent and rent-seeking theories. In this paper, we argue that the principal-agent theory has problems to account for the environment in which the agents offering and accepting corruption operate, and explain the importance of agents for survival of their environment. The rent-seeking theory, on the other hand, finds it difficult to establish socially effective legislation and ways to determine the barriers to entry that motivate agents to behave corruptly. Both problems, however, are vital for solving the problem of corruption. Lacking the knowledge of the agent’s environment (system) and their significance for survival of the system, the theory cannot define incentives that would discourage the agent from acting in a corrupted way. If the rent-seeking theory does not determine the barriers to entry that motivate agents to behave corruptly, it cannot determine the proper legislation that would deter corrupt behaviour and lead to economic development. For these reasons we investigate if both problems can be explained and solved within the alternative theory of redistribution systems and its part - the theory of parallel redistribution games.
XX
Most of real-life problems, including design, optimization, scheduling and control, etc., are inherently characterized by multiple conflicting objectives, and thus multi-objective linear programming (MOLP) problems are frequently encountered in the literature. One of the biggest difficulties in solving MOLP problems lies in the trade-off among objectives. Since the optimal solution of one objective may lead other objective(s) to bad results, all objectives must be optimized simultaneously. Additionally, the obtained solution will not satisfy all the objectives in the same satisfaction degree. Thus, it will be useful to generate a set of compromise solutions in order to present it to the decision maker (DM). With this motivation, after determining a modified payoff matrix for MOLP, all possible ratios are formed between all rows. These ratio matrices are considered a two person zero-sum game and solved by linear programming (LP) approach. Taking into consideration the results of the related game, the original MOLP problem is converted to a single objective LP problem. Since there exist numerous ratio matrices, a set of compromise solutions is obtained for MOLP problem. Numerical examples are used to demonstrate this approach.
EN
The objective of the paper is to present game theory as a tool to analyse conflict in the Common Agricultural Policy of the EU. Traditional game theory, as well as its relatively new branch- theory of moves was used in the paper to present the budgeting conflict in the CAP.
EN
Purchasing group can improve the chance of a higher return for individual entities in the supply chain. The greater sales occurs between companies, the higher the probability of deepening integration between them. Functioning of the purchasing group is, however, dependent on the justice of imputation the profits generated by it (discounts, cost reduction) for its entities. Article presents the use of cooperative game, in order to explain the possibility of optimizing and sharing the profits (payoffs), and in a longer perspective, build an integrated supply chain.
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Indirect control and power

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EN
To determine who has the power within a stock corporate company can be a quite complex prob-lem, especially when control is achieved through alliances between shareholders. This problem arises especially in cases of indirect control of corporations, that is, in situations involving shareholders and companies with cross-shareholdings. The first to solve the problem of measuring power in the case of indirect share control were Gianfranco Gambarelli and Guillermo Owen in [10]. In the following years, numerous other models were introduced. In this paper, we critically examine the models of: Gambarelli and Owen, Denti and Prati, Crama and Leruth, Karos and Peters, as well as Mercik and Lobos, taking into account two well-known, illustrative examples, one with an acyclic corporate structure and the other with a cyclic structure.
PL
Wiele międzynarodowych korporacji stosuje aparat opcji realnych przy wycenie projektów inwestycyjnych, jednak zakres tego wykorzystania w praktyce gospodarczej pozostaje poniżej oczekiwań. Celem artykułu jest wskazanie przesłanek, które mogą być przyczyną ograniczonego zastosowania koncepcji opcji realnych do wyceny inwestycji obarczonych ryzykiem przez firmy działające na rynku konkurencyjnym. Podejmowanie decyzji inwestycyjnych zostało przedstawione jako gra pomiędzy dwoma konkurentami. Wartość projektu jest wyznaczana w koncepcji opcji realnych, zatem problem jawi się jako gra opcyjna. Okazuje się, że konkurencja na rynku sprawia, iż większy wpływ na podejmowanie decyzji inwestycyjnych ma wartość strategiczna projektu niż rachunek ekonomiczny jego opłacalności. Konflikt interesów pomiędzy konkurentami jest jedną z przesłanek małego zainteresowania stosowaniem koncepcji opcji realnych przez firmy działające na rynku w warunkach silnej konkurencji. Warto także podkreślić, iż nieuwzględnienie konkurencji w wycenie opcji inwestycyjnej zawyża jej wartość. W artykule wykorzystano teoretyczne podstawy wyceny opcji i elementy teorii gier, jednak sposób sformułowania problemu i jego rozwiązanie są oryginalne.
EN
Many international corporations use real option valuation of investment project; however, the scale of its application in economic practice is still limited. The aim of the paper is to indicate factors limiting the application of the real options approach to evaluation of risky investments by firms operating in a competitive market. The problem has been formulated and solved using the game theory and real options valuation methods. It appears that in a competitive market the strategic value of the investment project has greater influence on the investment decision than its economic efficiency. Conflict of interests between competitors is one of the reasons why firms operating in a competitive market use real options approach so rarely. It is worth to stress, that if the firm does not take into account its competitor’s behaviour, a real option will be overvalued. Real options approach and the basic game theory have been used in the paper, but problem formulation and its solution are original.
RU
Многие международные корпорации применяют аппарат реальных опций при оценке инвестиционных проектов, однако диапазон этого применения в экономической прак- тике остается ниже ожиданий. Целью статьи является выявление проблем, которые мо- гут стать причиной ограниченного применения концепции реальных опций для оценки рисковых инвестиций фирмами, действующими на конкурентном рынке. Принятие ин- вестиционных решений было представлено как игра между двумя конкурентами. Стои- мость проекта определяется в концепции реальных опций и таким образом проблема вы- ступает как опционная игра. Оказывается, что конкуренция на рынке ведет к тому, что на принятие инвестиционных решений большее влияние имеет стратегическая стоимость проекта, а не оценка его рентабельности. Конфликт интересов между конкурентами яв- ляется одной из причин незначительного интереса к применению концепции реальных опций фирмами, действующими на рынке в условиях сильной конкуренции. Следует также подчеркнуть, что неучет конкуренции в оценке инвестиционной опции завышает ее стоимость. В статье использованы теоретические основы оценки опций и элементы теории игр, однако способ постановки проблемы и ее решение оригинальны.
EN
Research background: The article deals with implementing VMI between the supplier and customer. To assess whether the system will be implemented, the evolution game theory is used. The contribution is based on the limitations of the study of the evolutionary game theory approach to modelling VMI policies (Torres et al., 2014) and its later extension, The evolutionary game theory approach to modelling VMI policies (Torres & García-Díaz, 2018). It aims is to complement the studies and provide a comprehensive picture of the issue. Purpose of the article: The main objective of the contribution is to respond to the question whether the VMI system will be introduced between the supplier and customer. Methods: In the first phase, the matrix is analysed from the point of view of the game meaning and its limit parameters. The limit parameters are set taking into account the economic reality. The only examined states of the matrix are those where the result is not obvious. For the purposes of the contribution, we work with a 5-year period. A new software capable of calculating evolutionary focus and their stability is created. Sensitivity analysis is carried out for the individual parameters that affect the system behaviour. Findings & Value added: Value added is a complex description of the system and complementation of previous studies in this field. VMI is confirmed. The results obtained can be used for practical management, so that the managers are able to identify what the actual costs are and what the probability of introducing the system is. At the same time, they can identify the parameters that can be influenced by them and observe their impact on the shift of the system introduction probability.
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.
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Ten years of SING meetings

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EN
This paper provides some statistics on the SING meetings held from 2005 to 2014. Particular attention is paid to the tenth such meeting.
EN
Jazz band is a 3 player superadditive game in characteristic function form. Three players have to divide the payoff they can get, while being in a grand coalition, provided their individual and duo coalitions payoffs are known. Assumptions of individual and collective rationality lead to the notion of the core of the game. We discuss offers that cannot readily be refused [OCRR] as the solutions of the game in case of an empty core, when duo coalitions are the best options but only for two out of three players. The experiment shows that even in case of an empty core the most probable results are three-way coalitions and the share of the weakest player usually exceeds his OCRR. The Shapley value is introduced and its fairness is discussed as it lies at the side of the core while, on the other hand, the nucleolus lies exactly at the center of the core. We conclude that, in spite of that, the Shapley value is the best candidate for a fair sharing solution of the jazz band game and other similar games as, opposite to the other values, it is dependent both on individual and duo coalitions payoffs.
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EN
The article is devoted to the application of skills gained by students in Mathematics for Business and Economics to solve problems of the game theory. An application of the entry game analysis is considered. A real-life problem is described which consists of the application of the zero-sum game to an auction situation, followed by finding the optimal solution with respective recommendations.
EN
This paper presents an attempt to formalize the concept of the Triple Helix of university-government-industry interactions as a prototype of an innovation ecosystem. Such a formalization is based on game theory principles, methods and models, as well as the methods and instruments of the theory of optimal allocation of resources. The constructed game-theoretic model simulates the phases of R&D, the implementation and commercialization of a new project, as well as the risks and uncertainty in each of these innovation stages.
13
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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.
PL
Każda reforma Wspólnej Polityki Rolnej (WPR) wiąże się z pewnymi konsekwencjami – przede wszystkim dla producentów rolnych, ale również dla całego społeczeństwa. W artykule przedstawiono nowe podejście metodologiczne służące do określenia potencjalnych efektów reform polityki rolnej UE polegające na połączeniu modelu równowagi cząstkowej CAPRI i teorii gier. Istota tego podejścia polega na wyznaczeniu macierzy wypłat gry niekooperacyjnej przy założeniu, że użyteczności graczy, a w konsekwencji macierze wypłat, są wynikiem symulacji modelem CAPRI. Ilustracją jest analiza dwóch scenariuszy zakładanych zmian WPR dotyczących ograniczenia wsparcia wewnętrznego producentów rolnych w ramach I filaru (scenariusz 1) i liberalizacji handlu produktami rolnymi (scenariusz 2). W analizie spodziewanych efektów zaproponowanych scenariuszy uwzględniono zmiany w poziomie dobrobytu różnych grup społeczno-ekonomicznych w UE, a stronami konfliktu były Komisja Europejska i Światowa Organizacja Handlu. Z przedstawionych wariantów gier wynika, że najkorzystniejszym rozwiązaniem z punktu widzenia różnych grup interesariuszy jest pozostawienie I filaru i liberalizacja handlu rolnego.
EN
Each reform of the Common Agricultural Policy (CAP) is connected with some consequences – for agricultural produces, but also for all the society. The article presents a new methodological approach to the determination of the potential effects of reforms in the EU agricultural policy, which combines the CAPRI partial equilibrium model with game theory. The essence of this approach consists in defining the pay-off matrix of a noncooperative game on the assumption that the utilities of players, and consequently the pay-off matrices are the result of a simulation based on the CAPR model. This has been illustrated by analysing two scenarios of the assumed changes in the CAP concerning the internal support for agricultural producers provided in the framework of the pillar I (scenario 1) and trade liberalization for agricultural products (scenario 2). The analysis of the expected effects of both scenarios considers the changes in the well-being levels of various socio-economic groups within the EU, whereas, the two parties involved in the conflict are European Commission and World Trade Organization. The analysis of the presented game variants shows that the best solution from the point of view of various interest groups is leaving the pillar I combined with agricultural trade liberalization.
RU
Каждая реформа Общей аграрной политики (ОАП) влечет за собой определенные последствия, прежде всего для сельхозпроизводителей, но и для всего общества. В статье представлен новый методологический подход для решения задач по определению потенциальных эффектов реформ аграрной политики ЕС, основывающийся на соединении модели частичного равновесия CAPRI (Common Agricultural Policy Regionalised Impact) и теории игр. Суть этого подхода состоит в обозначении матрицы выплат некооператив- ной игры при условии, что пригодность игроков и матрицы выплат являются результатом симуляции при помощи модели CAPRI. Иллюстрацией этого подхода является анализ двух сценариев предполагаемых изменений ОАП, касающихся ограничения внутренней поддержки агропроизводителей: в рамках первой опоры ОАП (сценарий 1) и либерализации торговли сельхозпродукцией (сценарий 2). В анализе ожидаемых эффектов предложенных сценариев были учтены изменения в уровне благосостояния разных социально-экономических групп в ЕС, а сторонами конфликта были Еврокомиссия и Всемирная организация торговли. Из представленных вариантов игр следует, что самым выгодным решением с точки зрения разных групп интересов является сохранение первой опоры и либерализация торговли сельхозпродуктами.
EN
The purpose of the paper is to present in a concise manner the key theoretical issues related to mathematical modelling in political science, alongside selected examples of using mathematical modelling in research practice. In the process, the function of scientific models in the development of scientific theories is discussed, indicating the main types of scientific models. Then, selected elements of the theory of mathematical models are considered and the most common misunderstandings in using the language of mathematics in political science studies are described. Finally, selected examples of using mathematical models in studies of political phenomena are presented: a quadratic-hyperbolic model of the real global GDP growth dynamics and a game theory model of the transmission of cooperative behaviours among political elites were developed. The R programme was used to build the models.
EN
The article presents the application of game theory in the context of civil and military security. Game theory is used to study conflict situations involving more than one decision-maker. Special emphasis was given to the significant role of information in modern military operations. The article contains examples illustrating similarities between civil and military problems.
EN
We formulate and study a two-player – duel – game as a nonzero-sum discounted stochastic game. Players P1, and P2 are standing in place and, in each turn, one or both may shoot at the other player. If Pn shoots at Pm (m ≠ n), either he hits and kills him (with probability pn) or he misses him and Pm is unaffected (with probability 1 − pn). The process continues until at least one player dies; if nobody ever dies, the game lasts an infinite number of turns. Each player receives a unit payoff for each turn in which he remains alive; no payoff is assigned to killing the opponent. We show that the always-shooting strategy is a NE but, in addition, the game also possesses so-called cooperative (i.e., non-shooting) Nash equilibria in both stationary and nonstationary strategies. A certain similarity to the repeated Prisoner’s Dilemma is also noted and discussed.
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M&A Cooperative Games

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Cooperative game theory instruments application to the corporate finance M&A research issues provide an ability to extend the field considered and conclusions obtained. The paper presents the M&A cooperative games modeling and its empirical implementation to analyze the airline strategic alliance as M&A deal.
EN
An IT project consisting in implementing a management support information system is characterised by information asymmetry between the supplier and the client. The presented research results are part of the author’s broader research pointing to imperfections in the access to information amongst the providers and buyers of IT projects. The scope of this article is to present the methods of avoiding information asymmetry as part of an IT project implementation. The research results may be interesting for researchers specialising in the subject matter of IT project implementation and for practitioners completing IT projects.
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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