The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

A comparative study on decision-making methodology

Decision making (DM), the process of determining and selecting alternative decisions based on information and the preferences of decision makers (DMs), plays a significant role in our daily personal and professional lives. Many DM methods have been developed to assist DMs in their unique type of decision process. In this thesis, DM methods associated with two types of DM processes are studied: Decision-making under uncertainty (DMUU) and Multi-criteria decision making (MCDM). DMUU is making a decision when there are many unknowns or uncertainties about the kinds of states of nature (a complete description of the external factors) that could occur in the future to alter the outcome of a decision. DMUU has two subcategories: decision-making under strict uncertainty (DMUSU) and decision-making under risk (DMUR). Five classic DMUSU methods are Laplace’s insufficient reason principle, Wald’s Maximin, Savage’s Minimax regret, Hurwicz’s pessimism-optimism index criterion and Starr’s domain criterion. Furthermore, based on a review of the relation between a two-player game in game theory and DMUSU, Nash equilibrium is considered a method for approaching DMUSU as well. The well-known DMUR DM methods are expected monetary value, expected opportunity loss, most probable states of nature and expected utility. MCDM is a sub-discipline of operations research, where DMs evaluate multiple conflicting criteria in order to find a compromise solution subject to all the criteria. Numerous MCDM methods exist nowadays. The Analytic Hierarchy Process (AHP), the ELimination et Choix Traduisant la REalité (ELECTRE), the Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are the most employed of all the various MCDM methods. This PhD work focuses on presenting a comparative study of DM methods theoretically and evaluating the performance of different methods on a single decision problem. This contribution can guide DMs in gathering the relative objective and subjective information, structuring the decision problem and selecting the right DM method to make the decision that suits not only their subjective preferences, but also the objective facts. The case study used here is the selection of a sewer network construction plan. It is a representative and complex practical decision problem that requires the quality, life-cycle maintenance and performance of the selected sewer system to meet long-term planning for future climate changes and urban development. La prise de décision (DM), un processus de détermination et de sélection de décisions alternatives en fonction des informations et des préférences des décideurs (DM), apparaît largement dans notre vie personnelle et professionnelle quotidienne. Un grand nombre de méthodes DM ont été développées pour aider les DM dans leur type unique de processus de décision. Dans cette thèse, les méthodes DM associées à deux types de processus DM sont étudiées : la prise de décision sous incertitude (DMUU) et la prise de décision multicritère (MCDM). La DMUU doit prendre la décision lorsqu'il existe de nombreuses inconnues ou incertitudes sur le type d'états de la nature (une description complète des facteurs externes) qui pourraient se produire à l'avenir pour modifier le résultat d'une décision. La DMUU comprend deux sous-catégories : la prise de décision sous incertitude stricte (DMUSU) et la prise de décision sous risque (DMUR). Cinq méthodes classiques de DM pour DMUSU sont le principe de raison insuffisante de Laplace, le Waldimin Maximin, le regret Savage Minimax, le critère d'index pessimisme-optimisme de Hurwitz et le critère de domaine de Starr. En outre, l'examen de la relation entre un jeu à deux joueurs dans la théorie des jeux et l'équilibre DMUSU et Nash Equilibrium est également considéré comme l'une des méthodes pour résoudre le DMUSU. Les méthodes DM bien connues de DMUR sont la valeur monétaire attendue, la perte d'opportunité attendue, les états de nature les plus probables et l'utilité attendue. Le MCDM est une sous-discipline de la recherche opérationnelle, où les DM évaluent plusieurs critères conflictuels afin de trouver la solution compromise soumise à tous les critères. Un certain nombre de méthodes DM pour MCDM sont présentes de nos jours. Le processus de hiérarchie analytique (AHP), l'élimination et le choix traduisant la réalité (ELECTRE), les méthodes d'organisation du classement des préférences pour les évaluations d'enrichissement (PROMETHEE) et la technique de préférence par ordre de similitude et de solution idéale (TOPSIS) sont les plus choisies et utilisées des méthodes parmi toutes les différentes méthodes MCDM. Ce travail de thèse se concentre sur la présentation théorique d'une étude comparative des méthodes DM et l'évaluation des performances de différentes méthodes avec un problème de décision particulier. Cette contribution peut guider les DM à rassembler les informations relatives objectives et subjectives, à structurer le problème de décision et à sélectionner la bonne méthode de DM pour prendre la décision qui convient non seulement à leurs préférences subjectives, mais aussi aux faits objectifs. L'étude de cas utilisée ici est la sélection du plan de construction du réseau d'égouts. Il s'agit d'un problème de décision pratique représentatif et complexe qui nécessite la qualité, l'entretien du cycle de vie et les performances du réseau d'égouts sélectionné pour répondre à la planification à long terme des futurs changements climatiques et du développement urbain

Proceedings of Mathsport international 2017 conference

Proceedings of MathSport International 2017 Conference, held in the Botanical Garden of the University of Padua, June 26-28, 2017. MathSport International organizes biennial conferences dedicated to all topics where mathematics and sport meet. Topics include: performance measures, optimization of sports performance, statistics and probability models, mathematical and physical models in sports, competitive strategies, statistics and probability match outcome models, optimal tournament design and scheduling, decision support systems, analysis of rules and adjudication, econometrics in sport, analysis of sporting technologies, financial valuation in sport, e-sports (gaming), betting and sports

Multimedia Social Networks: Game Theoretic Modeling and Equilibrium Analysis

Multimedia content sharing and distribution over multimedia social networks is more popular now than ever before: we download music from Napster, share our images on Flickr, view user-created video on YouTube, and watch peer-to-peer television using Coolstreaming, PPLive and PPStream. Within these multimedia social networks, users share, exchange, and compete for scarce resources such as multimedia data and bandwidth, and thus influence each other's decision and performance. Therefore, to provide fundamental guidelines for the better system design, it is important to analyze the users' behaviors and interactions in a multimedia social network, i.e., how users interact with and respond to each other. Game theory is a mathematical tool that analyzes the strategic interactions among multiple decision makers. It is ideal and essential for studying, analyzing, and modeling the users' behaviors and interactions in social networking. In this thesis, game theory will be used to model users' behaviors in social networks and analyze the corresponding equilibria. Specifically, in this thesis, we first illustrate how to use game theory to analyze and model users' behaviors in multimedia social networks by discussing the following three different scenarios. In the first scenario, we consider a non-cooperative multimedia social network where users in the social network compete for the same resource. We use multiuser rate allocation social network as an example for this scenario. In the second scenario, we consider a cooperative multimedia social network where users in the social network cooperate with each other to obtain the content. We use cooperative peer-to-peer streaming social network as an example for this scenario. In the third scenario, we consider how to use the indirect reciprocity game to stimulate cooperation among users. We use the packet forwarding social network as an example. Moreover, the concept of ``multimedia social networks" can be applied into the field of signal and image processing. If each pixel/sample is treated as a user, then the whole image/signal can be regarded as a multimedia social network. From such a perspective, we introduce a new paradigm for signal and image processing, and develop generalized and unified frameworks for classical signal and image problems. In this thesis, we use image denoising and image interpolation as examples to illustrate how to use game theory to re-formulate the classical signal and image processing problems

Game Theoretic Model Predictive Control for Autonomous Driving

This study presents two closely-related solutions to autonomous vehicle control problems in highway driving scenario using game theory and model predictive control. We first develop a game theoretic four-stage model predictive controller (GT4SMPC). The controller is responsible for both longitudinal and lateral movements of Subject Vehicle (SV) . It includes a Stackelberg game as a high level controller and a model predictive controller (MPC) as a low level one. Specifically, GT4SMPC constantly establishes and solves games corresponding to multiple gaps in front of multiple-candidate vehicles (GCV) when SV is interacting with them by signaling a lane change intention through turning light or by a small lateral movement. SV’s payoff is the negative of the MPC’s cost function , which ensures strong connection between the game and that the solution of the game is more likely to be achieved by a hybrid MPC (HMPC). GCV’s payoff is a linear combination of the speed payoff, headway payoff and acceleration payoff. . We use decreasing acceleration model to generate our prediction of TV’s future motion, which is utilized in both defining TV’s payoffs over the prediction horizon in the game and as the reference of the MPC. Solving the games gives the optimal gap and the target vehicle (TV). In the low level , the lane change process are divided into four stages: traveling in the current lane, leaving current lane, crossing lane marking, traveling in the target lane. The division identifies the time that SV should initiate actual lateral movement for the lateral controller and specifies the constraints HMPC should deal at each step of the MPC prediction horizon. Then the four-stage HMPC controls SV’s actual longitudinal motion and execute the lane change at the right moment. Simulations showed the GT4SMPC is able to intelligently drive SV into the selected gap and accomplish both discretionary land change (DLC) and mandatory lane change (MLC) in a dynamic situation. Human-in-the-loop driving simulation indicated that GT4SMPC can decently control the SV to complete lane changes with the presence of human drivers. Second, we propose a differential game theoretic model predictive controller (DGTMPC) to address the drawbacks of GT4SMPC. In GT4SMPC, the games are defined as table game, which indicates each players only have limited amount of choices for a specific game and such choice remain fixed during the prediction horizon. In addition, we assume a known model for traffic vehicles but in reality drivers’ preference is partly unknown. In order to allow the TV to make multiple decisions within the prediction horizon and to measure TV’s driving style on-line, we propose a differential game theoretic model predictive controller (DGTMPC). The high level of the hierarchical DGTMPC is the two-player differential lane-change Stackelberg game. We assume each player uses a MPC to control its motion and the optimal solution of leaders’ MPC depends on the solution of the follower. Therefore, we convert this differential game problem into a bi-level optimization problem and solves the problem with the branch and bound algorithm. Besides the game, we propose an inverse model predictive control algorithm (IMPC) to estimate the MPC weights of other drivers on-line based on surrounding vehicle’s real-time behavior, assuming they are controlled by MPC as well. The estimation results contribute to a more appropriate solution to the game against driver of specific type. The solution of the algorithm indicates the future motion of the TV, which can be used as the reference for the low level controller. The low level HMPC controls both the longitudinal motion of SV and his real-time lane decision. Simulations showed that the DGTMPC can well identify the weights traffic vehicles’ MPC cost function and behave intelligently during the interaction. Comparison with level-k controller indicates DGTMPC’s Superior performance

Simulating a Sequential Coalition Formation Process for the Climate Change Problem: First Come, but Second Served?

We analyze stability of self-enforcing climate agreements based on a data set generated by the CLIMNEG world simulation model (CWSM), version 1.2. We consider two new aspects which appear important in actual treaty-making. First, we consider a sequential coalition formation process where players can make proposals which are either accepted or countered by other proposals. Second, we analyze whether a moderator, like an international organization, even without enforcement power, can improve upon globally suboptimal outcomes through coordinating actions by making recommendations that must be Pareto-improving to all parties. We discuss the conceptual difficulties of implementing our algorithm.International Climate Agreements, Sequential Coalition Formation, Coordination through Moderator, Integrated Assessment Model, Algorithm for Computations

Models of Political Economy

Models of Political Economy will introduce students to the basic methodology of political economics. It covers all core theories as well as new developments including: decision theory game theory mechanism design games of asymmetric information. Hannu Nurmi's text will prove to be invaluable to all students who wish to understand this increasingly technical field