Developing real option game models

By mixing concepts from both game theoretic analysis and real options theory, an investment decision in a competitive market can be seen as a ‘‘game’’ between firms, as firms implicitly take into account other firms’ reactions to their own investment actions. We review two decades of real option game models, suggesting which critical problems have been ‘‘solved’’ by considering game theory, and which significant problems have not been yet adequately addressed. We provide some insights on the plausible empirical applications, or shortfalls in applications to date, and suggest some promising avenues for future research.

The game to play: expanding the co-opetition proposal through the strategic games matrix

Purpose - Using Brandenburger and Nalebuff`s 1995 co-opetition model as a reference, the purpose of this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enable scholars and managers to identify which games may be played in response to the different conflict of interest situations faced by companies in their business environments. Design/methodology/approach - The literature on game theory and business strategy are reviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel games are described and modeled. Findings - The co-opetition model is not sufficient to realistically represent most of the conflict of interest situations faced by companies. It seeks to address this problem through development of the SGM, which expands upon Brandenburger and Nalebuff`s model by providing a broader perspective, through incorporation of an additional dimension (power ratio between players) and three novel, respectively, (rival, individualistic, and associative). Practical implications - This proposed model, based on the concepts of game theory, should be used to train decision- and policy-makers to better understand, interpret and formulate conflict management strategies. Originality/value - A practical and original tool to use game models in conflict of interest situations is generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on the SGM to suggest in which situations they Could be useful. Two innovative games are described to fit four different types of conflict situations that so far have no corresponding game in the literature. A test application of the SGM to a classic Intel Corporation strategic management case, in the complex personal computer industry, shows that the proposed method is able to describe, to interpret, to analyze, and to prescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.

Model of a game for improving integrated decisions in production management

This paper presents the results obtained with a business game whose model represents the decision making process related to two moments at an industrial company. The first refers to the project of the industrial plant, and the second to its management. The game model was conceived so the player's first decision would establish capacity and other parameters such as quantities of each product to produce, marketing expenses, research and development, quality, advertising, salaries, if purchases will be made in installments or in cash, if there will be credit sales and how many installments will be allowed and the number of workers in the assembly area. An experiment was conducted with employees of a Brazilian company. Data obtained indicate that the players have lack of contents, especially in finances. Although these results cannot be generalized, they confirm prior results with undergraduate and graduate students and they indicate the need for reinforcement in this undergraduate area. © 2012 Springer-Verlag.

Secret information acquisition in Cournot markets

Two-stage game models of information acquisition in stochastic oligopoliesrequire the unrealistic assumption that firms observe the precision ofinformation chosen by their competitors before determining quantities. Thispaper analyzes secret information acquisition as a one-stage game. Relativeto the two-stage game firms are shown to acquire less information. Policyimplications based on the two-stage game yield, therefore, too high taxes ortoo low subsidies for research activities. For the case of heterogeneousduopoly it is shown that comparative statics results partly depend on theobservability assumption.

Influence d’une augmentation du taux de testostérone sur les décisions d’approvisionnement chez les diamants mandarins mâles (Taeniopygia guttata)

Un animal qui s’approvisionne en groupe peut rechercher soi-même sa nourriture (tactique producteur) ou tenter de se joindre à des parcelles déjà découvertes par un autre individu (tactique chapardeur). Bien que les modèles de jeu producteur-chapardeur partent du principe que les gains moyens à l’équilibre associés à chacune de ces tactiques sont égaux et ne dépendent pas des caractéristiques des individus, de plus en plus d’études démontrent que le gain de chaque tactique est influencé par certaines caractéristiques phénotypiques (agressivité, capacités d’apprentissage,…). Dans cette étude, nous nous intéressons aux effets de la testostérone sur le choix des tactiques d’approvisionnement chez les mâles de diamant mandarin (Taeniopygia guttata). La testostérone est connue pour influencer le développement du cerveau et l’agressivité, nous avons donc testé les effets d’une exposition prénatale à la testostérone ainsi que durant l’âge adulte sur le choix des tactiques d’approvisionnement lorsque la nourriture est cryptique ou défendable. Nous avons réalisé deux expériences : nous avons tout d’abord utilisé la longueur du tarse ainsi que la différence entre les longueurs des doigts 2 et 4 comme des indicateurs de l’exposition prénatale à la testostérone puis testé si ces différences morphologiques se traduisent par des différences dans le choix des tactiques dans une condition défendable et une condition cryptique. Nous avons trouvé que le choix des tactiques chez les diamants mandarins était limité par le phénotype. Une exposition précoce à la testostérone au cours du développement prénatal pourrait donc être la cause d’au moins une part de la variation observée dans le choix des tactiques d’approvisionnement. Ensuite, nous avons manipulé le taux de testostérone plasmatique chez des mâles adultes grâce à des implants hormonaux sous-cutanés puis comparé le comportement des individus lorsqu’ils portaient un implant hormonal et un implant contrôle et ce, dans chacune des deux conditions d’approvisionnement. Nous n’avons mis en évidence aucun effet du taux de testostérone plasmatique sur le choix des tactiques à l’âge adulte. Nos résultats sont en accord avec l’hypothèse que le choix des tactiques d’approvisionnement peut être influencé par les hormones. Notre conclusion est que les hormones stéroïdiennes peut affecter le choix des tactiques via l’existence d’effets maternels dans le jeu producteur-chapardeur.

Modelagem em programação linear para resolução de jogos fuzzy intervalares

A teoria de jogos modela estratégias entre agentes (jogadores), os quais possuem recompensas ao fim do jogo conforme suas ações. O melhor par de estratégias para os jogadores constitui uma solução de equilíbrio. Porém, nem sempre se consegue estimar os dados do problema. Diante disso, os parâmetros incertos presentes em modelos de jogos são formalizados pela teoria fuzzy. Assim, a teoria fuzzy auxilia a teoria de jogos, formando jogos fuzzy. Dessa forma, parâmetros, como as recompensas, tornam-se números fuzzy. Mais ainda, quando há incerteza na representação desses números fuzzy utilizam-se os números fuzzy intervalares. Então, neste trabalho modelos de jogos fuzzy intervalares são analisados e métodos computacionais são desenvolvidos para a resolução desses jogos. Por fim, realizam-se simulações de programação linear para observar melhor a aplicação das teorias estudadas e avaliar a proposta.

Game Theory Models for Multi-Robot Patrolling of Infraestructures

Abstract This work is focused on the problem of performing multi‐robot patrolling for infrastructure security applications in order to protect a known environment at critical facilities. Thus, given a set of robots and a set of points of interest, the patrolling task consists of constantly visiting these points at irregular time intervals for security purposes. Current existing solutions for these types of applications are predictable and inflexible. Moreover, most of the previous centralized and deterministic solutions and only few efforts have been made to integrate dynamic methods. Therefore, the development of new dynamic and decentralized collaborative approaches in order to solve the aforementioned problem by implementing learning models from Game Theory. The model selected in this work that includes belief‐based and reinforcement models as special cases is called Experience‐Weighted Attraction. The problem has been defined using concepts of Graph Theory to represent the environment in order to work with such Game Theory techniques. Finally, the proposed methods have been evaluated experimentally by using a patrolling simulator. The results obtained have been compared with previous available

Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.

An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

This paper presents the main achievements of the author’s PhD dissertation. The work is dedicated to mathematical and semi-empirical approaches applied to the case of Bulgarian wildland fires. After the introductory explanations, short information from every chapter is extracted to cover the main parts of the obtained results. The methods used are described in brief and main outcomes are listed. ACM Computing Classification System (1998): D.1.3, D.2.0, K.5.1.

Multifractal regime transition in a modified minority game model

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual minority game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the structure function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (non-linear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the wavelet transform modulus maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes. (C) 2009 Elsevier Ltd. All rights reserved.

A vaccination game based on public health actions and personal decisions

Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns. (C) 2011 Elsevier B.V. All rights reserved.

Strategic bidding in electricity markets: an agent-based simulator with game theory for scenario analysis

Electricity markets are complex environments, involving a large number of different entities, with specific characteristics and objectives, making their decisions and interacting in a dynamic scene. Game-theory has been widely used to support decisions in competitive environments; therefore its application in electricity markets can prove to be a high potential tool. This paper proposes a new scenario analysis algorithm, which includes the application of game-theory, to evaluate and preview different scenarios and provide players with the ability to strategically react in order to exhibit the behavior that better fits their objectives. This model includes forecasts of competitor players’ actions, to build models of their behavior, in order to define the most probable expected scenarios. Once the scenarios are defined, game theory is applied to support the choice of the action to be performed. Our use of game theory is intended for supporting one specific agent and not for achieving the equilibrium in the market. MASCEM (Multi-Agent System for Competitive Electricity Markets) is a multi-agent electricity market simulator that models market players and simulates their operation in the market. The scenario analysis algorithm has been tested within MASCEM and our experimental findings with a case study based on real data from the Iberian Electricity Market are presented and discussed.

Strategic Bidding in Electricity Markets: An agent-based simulator with game theory for scenario analysis

Electricity markets are complex environments, involving a large number of different entities, with specific characteristics and objectives, making their decisions and interacting in a dynamic scene. Game-theory has been widely used to support decisions in competitive environments; therefore its application in electricity markets can prove to be a high potential tool. This paper proposes a new scenario analysis algorithm, which includes the application of game-theory, to evaluate and preview different scenarios and provide players with the ability to strategically react in order to exhibit the behavior that better fits their objectives. This model includes forecasts of competitor players’ actions, to build models of their behavior, in order to define the most probable expected scenarios. Once the scenarios are defined, game theory is applied to support the choice of the action to be performed. Our use of game theory is intended for supporting one specific agent and not for achieving the equilibrium in the market. MASCEM (Multi-Agent System for Competitive Electricity Markets) is a multi-agent electricity market simulator that models market players and simulates their operation in the market. The scenario analysis algorithm has been tested within MASCEM and our experimental findings with a case study based on real data from the Iberian Electricity Market are presented and discussed.

Decision Support for Energy Contracts Negotiation with Game Theory and Adaptive Learning

This paper presents a decision support methodology for electricity market players’ bilateral contract negotiations. The proposed model is based on the application of game theory, using artificial intelligence to enhance decision support method’s adaptive features. This model is integrated in AiD-EM (Adaptive Decision Support for Electricity Markets Negotiations), a multi-agent system that provides electricity market players with strategic behavior capabilities to improve their outcomes from energy contracts’ negotiations. Although a diversity of tools that enable the study and simulation of electricity markets has emerged during the past few years, these are mostly directed to the analysis of market models and power systems’ technical constraints, making them suitable tools to support decisions of market operators and regulators. However, the equally important support of market negotiating players’ decisions is being highly neglected. The proposed model contributes to overcome the existing gap concerning effective and realistic decision support for electricity market negotiating entities. The proposed method is validated by realistic electricity market simulations using real data from the Iberian market operator—MIBEL. Results show that the proposed adaptive decision support features enable electricity market players to improve their outcomes from bilateral contracts’ negotiations.

Evolution of reputation in networks: A mean field game approach

This work models the competitive behaviour of individuals who maximize their own utility managing their network of connections with other individuals. Utility is taken as a synonym of reputation in this model. Each agent has to decide between two variables: the quality of connections and the number of connections. Hence, the reputation of an individual is a function of the number and the quality of connections within the network. On the other hand, individuals incur in a cost when they improve their network of contacts. The initial value of the quality and number of connections of each individual is distributed according to an initial (given) distribution. The competition occurs over continuous time and among a continuum of agents. A mean field game approach is adopted to solve the model, leading to an optimal trajectory for the number and quality of connections for each individual.