A Note on the Balancedness and the Concavity of Highway Games

A highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices, a cost function on the edges of the graph and a set of players, each in need of constructing a connection between a specific entry and exit vertex. Mosquera and Zarzuelo (2006) introduce highway problems and the corresponding cooperative cost games called high- way games to address the problem of fair allocation of the construction costs in case the underlying graph is a chain. In this note, we study the concavity and the balancedness of highway games on more general graphs. A graph G is called highway-game concave if for each highway problem in which G is the underlying graph the corresponding highway game is concave. The main result of our study is that a graph is highway-game concave if and only if it is weakly triangular. Moreover, we provide sufficient conditions on highway problems defined on cyclic graphs such that the corresponding highway games are balanced.cooperative games;highway games;cost sharing

A Cooperative Approach to Sequencing and Connection Problems.

There are many economic settings in which a group of agents wishes to undertake a joint enterprise in order to save costs. The success of such enterprises often relies on agreements on how to share the cost savings generated. The central issue of this monograph is to address cost allocation problems arising from sequencing problems and connection problems. Sequencing problems consider a group of agents who are waiting to be served in a facility and focuses on the problem of the allocation of the cost savings that can be obtained by switching from an initial service order to an optimal one. Connection problems consider the cost allocation problems arising from situations in which a group of agents wishes to collaborate and jointly invest in the construction or the maintenance of a common network. The methods we use in this monograph to analyze the cost allocation problems arising from sequencing and connection problems mainly rely on models of cooperative transferable utility games.

Cost allocation in connection and conflict problems on networks: a cooperative game theoretic approach

This thesis examines settings where multiple decision makers with conflicting interests benefit from cooperation in joint combinatorial optimisation problems. It draws on cooperative game theory, polyhedral theory and graph theory to address cost sharing in joint single-source shortest path problems and joint weighted minimum colouring problems. The primary focus of the thesis are problems where each agent corresponds to a vertex of an undirected complete graph, in which a special vertex represents the common supplier. The joint combinatorial optimisation problem consists of determining the shortest paths from the supplier to all other vertices in the graph. The optimal solution is a shortest path tree of the graph and the aim is to allocate the cost of this shortest path tree amongst the agents. The thesis defines shortest path tree problems, proposes allocation rules and analyses the properties of these allocation rules. It furthermore introduces shortest path tree games and studies the properties of these games. Various core allocations for shortest path tree games are introduced and polyhedral properties of the core are studied. Moreover, computational results on finding the core and the nucleolus of shortest path tree games for the application of cost allocation in Wireless Multihop Networks are presented. The secondary focus of the thesis are problems where each agent is interested in having access to a number of facilities but can be in conflict with other agents. If two agents are in conflict, then they should have access to disjoint sets of facilities. The aim is to allocate the cost of the minimum number of facilities required by the agents amongst them. The thesis models these cost allocation problems as a class of cooperative games called weighted minimum colouring games, and characterises total balancedness and submodularity of this class of games using the properties of the underlying graph

A survey of random processes with reinforcement

The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

‘Geoliteracia’, ‘cartologia’, desenvolvimento cognitivo e um jogo móvel

Some researches in education science develop educative games on mobile devices for letting elementary school students play outdoor to learn geographic facts, concepts, and patterns. The challenge is about improving their geographic literacy and fluency, or ‘geoliteracy’, and their map-reading competencies, called cartology, before adolescence. There a critical stumbling ‘threshold’ can impede their geospatial cognitive development, which result in a majority of adults being not geographically literate neither efficient, in real-life context, for reading and using maps. Designing a mobile educative serious game implies applying conceptual and pragmatic methods for both learning and teaching geospatial competencies accordingly to school curriculum. The theoretical framework presented links maps to cartographical semiology, the children’s cognitive development stages for geospatial representation, and an experiential learning cycle model. The latter sequentially supports three main cartographic processes of map-making: reflexive visualization, and map-reading, which sustain any geographical reasoning. The mobile game proposed combines components of increasing complexity where the map plays the main role in the course of different activities: scenarios of typical “rounds” and rules of the game within local terrain; types of geometrical and geospatial trajectories to trace and follow while playing; and specific themes relevant to school subjects. Thus, geographical discussions stop worrying about where, to worry about the reason of situations and the occurrence of phenomena.Algunas investigaciones en ciencias de la educación desarrollan juegos educativos en dispositivos móviles para incentivar el aprendizaje de hechos, conceptos y modelos geográficos en estudiantes de escuelas primarias. El desafío consiste en mejorar su alfabetización y fluidez geográfica, o geoalfabetización, y sus competencias en lectura de mapas antes de la adolescencia, sintetizadas aquí bajo la denominación de cartología, la cual parece ser un umbral crítico que obstruye el desarrollo cognitivo geoespacial de los adultos. Diseñar un juego educativo móvil implica integrar métodos conceptuales y prácticos para la enseñanza y aprendizaje de las competencias geoespaciales, conforme al currículo escolar. El marco teórico que se presenta vincula los mapas con la semiología cartográfica, las etapas de desarrollo cognitivo del niño referentes a la representación del espacio geográfico y el ciclo de aprendizaje experiencial. Este último supone una serie de procesos cartográficos esenciales que sirven de base a cualquier análisis o razonamiento geográfico: creación de mapas, visualización reflexiva y lectura cartográfica. El juego que se propone conjuga componentes de creciente complejidad en los cuales el mapa es protagonista en el transcurso de diferentes actividades: rondas típicas con reglas particulares sobre terrenos determinados; trayectorias geométricas y geoespaciales por trazar y seguir durante el juego; temas específicos relacionados con las asignaturas escolares y con los objetivos propuestos por los maestros, etc. Así, las discusiones geográficas dejan de preocuparse por el dónde para inquietarse por el porqué de las situaciones y el acontecer de los fenómenos.Algumas pesquisas nas ciências da educação desenvolvem jogos educativos para dispositivos móveis através dos quais alunos da escola primária aprendem fatos, conceitos e modelos geográficos brincando ao ar livre. O desafio é melhorar a literacia e a fluência geográfica desses alunos, ou sua ‘geoliteracia’, e suas competências para ler mapas, a chamada ‘cartologia’, antes da adolescência, quando surge um limiar crítico que pode impedir o desenvolvimento cognitivo geoespacial das crianças. A maioria de adultos não são geograficamente letrados nem eficientes para ler e usar mapas. Conceber um jogo educativo móvel integra métodos conceituais e práticos para o ensino e a aprendizagem das competências geoespaciais, conforme o currículo escolar. O quadro teórico apresentado conecta os mapas à semiologia cartográfica, os estágios de desenvolvimento cognitivo das crianças no que se refere às representações do espaço geográfico e o ciclo de aprendizagem experiencial. Este último supõem uma sequência de três processos cartográficos principais que servem de base a qualquer raciocínio geográfico: criação de mapas, visualização reflexiva e leitura de mapas. O jogo que é proposto combina componentes de complexidade crescente onde o mapa é o protagonista no decorrer de diferentes atividades: cenários com ‘rondadas’ e regras típicas do jogo num determinado terreno; tipos de trajetórias geométricas e geoespaciais a serem traçadas e seguidas durante o jogo; temas específicos pertinentes aos assuntos escolares. Assim, as discussões geográficas deixam de se preocupar sobre onde para questionar a razão das situações e a ocorrência dos fenômenos

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Evolution of the Secondary Spectrum Market

The secondary spectrum market where primaries (license holders) lease the secondaries (unlicensed users) in lieu of the financial remuneration can eliminate the inefficiencies of the static spectrum allocation policy. We redress some of the challenges that have inhibited the wide scale deployment of the secondary spectrum market. We first consider a secondary spectrum market where the primaries quote their prices for their available channels at a single location. The transmission rates offered by the channels of primaries evolve randomly because of the fading and noise. The secondaries decide to buy among the channels based on the transmission rate and the prices. We formulate the problem as a non cooperative game with the primaries as players. Each primary selects a price based on its own channel state only, as it is unaware of the channel states of the other primaries. We show that under the unique NE strategy profile a primary prices its channel to render the channel which provides high transmission rate more preferable; this negates the perception that prices ought to be selected to render channels equally preferable to the secondary regardless of their transmission rates. Next, we consider the setting where the secondary spectrum market operates over multiple locations. Each primary needs to select an independent set in a conflict graph and the price at each location. We consider two scenarios--i) the number of locations is small, and ii) the number of locations is large. We show that when the number of locations is small, in a symmetric NE strategy, each primary sells its channel to an independent set whose cardinality exceeds a certain threshold. The threshold also decreases as the transmission rate offered by the channel decreases. The symmetric NE is unique in a widely seen conflict graph-the linear conflict graph. In contrast, when the number of locations is large, a primary only sells its channel in the maximum independent set and the symmetric NE in not unique in the linear conflict graph. Subsequently, we consider the setting where a primary owns a channel at a single location and can acquire the competitor\u27s channel state information (C-CSI) by incurring a cost. Each primary now needs to decide whether to acquire the C-CSI or not and a price based on the information it has. We formulate the problem as a non cooperative game with two primaries as players and characterize the NE strategies. We first characterize the Nash Equilibrium (NE) of this game for a symmetric model where the C-CSI is perfect. We show that the payoff of a primary is independent of the C-CSI acquisition cost. We then generalize our analysis to allow for imperfect estimation and cases where the two primaries have different C-CSI costs or different channel availabilities. Our results show interestingly that the payoff of a primary increases when there is estimation error. We also show that surprisingly, the expected payoff of a primary may decrease when the C-CSI acquisition cost decreases when primaries have different availabilities. Finally, we consider the setting where a primary allows multiple secondaries use the channel of a primary at a location. The interference must be limited at each primary-user terminal (primary-UT) in order to maintain a quality of service for each primary-UT. The secondary-base stations (secondary-BSs) are self-interested entities and only maximize their own utilities which makes it difficult to obtain a simple interference mitigation policy. We formulate the problem as a non cooperative coupled constrained concave game. We use the concept of the normalized Nash equilibrium (NNE) since it caters to the distributed setting. We develop a distributed algorithm which converges to the unique NNE for a large class of utility functions. In the distributed algorithm, the secondary-BSs do not need to exchange information among themselves, and the minimal cooperation from the primary-UTs. When the NNE is not unique or difficult to compute, we introduce the concept of WNNE which retains most of the properties of the NNE, but it can be computed easily compared to the NNE

Computing Correlated Equilibria in Partially Observable Stochastic Games

V reálném světě se musíme vypořádávat se situacemi vyžadujícími kooperaci zúčastněných agentů při zachování jejich racionality. Takovéto problémy odpovídají herně teoretickému konceptu korelovaného ekvilibria. Existuje několik prací, které se zabývají výpočtem korelovaného equilibria v stochastických hrách. V současnosti však neexistuje žádný algoritmus, který by byl schopen počítat korelované ekvilibrium pro obecné částečně pozorovatelné stochastické hry. V této práci představujeme první algoritmus pro aproximaci korelovaného ekvilibria v částečně pozorovatelných stochastických hrách, který řeší tyto hry iterativně pomocí postupného zvětšování vygenerované podmnožiny belief stavů. Přestože náš algoritmus nemá žádné garance optimality, ukazujeme, že je schopen nalézt přijatelná řešení.In the real world, we have to deal with situations requiring cooperation of participating agents keeping their rationality. These problems are addressed by the game theoretical concept of correlated equilibrium. There are some works focusing on the problem of computing correlated equilibria in stochastic games. So far there is no algorithm capable of computing correlated equilibria in general partially observable stochastic games. In this work, we propose the first algorithm for approximating correlated equilibria in partially observable stochastic games that iteratively solves these games using gradually expanding generated subset of belifestates. Even though the algorithm has no optimality guarantees, we show that it is capable to compute reasonable solutions