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The aim of this paper is to present a proposal regarding the possible stabilization of the rapid variations on the value of government bonds issued by the States, using the ``Game Theory". In particular, we focus our attention on three players: a large bank that has immediate access to the market of government bonds (hereinafter called Speculator, our first player), the European Central Bank (ECB, the second player) and the State in economic difficulty (our third player). We propose on financial transactions the introduction of a tax (cashed directly by the State in economic difficulty), which hits only the speculative profits. We show that the above tax would probably be able to avert the speculation, and, even in case of speculation on its government bonds, the State manages to pull itself out of the crisis. Finally, we also propose a cooperative solution that enables all economic actors involved (the Speculator, the ECB and the State) to obtain a profit.

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8], [9], and already employed by himself and others in [4], [5], [7]) to the classic Cournot Duopoly (1838), classic oligopolistic market in which there are two enterprises producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ, as possible strategies, the quantities of the commodity produced. The main solutions proposed in literature for this kind of duopoly are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Cournot Duopoly as a differentiable game (a game with differentiable payoff functions) and studying it by the new topological methodologies introduced by D. Carfì, we obtain an exhaustive and complete vision of the entire payoff space of the Cournot game (this also in asymmetric cases with the help of computers) and this total view allows us to analyze critically the classic solutions and to find other ways of action to select Pareto strategies. In order to illustrate the application of this topological methodology to the considered infinite game, several compromise decisions are considered, and we show how the complete study gives a real extremely extended comprehension of the classic model.

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8], [9]; already employed by himself and others in [4], [5], [7]) and some new algorithms using the software wxMaxima 11.04.0, in order to reach a total scenario knowledge (that is the total knowledge of the payoff space of the interaction) of the classic Cournot Duopoly (1838), viewed as a complex interaction between two competitive subjects, in a particularly interesting asymmetric case. The software wxMaxima is an interface for the computer algebra system Maxima. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, sets, vectors and matrices.

The aim of this paper is to propose a methodology to stabilize the currency markets by adopting Game Theory. Our idea is to save the Euro from the speculative attacks (due the crisis of the Euro-area States), and this goal is reached by the introduction, by the normative authority, of a financial transactions tax. Specifically, we focus on two economic operators: a real economic subject (as for example the Ferrari S.p.A., our first player), and a financial institute of investment (the Unicredit Bank, our second player). The unique solution which allows both players to win something, and therefore the only one collectively desirable, is represented by an agreement between the two subjects. So the Ferrari artificially causes an inconsistency between currency spot and futures markets, and the Unicredit takes the opportunity to win the maximum possible collective sum, which later will be divided with the Ferrari by contract.

The paper aims at providing a Game Theory model of coopetition which addresses the problem of the global Green Economy. The Green Economy is a theoretical model of sustainable development. This sustainable development model should lead to reduce emissions of greenhouse gases, determine the reduction of global pollution and the establishment of a sustainable and lasting global Green Economy, using mainly renewable resources. The paper applies the notion of coopetition, originally devised at microeconomic level, at a country level. The country has to decide whether it wants to collaborate with the rest of the world in getting an efficient Green Economy, even if the country is competing in the global scenario. The model provides a win-win solution, that shows the convenience for each country to participate actively to a program of sustainability and efficient resource allocation within a coopetitive framework.

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8] and [9]) and already employed by himself and others in [4], [5], [7]) and some new algorithms employing the software wxMaxima 11.04.0 in order to reach a total knowledge of the classic Bertrand Duopoly (1883), viewed as a complex interaction between two competitive subjects, in a particularly difficult asymmetric case. The software wxMaxima is an interface for the computer algebra system Maxima. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, systems of linear equations, polynomials, and sets, vectors, matrices. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions. The Bertrand Duopoly is a classic oligopolistic market in which there are two enterprises producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ as possible strategies the unit prices of their products, contrary to the Cournot duopoly, in which the enterprises decide to use the quantities of the commodity produced as strategies. The main solutions proposed in literature for this kind of duopoly (as in the case of Cournot duopoly) are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Bertrand Duopoly as a differentiable game (games with differentiable payoff functions) and studying it by the new topological methodologies introduced by D. Carfì, we obtain an exhaustive and complete vision of the entire payoff space of the Bertrand game (this also in asymmetric cases with the help of wxMaxima 11.04.0) and this total view allows us to analyze critically the classic solutions and to find other ways of action to select Pareto strategies, in the asymmetric cases too. In order to illustrate the application of this topological methodology to the considered infinite game we show how the complete study gives a real extremely extended comprehension of the classic model.

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8] and [9]) and al-ready employed by himself and others in [4], [5], [7]) to the classic Bertrand Duopoly (1883), classic oligopolistic market in which there are two enterprises producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ as possible strategies the unit prices of their product, contrary to the Cournot duopoly, in which the enterprises decide to use the quantities of the commodity produced as strategies. The main solutions proposed in literature for this kind of duopoly (as in the case of Cournot duopoly) are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Bertrand Duopoly as a differentiable game (games with differentiable payoff functions) and studying it by the new topological methodologies introduced by D. Carfì, we obtain an exhaustive and complete vision of the entire payoff space of the Bertrand game (this also in asymmetric cases with the help of computers) and this total view allows us to analyze critically the classic solutions and to find other ways of action to select Pareto strategies. In order to illustrate the application of this topological methodology to the considered infinite game, several compromise pricing-decisions are considered, and we show how the complete study gives a real extremely extended comprehension of the classic model.

In the present work we propose an original analytical model of coopetitive games. We try to apply this analytical model of coopetition - based on Game Theory and conceived at a macro level - to the Greek crisis, suggesting feasible solutions in a cooperative perspective for the divergent interests which drive the economic policies in the euro area.

In this paper we propose a concept of rationalizable solution for two-player decision-form games: the solution by iterated elimination of non-reactive strategies. Several original theorems are proved about this kind of solution. We study the relations between solutions by iterated elimination of non reactive strategies and game equilibria. We present an existence theorem for bistrategies surviving the iterated elimination and an existence theorem for solution by iterated elimination in contracting games. We, also, show that an equilibrium of a game survives iterated elimination of non-reactive strategies. At the end we prove a characterization of solvability by iterated elimination of non-reactive strategies.