Coopetitive games and applications

In this paper (based on researches conducted for three years) we define and apply the model of coopetitive game (in the sense recently introduced by David Carfì) to Economic Policy, Green Economy and Financial issues and in particular to the crisis of the Euro Zone (as already done in some published articles). The Crisis within the Euro Area has become frequent during 2010 and 2011. First was the Greek economy to face a default problem of its sovereign debt, then 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 coopetitive game model conceived at a macro level, feasible solutions in a cooperative perspective, taking account of the divergent interests that drive the economic policies in Germany and Greece. We conduct a deep study of the particular model proposed, namely, for the analysis we conduct a Complete Analysis of the coopetitive game - in the sense introduced and already applied by D. Carfì in several papers. The key points of our coopetitive exam are essentially the following ones: 1) the complete study of an initial game G(0), in the Carfì’s sense, from which we obtain also a precise knowledge of its payoff space; 2) the study of a curve g of games with starting point the game G(0), by methodologies of essentially geometric nature; 3) the determination of the path of Nash equilibria (of the games forming the curve g) (that we will use to the selection of coopetitive Pareto strategies, see point 4); 4) the determination of the Pareto maximal boundary of the coopetitive game (that is the maximal boundary of the union of the payoff spaces of the games forming the curve g); 5) the determination of compromise solutions for our strategic interaction. From an applicative point of view, our aim is to improve the position of the whole Euro area, also making a contribution to expand the set of macroeconomic policy tools. By means of our general analytical framework of coopetitive game, we show the strategies that could bring to feasible solutions in a cooperative perspective for the different country of the Euro zone (Germany and Greece in particular), where these feasible solutions aim at offering win-win outcomes for all countries in the EMU, letting them to share the pie fairly within a growth path represented by a non-zero sum coopetitive game. A remarkable analytical result of our work consists in the determination of a natural win-win solution by a new coopetitive selection method on the transferable utility Pareto boundary of the coopetitive game. Moreover the paper proposes a coopetitive model for the Green Economy. It addresses the issue of the climate change policy and the creation and diffusion of low-carbon technologies. In the present paper the complex construct of coopetiton is applied at macroeconomic level. The model, based on Game Theory, enables us to offer a set of possible solutions in a coopetitive context, allowing us to find a Pareto solution in a win-win scenario. The model, which is based on the assumption that each country produces a level of output which is determined in a non-cooperative game of Cournot-type and that considers at the same time a coopetitive strategy regarding the low technologies will suggest a solution that show the convenience for each country to participate actively to a program of low carbon technologies within a coopetitive framework to address a policy of climate change, thus aiming at balancing the environmental imbalances. JEL Classification: F40, E6, D7, C71, C72, C78, Q42, Q48, Q 50, Q55, C71, C72, C78.