David Carfì

CRISIS IN THE EURO AREA. COOPETITIVE GAME SOLUTIONS AS NEW POLICY TOOLS

The crisis within the Euro area have become frequent during 2010. First was the Greek economy to face a default problem of its sovreign debt, in November it was Ireland who has been in a serious financial situation at the verge of collapse causing difficulties to the euro. In this contribution we focus on the Greek crisis and we suggest, through a model of coopetition based on game theory and conceived at a macro level, feasible solutions in a cooperative perspective for the divergent interests which drive the economic policies in Germany and Greece, with the aim of improving the position of Greece, Germany and the whole Euro area and also giving a contribution to expand the set of macroeconomic policy tools. By means of our general analytical framework of coopetition, we show the strategies that could bring to feasible solutions in a cooperative perspective for Germany and Greece, where these feasible solutions aim at offering a win-win outcome for both countries, letting them to share the pie fairly within a growth path represented by a non-zero sum game. A remarkable analytical result of our work consists in the determination of the win-win solution by a new selection method on the transferable utility Pareto boundary of the coopetitive game.

Optimal boundaries for decisions

In this paper we state and prove some new results about the optimal boundaries. These boundaries (also called Pareto boundaries or efficiency boundaries or maximal/minimal boundaries) are of increasing importance in the applications to Decision Theory and Economics. First of all the Pareto boundaries are the first and most important generalization of the optima of decision constraints. On the other hand, if f is a real functional (utility function) defined on a non empty set X (of choices or economic strategies) and K is a part of X, the determination of the optimal boundaries of the part K, with respect to some preference relation ≤ of X for which the function f is strictly increasing, allows to reduce the optimization problem of finding the minimum of the functional f upon the part K to the problem of finding the minimum of f upon the minimal boundary of K. We note that the minimal boundary of K is, in general, greatly smaller than the initial decision constraint K. An economic application to the Cournot duopoly is presented.

A coopetitive approach to financial markets stabilization and risk management

The aim of this paper is to propose a methodology to stabilize the financial markets by adopting Game Theory, in particular, the Complete Study of a Differentiable Game and the new mathematical model of Coopetitive Game, proposed recently in the literature by D. Carfi. Specifically, we will focus on two economic operators: a real economic subject and a financial institute (a bank, for example) with a big economic availability. For this purpose we will discuss about an interaction between the two above economic subjects: the Enterprise, our first player, and the Financial Institute, our second player. The only solution which allows both players to win something, and therefore the only one collectively desirable, is represented by an agreement between the two subjects: the Enterprise artificially causes an inconsistency between spot and future markets, and the Financial Institute, who was unable to make arbitrages alone, because of the introduction by the normative authority of a tax on economic transactions (that we propose to stabilize the financial market, in order to protect it from speculations), takes the opportunity to win the maximum possible collective (social) sum, which later will be divided with the Enterprise by contract. We propose hereunder two kinds of agreement: a fair transferable utility agreement on the an initial natural interaction and a same type of compromise on a quite extended coopetitive context.

Non-reactive strategies in decision-form games

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.

A model for coopetitive games

In the present introductory work we propose an original analytical model of coopetitive game. We suggest possible general and feasible solutions; in particular, from a coopetitive perspective, we suggest compromise solutions - for our coopetitive game, by using Kalai-Smorodinsky method.

Asymmetric R&D Alliances and Coopetitive Games

In this paper we show how the study of asymmetric R&D alliances, that are those between young and small firms and large and MNEs firms for knowledge exploration and/or exploitation, requires the adoption of a coopetitive framework which consider both collaboration and competition. We draw upon the literature on asymmetric R&D collaboration and coopetition to propose a mathematical model for the coopetitive games which is particularly suitable for exploring asymmetric R&D alliances.

The family of operators associated with a capitalization law

In the present paper we conduct a deep study on some basic concepts offinancial mathematics, showing their analitic and geometric nature. We define the new concept of family of the capitalization factors of a capitalization. The main theorems of the paper are Let F be a capitalization law. Then F is strong if and only if the family of operators associated with F is an invertible one parameter family. Let F: R^3 -> R be a capitalization law, then F is separable if and only if the family of operators associated with F is a one parameter group.

Asymmetric Cournot Duopoly: A Game Complete Analysis

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfi 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.

MODEL OF POSSIBLE COOPERATION IN FINANCIAL MARKETS IN PRESENCE OF TAX ON SPECULATIVE TRANSACTIONS

In this paper, we propose an economic and mathematical model to protect the financial markets from speculative attacks, by introducing a tax on financial speculative transactions. By using Game Theory, we focus on the interaction between two general players: a real economic subject (we call Enterprise) acting with hedging scopes and a bank (we call Financial Institute) acting with speculative purposes. We find different equilibria of our game, by considering friendly, selfless, selfish, fearful or aggressive behavior of players; we note that no equilibrium is good for both players, and each of them prevent at least one of the two economic subjects to obtain profits. So, we propose two different transferable utility solutions, in order to achieve a result satisfying both economic subjects and, at the same time, to achieve a condition promoting the stability of the financial markets in which our two players are interacting.

Global Green Economy and Environmental Sustainability: A Coopetitive Model

This paper provides a coopetitive model for a global green economy taking into account the environmental sustainability. In particular we propose a differentiable coopetitive game G (in the sense recently introduced by D. Carfi) to represent a basic green economy interaction among a country c and the rest of the world w. Our game G is a linear parametric (Euclidean) perturbation of the classic Cournot duopoly. In the paper we offer the complete study of the proposed model and in particular a deep examination of its possible coopetitive solutions.