Dynamics Games and Science : International Conference and Advanced School Planet Earth DGS II Portugal August 28–September 6 2013 Preface Foreword 1 Corruption Inequality and Income Taxation: E. Accinelli et al 2 Discrete Symmetric Planar Dynamics: B. Alarcón et al 3 Decision Analysis in a Model of Sports Pricing Under Uncertain Demand: A.A. Álvarez López et al 4 Growth Diagrams and Non Symmetric Cauchy Identities on NW (SE) Near Staircases: O. Azenhas et al 5 Clustering Techniques Applied on Cross Sectional Unemployment Data: C. Balsa et al 6 A Note on the Dynamics of Linear Automorphisms of a Convolution Measure Algebra: A. Baraviera et al 7 Periodic Homogenization of Deterministic Control Problems via Limit Occupational Measures: M. Bardi et al 8 On Gradient like Properties of Population Games Learning Models and Self Reinforced Processes: M. Benaim 9 Wave Interaction with Floating Bodies in a Stratified Multilayer Fluid: F.S. Cal et al 10 Shannon Switching Game and Directed Variants: A.P. Cláudio et al 11 A Proposal to Measure the Functional Efficiency of Futures Markets: M. Consuegra et al 12 On the Fundamental Bifurcation Theorem for Semelparous Leslie Models: J.M. Cushing 13 Review on Non Perturbative Reducibility of Quasi Periodically Forced Linear Flows with two Frequencies: J. Lopes Dias 14 Collateral Versus Default History: M. Faias et al 15 Regularity for Mean Field Games Systems with Initial Initial Boundary Conditions: the Subquadratic Case: D.A. Gomes et al 16 A Budget Setting Problem: O. Gomes 17 Dynamic Political Effects in a Neoclassic Growth Model with Healthcare and Creative Activities: L. Guimaraes et al 18 An Introduction to Geometric Gibbs Theory: Y. Jiang 19 Sphere Rolling on Sphere Alternative Approach to Kinematics and Constructive Proof of Controllability: F. Silva Leite et al 20 The Dual Potential the Involution Kernel and Transport in Ergodic Optimization: A. O. Lopes et al 21 Rolling Maps for the Essential Manifold: L. Machado et al 22 Singleton Free Set Partitions Avoiding a 3 Element Set: R. Mamede 23 Some Results on the Krein Parameters of an Association Scheme: V. Moco Mano et al 24 A Periodic Bivariate Integer Valued Autoregressive Model: M. Monteiro et al 25 The Macrodynamics of Employment under Uncertainty: P.R. Mota et al 26 A State Space Model Approach for Modelling the Population Dynamics of Black Scabbardfish in Portuguese Mainland Waters: I. Natário et al 27 Entropy and Negentropy: Applications in Game Theory: E. Oliva 28 Micro Econometric Analysis of New Household Formation in Spain: O. Montoro Peinado 29 An Adaptive Approach for Skin Lesion Segmentation in Dermoscopy Images Using a Multiscale Local Normalization: J. Pereira et al 30 Chaotic Dynamics and Synchronization of von Bertalanffy’s Growth Models: J. Leonel Rocha et al 31 Three Dimensional Flows: From Hyperbolicity to Quasi Stochasticity: A.A. P. Rodrigues 32 Dengue in Madeira Island: H.S. Rodrigues et al 33 The Number of Saturated Numerical Semi groups with a Determinate Genus: J.C. Rosales et al 34 Modern Forecasting of NOEM Models: M. Sànchez Sánchez 35 An Overview of Quantitative Continuous Compound Analysis: R. Santos et al 36 Varying the Money Supply of Commercial Banks: M. Shubik et al 37 Optimal Control of Tuberculosis: A Review: C.J. Silva et al 38 A Bayesian Modelling of Wildfires in Portugal: G.L. Silva et al 39 Minimum H Decompositions of Graphs and its Ramsey Version A Survey: T. Sousa The focus of this volume is research carried out as part of the program Mathematics of Planet Earth which provides a platform to showcase the essential role of mathematics in addressing problems of an economic and social nature and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global economic and social challenges. Earth is a planet with dynamic processes in its mantle oceans and atmosphere creating climate causing natural disasters and influencing fundamental aspects of life and life supporting systems. In addition to these natural processes human activity has developed highly complex systems including economic and financial systems; the World Wide Web; frameworks for resource management transportation energy production and utilization; health care delivery and social organizations. This development has increased to the point where it impacts the stability and equilibrium in human societies. Issues such as financial and economic crisis sustainability management of resources risk analysis and global integration have come to the fore. Written by some of the world’s leading specialists this book presents the proceedings of the International Conference and Advanced School Planet Earth Dynamics Games and Science II held in Lisbon Portugal 28 August 6 September 2013 which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book describes the state of the art in advanced research and ultimate techniques in modeling natural economic and social phenomena. It constitutes a tool and a framework for researchers and graduate students both in mathematics and applied sciences focusing mainly on dynamical systems game theory and applied sciences