Regularity of Wiener-Hopf plus Hankel operators

In this thesis we consider Wiener-Hopf-Hankel operators with Fourier symbols in the class of almost periodic, semi-almost periodic and piecewise almost periodic functions. In the first place, we consider Wiener-Hopf-Hankel operators acting between L2 Lebesgue spaces with possibly different Fourier matrix symbols in the Wiener-Hopf and in the Hankel operators. In the second place, we consider these operators with equal Fourier symbols and acting between weighted Lebesgue spaces Lp(R;w), where 1 < p < 1 and w belongs to a subclass of Muckenhoupt weights. In addition, singular integral operators with Carleman shift and almost periodic coefficients are also object of study. The main purpose of this thesis is to obtain regularity properties characterizations of those classes of operators. By regularity properties we mean those that depend on the kernel and cokernel of the operator. The main techniques used are the equivalence relations between operators and the factorization theory. An invertibility characterization for the Wiener-Hopf-Hankel operators with symbols belonging to the Wiener subclass of almost periodic functions APW is obtained, assuming that a particular matrix function admits a numerical range bounded away from zero and based on the values of a certain mean motion. For Wiener-Hopf-Hankel operators acting between L2-spaces and with possibly different AP symbols, criteria for the semi-Fredholm property and for one-sided and both-sided invertibility are obtained and the inverses for all possible cases are exhibited. For such results, a new type of AP factorization is introduced. Singular integral operators with Carleman shift and scalar almost periodic coefficients are also studied. Considering an auxiliar and simpler operator, and using appropriate factorizations, the dimensions of the kernels and cokernels of those operators are obtained. For Wiener-Hopf-Hankel operators with (possibly different) SAP and PAP matrix symbols and acting between L2-spaces, criteria for the Fredholm property are presented as well as the sum of the Fredholm indices of the Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. By studying dependencies between different matrix Fourier symbols of Wiener-Hopf plus Hankel operators acting between L2-spaces, results about the kernel and cokernel of those operators are derived. For Wiener-Hopf-Hankel operators acting between weighted Lebesgue spaces, Lp(R;w), a study is made considering equal scalar Fourier symbols in the Wiener-Hopf and in the Hankel operators and belonging to the classes of APp;w, SAPp;w and PAPp;w. It is obtained an invertibility characterization for Wiener-Hopf plus Hankel operators with APp;w symbols. In the cases for which the Fourier symbols of the operators belong to SAPp;w and PAPp;w, it is obtained semi-Fredholm criteria for Wiener-Hopf-Hankel operators as well as formulas for the Fredholm indices of those operators.

The player and video game interplay in the gameplay experience construct

Among the many discussions and studies related to video games, one of the most recurrent, widely debated and important relates to the experience of playing video games. The gameplay experience – as appropriated in this study – is the result of the interplay between two essential elements: a video game and a player. Existing studies have explored the resulting experience of video game playing from the perspective of the video game or the player, but none appear to equally balance both of these elements. The study presented here contributes to the ongoing debate with a gameplay experience model. The proposed model, which looks to equally balance the video game and the player elements, considers the gameplay experience to be both an interactive experience (related to the process of playing the video game) and an emotional experience (related to the outcome of playing the video game). The mutual influence of these two experiences during video game play ultimately defines the gameplay experience. To this gameplay experience contributes several dimensions, related to both the video game and player: the video game includes a mechanics, interface and narrative dimension; the player includes a motivations, expectations and background dimension. Also, the gameplay experience is initially defined by a gameplay situation, conditioned by an ambient in which gameplay takes place and a platform on which the video game is played. In order to initially validate the proposed model and attempt to show a relationship among the multiple model dimensions, a multi-case study was carried out using two different video games and player samples. In one study, results show significant correlations between multiple model dimensions, and evidence that video game related changes influence player motivations as well as player visual behavior. In specific player related analysis, results show that while players may be different in terms of background and expectations regarding the game, their motivation to play are not necessarily different, even if their performance in the game is weak. While further validation is necessary, this model not only contributes to the gameplay experience debate, but also demonstrates in a given context how player and video game dimensions evolve during video game play.

Sex-related invariance across cultures in an online role-playing game

This study examines the Social Dominance Orientation of players of the online roleplaying game World of Warcraft. The World of Warcraft offers an opportunity to investigate social dominance and biological sex differences in an environment where there is no cultural dominance of one sex over another. Social Dominance Orientation has been found to be different between males and females, with males scoring higher. However, this might be the consequence of social context. To this end sex differences between male and female players were investigated in the World of Warcraft environment, as well as the effects of chosen character sex. Player sex and character sex were found to have effects on Social Dominance Orientation. These results add further support to claims that Social Dominance Orientation has the characteristics of a sexually selected disposition to acquire resources and out-compete rival groups.

Introducing Game Development into the Computing Curriculum: a Progressive Methodology

The Computer Game industry is big business, the demand for graduates is high, indeed there is a continuing shortage of skilled employees. As with most professions, the skill set required is both specific and diverse. There are currently over 30 Higher Education Institutions (HEIs) in the UK offering Computer games related courses. We expect that as the demand from the industry is sustained, more HEIs will respond with the introduction of game-related degrees. This is quite a considerable undertaking involving many issues from integration of new modules or complete courses within the existing curriculum, to staff development. In this paper we share our experiences of introducing elements of game development into our curriculum. This has occurred over the past two years, starting with the inclusion of elements of game development into existing programming modules, followed by the validation of complete modules, and culminating in a complete degree course. Our experience is that our adopting a progressive approach to development, spread over a number of years, was crucial in achieving a successful outcome.

For the Good of the Game(?): The Legacy of the Football Trust, the Football Pools & the Dangerous Seduction of Political Promise

During the late twentieth century, the United Kingdom’s football infrastructure and spectatorship underwent transformation as successive stadia disasters heightened political and public scrutiny of the game and prompted industry change. Central to this process was the government’s formation of an independent charitable organization to oversee subsequent policy implementation and grant-aid provision to clubs for safety, crowd, and spectator requirements. This entity, which began in 1975 focusing on ground improvement, developed into the Football Trust. The Trust was funded directly by the football pools companies who ran popular low-stakes football betting enterprises. Working in association with the Pools Promoters Association (PPA), and demonstrating their social responsibility towards the game’s constituents, the pools resourced a wide array of Trust activities. Yet irrespective of government mandate, the PPA and Trust were continually confronted by political and economic obstacles that threatened the effectiveness of their arrangements. In this paper the history of the Football Trust is investigated, along with its partnership with the PPA, and its relationship with the government within the context of broader political shifts, stadia catastrophes, official inquiries, and commercial threats. It is contended that while the Trust/PPA partnership had a respectable legacy, their history afforded little protection against adverse contemporary conditions.

Transmission cost allocation using cooperative game theory: a comparative study

In this paper is presented a Game Theory based methodology to allocate transmission costs, considering cooperation and competition between producers. As original contribution, it finds the degree of participation on the additional costs according to the demand behavior. A comparative study was carried out between the obtained results using Nucleolus balance and Shapley Value, with other techniques such as Averages Allocation method and the Generalized Generation Distribution Factors method (GGDF). As example, a six nodes network was used for the simulations. The results demonstrate the ability to find adequate solutions on open access environment to the networks.

TimeMesh: an educational historical game

The TIMEMESH game, developed in the scope of the European Project SELEAG, is an educational game for learning history, culture and social relations. It is supported by an extensible, online, multi-language, multi-player, collaborative and social platform for sharing and acquiring knowledge of the history of European regions. The game has been already used, with remarkable success, in different European countries like Portugal, Spain, England, Slovenia, Estonia and Belgium.

On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 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.

Coalition of distributed generation units to Virtual Power Players - a game theory approach

Smart Grids (SGs) have emerged as the new paradigm for power system operation and management, being designed to include large amounts of distributed energy resources. This new paradigm requires new Energy Resource Management (ERM) methodologies considering different operation strategies and the existence of new management players such as several types of aggregators. This paper proposes a methodology to facilitate the coalition between distributed generation units originating Virtual Power Players (VPP) considering a game theory approach. The proposed approach consists in the analysis of the classifications that were attributed by each VPP to the distributed generation units, as well as in the analysis of the previous established contracts by each player. The proposed classification model is based in fourteen parameters including technical, economical and behavioural ones. Depending of the VPP strategies, size and goals, each parameter has different importance. VPP can also manage other type of energy resources, like storage units, electric vehicles, demand response programs or even parts of the MV and LV distribution network. A case study with twelve VPPs with different characteristics and one hundred and fifty real distributed generation units is included in the paper.

A framework for real time MMO game content generation

Com o aumento de plataformas móveis disponíveis no mercado e com o constante incremento na sua capacidade computacional, a possibilidade de executar aplicações e em especial jogos com elevados requisitos de desempenho aumentou consideravelmente. O mercado dos videojogos tem assim um cada vez maior número de potenciais clientes. Em especial, o mercado de jogos massive multiplayer online (MMO) tem-se tornado muito atractivo para as empresas de desenvolvimento de jogos. Estes jogos suportam uma elevada quantidade de jogadores em simultâneo que podem estar a executar o jogo em diferentes plataformas e distribuídos por um "mundo" de jogo extenso. Para incentivar a exploração desse "mundo", distribuem-se de forma inteligente pontos de interesse que podem ser explorados pelo jogador. Esta abordagem leva a um esforço substancial no planeamento e construção desses mundos, gastando tempo e recursos durante a fase de desenvolvimento. Isto representa um problema para as empresas de desenvolvimento de jogos, e em alguns casos, e impraticável suportar tais custos para equipas indie. Nesta tese e apresentada uma abordagem para a criação de mundos para jogos MMO. Estudam-se vários jogos MMO que são casos de sucesso de modo a identificar propriedades comuns nos seus mundos. O objectivo e criar uma framework flexível capaz de gerar mundos com estruturas que respeitam conjuntos de regras definidas por game designers. Para que seja possível usar a abordagem aqui apresentada em v arias aplicações diferentes, foram desenvolvidos dois módulos principais. O primeiro, chamado rule-based-map-generator, contem a lógica e operações necessárias para a criação de mundos. O segundo, chamado blocker, e um wrapper à volta do módulo rule-based-map-generator que gere as comunicações entre servidor e clientes. De uma forma resumida, o objectivo geral e disponibilizar uma framework para facilitar a geração de mundos para jogos MMO, o que normalmente e um processo bastante demorado e aumenta significativamente o custo de produção, através de uma abordagem semi-automática combinando os benefícios de procedural content generation (PCG) com conteúdo gráfico gerado manualmente.

Three essays on game theory and bargaining

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

Avatars and the «Imitation Game» – can machines smile?

Considering Alan Turing’s challenge in «Computing Machinery and Intelligence» (1950) – can machines play the «imitation game»? – it is proposed that the requirements of the Turing test are already implicitly being used for checking the credibility of virtual characters and avatars. Like characters, Avatars aim to visually express emotions (the exterior signs of the existence of feeling) and its creators have to resort to emotion codes. Traditional arts have profusely contributed for this field and, together with the science of anatomy, shaped the grounds for current Facial Action Coding System (FACS) and their databases. However, FACS researchers have to improve their «instruction tables» so that the machines will be able, in a near future, to be programmed to carry out the operation of recognizing human expressions (face and body) and classify them adequately. For the moment, the reproductions have to resort to the copy of real life expressions, and the presente smile of avatars comes from mirroring their human users.

Spiteful Strategies. The ontogeny and the practice of spite in human interaction: an experimental game theory approach and empirical applications

As estratégias de malevolência implicam que um indivíduo pague um custo para infligir um custo superior a um oponente. Como um dos comportamentos fundamentais da sociobiologia, a malevolência tem recebido menos atenção que os seus pares o egoísmo e a cooperação. Contudo, foi estabelecido que a malevolência é uma estratégia viável em populações pequenas quando usada contra indivíduos negativamente geneticamente relacionados pois este comportamento pode i) ser eliminado naturalmente, ou ii) manter-se em equilíbrio com estratégias cooperativas devido à disponibilidade da parte de indivíduos malevolentes de pagar um custo para punir. Esta tese propõe compreender se a propensão para a malevolência nos humanos é inerente ou se esta se desenvolve com a idade. Para esse efeito, considerei duas experiências de teoria de jogos em crianças em ambiente escolar com idades entre os 6 e os 22 anos. A primeira, um jogo 2x2 foi testada com duas variantes: 1) um prémio foi atribuído a ambos os jogadores, proporcionalmente aos pontos acumulados; 2), um prémio foi atribuído ao jogador com mais pontos. O jogo foi desenhado com o intuito de causar o seguinte dilema a cada jogador: i) maximizar o seu ganho e arriscar ter menos pontos que o adversário; ou ii) decidir não maximizar o seu ganho, garantindo que este não era inferior ao do seu adversário. A segunda experiência consistia num jogo do ditador com duas opções: uma escolha egoísta/altruísta (A), onde o ditador recebia mais ganho, mas o seu recipiente recebia mais que ele e uma escolha malevolente (B) que oferecia menos ganhos ao ditador que a A mas mais ganhos que o recipiente. O dilema era que se as crianças se comportassem de maneira egoísta, obtinham mais ganho para si, ao mesmo tempo que aumentavam o ganho do seu colega. Se fossem malevolentes, então prefeririam ter mais ganho que o seu colega ao mesmo tempo que tinham menos para eles próprios. As experiências foram efetuadas em escolas de duas áreas distintas de Portugal (continente e Açores) para perceber se as preferências malevolentes aumentavam ou diminuíam com a idade. Os resultados na primeira experiência sugerem que (1) os alunos compreenderam a primeira variante como um jogo de coordenação e comportaram-se como maximizadores, copiando as jogadas anteriores dos seus adversários; (2) que os alunos repetentes se comportaram preferencialmente como malevolentes, mais frequentemente que como maximizadores, com especial ênfase para os alunos de 14 anos; (3) maioria dos alunos comportou-se reciprocamente desde os 12 até aos 16 anos de idade, após os quais começaram a desenvolver uma maior tolerância às escolhas dos seus parceiros. Os resultados da segunda experiência sugerem que (1) as estratégias egoístas eram prevalentes até aos 6 anos de idade, (2) as tendências altruístas emergiram até aos 8 anos de idade e (3) as estratégias de malevolência começaram a emergir a partir dos 8 anos de idade. Estes resultados complementam a literatura relativamente escassa sobre malevolência e sugerem que este comportamento está intimamente ligado a preferências de consideração sobre os outros, o paroquialismo e os estágios de desenvolvimento das crianças.************************************************************Spite is defined as an act that causes loss of payoff to an opponent at a cost to the actor. As one of the four fundamental behaviours in sociobiology, it has received far less attention than its counterparts selfishness and cooperation. It has however been established as a viable strategy in small populations when used against negatively related individuals. Because of this, spite can either i) disappear or ii) remain at equilibrium with cooperative strategies due to the willingness of spiteful individuals to pay a cost in order to punish. This thesis sets out to understand whether propensity for spiteful behaviour is inherent or if it develops with age. For that effect, two game-theoretical experiments were performed with schoolboys and schoolgirls aged 6 to 22. The first, a 2 x 2 game, was tested in two variants: 1) a prize was awarded to both players, proportional to accumulated points; 2), a prize was given to the player with most points. Each player faced the following dilemma: i) to maximise pay-off risking a lower pay-off than the opponent; or ii) not to maximise pay-off in order to cut down the opponent below their own. The second game was a dictator experiment with two choices, (A) a selfish/altruistic choice affording more payoff to the donor than B, but more to the recipient than to the donor, and (B) a spiteful choice that afforded less payoff to the donor than A, but even lower payoff to the recipient. The dilemma here was that if subjects behaved selfishly, they obtained more payoff for themselves, while at the same time increasing their opponent payoff. If they were spiteful, they would rather have more payoff than their colleague, at the cost of less for themselves. Experiments were run in schools in two different areas in Portugal (mainland and Azores) to understand whether spiteful preferences varied with age. Results in the first experiment suggested that (1) students understood the first variant as a coordination game and engaged in maximising behaviour by copying their opponent’s plays; (2) repeating students preferentially engaged in spiteful behaviour more often than maximising behaviour, with special emphasis on 14 year-olds; (3) most students engaged in reciprocal behaviour from ages 12 to 16, as they began developing higher tolerance for their opponent choices. Results for the second experiment suggested that (1) selfish strategies were prevalent until the age of 6, (2) altruistic tendencies emerged since then, and (3) spiteful strategies began being chosen more often by 8 year-olds. These results add to the relatively scarce body of literature on spite and suggest that this type of behaviour is closely tied with other-regarding preferences, parochialism and the children’s stages of development.

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.