Interaction between Dutch soccer teams and fans: a mathematical analysis through cooperative game theory

Inspired by the first lustrum of the Club Positioning Matrix (CPM) for professional Dutch soccer teams, we model the interaction between soccer teams and their potential fans as a cooperative cost game based on the annual voluntary sponsorships of fans in order to validate their fan registration in a central database. We introduce a natural cost allocation to the soccer teams, based in a natural manner on the sponsorships of fans. The game theoretic approach is twofold. On the one hand, an appropriate cost game called “fan data cost game” is developed and on the other, it is shown that the former natural cost allocation agrees with the solution concept called “nucleolus” of the fan data cost game

What Do You Want From Me? Adapting Systems to the Uncertainty of Human Preferences

Autonomous systems, like drones and self-driving cars, are becoming part of our daily lives. Multiple people interact with them, each with their own expectations regarding system behaviour. To adapt system behaviour to human preferences, we propose and explore a game-theoretic approach. In our architecture, autonomous systems use sensor data to build game-theoretic models of their interaction with humans. In these models, we represent human preferences with types and a probability distribution over them. Game-theoretic analysis then outputs a strategy, that determines how the system should act to maximise utility, given its beliefs over human types. We showcase our approach in a search-and-rescue (SAR) scenario, with a robot in charge of locating victims. According to social psychology, depending on their identity some people are keen to help others, while some prioritise their personal safety. These social identities define what a person favours, so we can map them directly to game-theoretic types. We show that our approach enables a SAR robot to take advantage of human collaboration, outperforming non-adaptive configurations in average number of successful evacuations

Modelling the Strategic Interactions of Driver Manoeuvres

Driving is naturally an interactive task where individual drivers are continuously manoeuvring based on expectations and beliefs regarding actions of other drivers. However mathematical models of interaction are seldom used for modelling driver manoeuvres. The dominant modelling methods rather assume there is a one-dimensional interaction between the stimuli provided by a driver, and the response of any conflicting drivers. This oversight of the inter-relation between conflicting drivers’ actions fails to scientifically evaluate key aspects of the safety and efficiency of driver interactions: behavioural norms of interaction, and moral hazards of interaction. Improving modelling of driver conflicts is important to evaluate the safety of existing road infrastructure and proposed technology measures that aim to improve driver safety. Thus Game Theory which is a framework for mathematical models of interaction has been emerging as a research area within traffic analysis. Given this, game theoretic literature for driver manoeuvres still poses a lacuna in the investigation of modelling sub-processes that are critical for accurate game theoretic predictions against reality. These modelling aspects are the specification of payoff functions for decisions, and methods to mathematically calculate interaction game solutions. The research project within this thesis accordingly develops game theoretic models that investigate the importance of risk attitude and risk perception parameters in payoff functions for interactive driver manoeuvres, and efficacy of a Quantal Response Equilibrium game solution. An empirical approach is used to calibrate and verify the significance of the proposed game theoretic models and frameworks against observed driver interactions. In particular, field data of an experiment conducted in an experimental economics laboratory is used, as well as GPS trajectory of vehicles merging at an on-ramp along Interstate 80 in Emeryville, California. The studies find that the introduction of risk-related parameters in payoff functions for interactive decisions is important to explain observed driver interactions and a Quantal Response Equilibrium game solution is able to provide good fit to observations. The key contributions of the research project are novel approaches for improved modelling of interaction in driver manoeuvres. The modelling approaches help to more accurately evaluate existing and proposed measures towards traffic safety and efficiency

Measuring multivariate redundant information with pointwise common change in surprisal

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more predictor variables Xi . It can be thought of as quantifying overlapping information content or similarities in the representation of S between the Xi . We present a new measure of redundancy which measures the common change in surprisal shared between variables at the local or pointwise level. We provide a game-theoretic operational definition of unique information, and use this to derive constraints which are used to obtain a maximum entropy distribution. Redundancy is then calculated from this maximum entropy distribution by counting only those local co-information terms which admit an unambiguous interpretation as redundant information. We show how this redundancy measure can be used within the framework of the Partial Information Decomposition (PID) to give an intuitive decomposition of the multivariate mutual information into redundant, unique and synergistic contributions. We compare our new measure to existing approaches over a range of example systems, including continuous Gaussian variables. Matlab code for the measure is provided, including all considered examples

Transforming Energy Networks via Peer to Peer Energy Trading: Potential of Game Theoretic Approaches

Peer-to-peer (P2P) energy trading has emerged as a next-generation energy management mechanism for the smart grid that enables each prosumer of the network to participate in energy trading with one another and the grid. This poses a significant challenge in terms of modeling the decision-making process of each participant with conflicting interest and motivating prosumers to participate in energy trading and to cooperate, if necessary, for achieving different energy management goals. Therefore, such decision-making process needs to be built on solid mathematical and signal processing tools that can ensure an efficient operation of the smart grid. This paper provides an overview of the use of game theoretic approaches for P2P energy trading as a feasible and effective means of energy management. As such, we discuss various games and auction theoretic approaches by following a systematic classification to provide information on the importance of game theory for smart energy research. Then, the paper focuses on the P2P energy trading describing its key features and giving an introduction to an existing P2P testbed. Further, the paper zooms into the detail of some specific game and auction theoretic models that have recently been used in P2P energy trading and discusses some important finding of these schemes.Comment: 38 pages, single column, double spac

Energy-Efficient Resource Allocation in Wireless Networks: An Overview of Game-Theoretic Approaches

An overview of game-theoretic approaches to energy-efficient resource allocation in wireless networks is presented. Focusing on multiple-access networks, it is demonstrated that game theory can be used as an effective tool to study resource allocation in wireless networks with quality-of-service (QoS) constraints. A family of non-cooperative (distributed) games is presented in which each user seeks to choose a strategy that maximizes its own utility while satisfying its QoS requirements. The utility function considered here measures the number of reliable bits that are transmitted per joule of energy consumed and, hence, is particulary suitable for energy-constrained networks. The actions available to each user in trying to maximize its own utility are at least the choice of the transmit power and, depending on the situation, the user may also be able to choose its transmission rate, modulation, packet size, multiuser receiver, multi-antenna processing algorithm, or carrier allocation strategy. The best-response strategy and Nash equilibrium for each game is presented. Using this game-theoretic framework, the effects of power control, rate control, modulation, temporal and spatial signal processing, carrier allocation strategy and delay QoS constraints on energy efficiency and network capacity are quantified.Comment: To appear in the IEEE Signal Processing Magazine: Special Issue on Resource-Constrained Signal Processing, Communications and Networking, May 200

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201