In the last 30 years, derivatives have become increasingly important in the world of finance. Their frequent use has caused instability on financial markets, so as to leave ample opportunities for profit to speculators with large capitals. Just the sudden price fluctuations and the strong speculative pressures have exacerbated the present economic crisis. The current financial system is based on virtual money which does not confluence into the real economy, remaining stuck in the finance world ("credit crunch" phenomenon). So, it becomes appropriate to establish the "rules of the game," in order to redistribute the social wealth in a way at least close to the equity concept. Just this, as much as possible, we try to do in this work: we study a game theory model in which we see as a simple method (the application of a tax on speculative financial transactions) can cure a sick system, stabilizing the financial markets. The objective can be realized, as we shall see, without inhibiting the profit opportunity, nor for businesses nor for speculators. Also, in a second coopetitive game theory model, we propose a solution to the credit crunch, in order to allow a global economic recovery.

In this insightful and original book, Game Complete Analysis of Classic Economic Duopolies, David Carfi and Emanuele Perrone propose a game complete analysis of Cournot and Bertrand (symmetric and asymmetric) duopolies. Looking in more detail at the outline of the volume, Chapter 1 is an introductory chapter to the Complete Analysis of Differentiable Games, applied in the other four chapters. In Chapter 2 and 4, Carfi and Perrone deal with symmetric Cournot and Bertrand duopolies. The authors apply the Complete Analysis of Differentiable Games to the classic symmetric duopolies, an economic situation in which there are two firms producing the same commodity and selling it in the same market. In Chapter 3 and 5 the authors, again, apply the Complete Analysis of Differentiable Games and also some new algorithms, employing the software wxMaxima 11.04.0, in order to reach a total knowledge of the two classic duopolies, viewed as complex interactions between two competitive subjects, in two exemplar asymmetric cases. In conclusion, readers will find an interesting, original, sophisticated and surprising volume to read, about an evergreen and classic economic subject.

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.