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This book gathers carefully selected works in Mathematical Economics, on myriad topics including General Equilibrium, Game Theory, Economic Growth, Welfare, Social Choice Theory, Finance. It sheds light on the ongoing discussions that have brought together leading researchers from Latin America and Southern Europe at recent conferences in venues like Porto, Portugal; Athens, Greece; and Guanajuato, Mexico. With this volume, the editors not only contribute to the advancement of research in these areas, but also inspire other scholars around the globe to collaborate and research these vibrant, emerging topics.

After 9/11 the problem of "ungrievable lives" has taken a central place in Judith Butler's philosophical work. However, in her latest works, she tries to imagine a new kind of political mobilization not only capable of breaking into the hegemonic cultural framework, which is responsible for the exclusion of some lives from the human domain, but also capable of putting at centre-stage the bodily dimension of all human beings with their needs and demands. In the first part of this article I give a brief overview of the processes of disavowal and derealisation, focusing especially on the media representation of contemporary wars that influence our cognitive schemes by applying a different human value to other populations and social groups. In the second part of the article I discuss the bodily mobilizations of those very subjects whose lives are made unworthy and unliveable by virtue of current "frameworks of intelligibility".

Inspired by the Daley-Kendall and Goffman-Newill models, we propose an Ignorant-Believer-Unbeliever rumor (or fake news) spreading model with the following characteristics: (i) a network contact between individuals that determines the spread of rumors; (ii) the value (cost versus benefit) for individuals who search for truthful information (learning); (iii) an impact measure that assesses the risk of believing the rumor; (iv) an individual search strategy based on the probability that an individual searches for truthful information; (v) the population search strategy based on the proportion of individuals of the population who decide to search for truthful information; (vi) a payoff for the individuals that depends on the parameters of the model and the strategies of the individuals. Furthermore, we introduce evolutionary information search dynamics and study the dynamics of population search strategies. For each value of searching for information, we compute evolutionarily stable information (ESI) search strategies (occurring in non-cooperative environments), which are the attractors of the information search dynamics, and the optimal information (OI) search strategy (occurring in (eventually forced) cooperative environments) that maximizes the expected information payoff for the population. For rumors that are advantageous or harmful to the population (positive or negative impact), we show the existence of distinct scenarios that depend on the value of searching for truthful information. We fully discuss which evolutionarily stable information (ESI) search strategies and which optimal information (OI) search strategies eradicate (or not) the rumor and the corresponding expected payoffs. As a corollary of our results, a recommendation for legislators and policymakers who aim to eradicate harmful rumors is to make the search for truthful information free or rewarding.

We consider two firms, located in different countries, selling the same homogeneous good in both countries. In each country there is a non negative tariff on imports of the good produced in the other country. We suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We analyse the effect of the production costs uncertainty on the profits of the firms and also on the welfare of the governments.

We consider a trade policy model, where the costs of the home firm are private information but can be signaled through the output levels of the firm to a foreign competitor and a home policymaker. We compute the separating equilibrium and the Bayesian Nash equilibrium, and we compare the subsidies, firms' expected profits and home government's welfare in both equilibria, for different values of the own price effect parameter.

We consider two Cournot firms, one located in the home country and the other in the foreign country, producing substitute goods for consumption in a third country. We suppose that neither the home government nor the foreign firm know the costs of the home firm, while the foreign firm cost is common knowledge. We determine the separating sequential equilibrium outputs.

We study a dichotomous decision model, where individuals can make the decision yes or no and can influence the decisions of others. We characterize all decisions that form Nash equilibria. Taking into account the way individuals influence the decisions of others, we construct the decision tilings where the axes reflect the personal preferences of the individuals for making the decision yes or no. These tilings characterize geometrically all the pure and mixed Nash equilibria. We show, in these tilings, that Nash equilibria form degenerated hysteresis with respect to the dynamics, with the property that the pure Nash equilibria are asymptotically stable and the strict mixed equilibria are unstable. These hysteresis can help to explain the sudden appearance of social, political and economic crises. We observe the existence of limit cycles for the dynamics associated to situations where the individuals keep changing their decisions along time, but exhibiting a periodic repetition in their decisions. We introduce the notion of altruist and individualist leaders and study the way that the leader can affect the individuals to make the decision that the leader pretends.

We study a dichotomous decision model, where individuals can make the decision yes or no and can influence the decisions of others. We characterize all decisions that form Nash equilibria. Taking into account the way individuals influence the decisions of others, we construct the decision tilings where the axes reflect the personal preferences of the individuals for making the decision yes or no. These tilings characterize geometrically all the pure and mixed Nash equilibria. We show, in these tilings, that Nash equilibria form degenerated hysteresis with respect to the dynamics, with the property that the pure Nash equilibria are asymptotically stable and the strict mixed equilibria are unstable. These hysteresis can help to explain the sudden appearance of social, political and economic crises. We observe the existence of limit cycles for the dynamics associated to situations where the individuals keep changing their decisions along time, but exhibiting a periodic repetition in their decisions. We introduce the notion of altruist and individualist leaders and study the way that the leader can affect the individuals to make the decision that the leader pretends.

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

Intro -- Preface -- Acknowledgments -- Contents -- List of Contributors -- 1 Breaking the Circular Flow: A Dynamic Programming Approach to Schumpeter -- 1.1 Context and Circular Flow -- 1.1.1 The Evolution of Control -- 1.1.2 The Circular Flow and Equilibrium -- 1.1.3 Types of Innovation -- 1.1.4 Property Rights, Information, and Appropriation -- 1.2 How to Finance Innovation -- 1.3 Models with Cost Innovation -- 1.4 Robinson Crusoe in a Nonmonetary Economy -- 1.4.1 Innovation by Robinson Crusoe -- 1.4.2 A Risk-Neutral Crusoe -- 1.4.2.1 A Numerical Example -- 1.4.3 A Risk-Averse Robinson Crusoe with Proportional Production -- 1.4.3.1 Innovation by a Risk-Averse Robinson Crusoe -- 1.4.4 Innovation Over Many Periods -- 1.4.5 Lessons from Crusoe's Innovation -- 1.5 Finance and Innovation -- 1.5.1 Physical and Financial Assets, Innovation,and Equilibrium -- 1.6 The Closed Economy as a Sensing, Evaluating,and Control Mechanism -- 1.6.1 Individual or Representative Agents? -- 1.6.2 On Money, Credit, Banks, and Central Banks -- 1.7 The Separation of Management and Ownership -- 1.8 A Closed Economy Prior to Innovation: The Circular Flow of Money Illustrated -- 1.9 Innovation in an Asset-Poor Economy: Breakingthe Circular Flow -- 1.9.1 The Meaning of an Asset-Poor Economy -- 1.9.2 Innovation in an Asset-Poor Economy -- 1.9.2.1 A Model with Managerial Control and Central Bank Lending -- 1.9.2.2 Stationary Equilibrium and the Question of Convergence -- 1.9.2.3 The Modeling of Central Bank Profits -- 1.9.3 Two Simple Examples -- 1.9.3.1 Robinson Crusoe Revisited -- 1.9.3.2 A Simple Monetary Economy -- 1.10 Summary Remarks -- References -- 2 A Review in Campaigns: Going Positive and Negative -- 2.1 Introduction -- 2.2 Negative Campaigns in Different Fields -- 2.3 Modeling Negative Campaigns: An Economic Approach -- 2.4 Final Remarks -- References.