The Computational Difficulty of Bribery in Qualitative Coalitional Games

Qualitative coalitional games (QCG) are representations of coalitional games in which self interested agents, each with their own individual goals, group together in order to achieve a set of goals which satisfy all the agents within that group. In such a representation, it is the strategy of the agents to find the best coalition to join. Previous work into QCGs has investigated the computational complexity of determining which is the best coalition to join. We plan to expand on this work by investigating the computational complexity of computing agent power in QCGs as well as by showing that insincere strategies, particularly bribery, are possible when the envy-freeness assumption is removed but that it is computationally difficult to identify the best agents to bribe.Bribery, Coalition Formation, Computational Complexity

Risk analysis sampling methods in terrorist networks based on the Banzhaf value

This article introduces the Banzhaf and the Banzhaf–Owen values as novel measures of risk analysis of a terrorist attack, determining the most dangerous terrorists in a network. This new approach counts with the advantage of integrating at the same time the complete topology (i.e., nodes and edges) of the network and a coalitional structure on the nodes of the network. More precisely, the characteristics of the nodes (e.g., terrorists) of the network and their possible relationships (e.g., types of communication links), as well as coalitional information (e.g., level of hierarchies) independent of the network. First, for these two new measures of risk analysis, we provide and implement approximation algorithms. Second, as illustration, we rank the members of the Zerkani network, responsible for the attacks in Paris (2015) and Brussels (2016). Finally, we give a comparison between the rankings established by the Banzhaf and the Banzhaf–Owen values as measures of risk analysisMinisterio de Ciencia e Innovación, Grant/Award Numbers: PGC2018-097965-B-I00, PID2021-124030NB-C32; Xunta de Galicia, Grant/Award Number: ED431C 2021/24; Ministerio de Ciencia, Innovación y Universidades, Grant/Award Number: MTM2017-87197-C3-3-PS

Optimization and Allocation in Some Decision Problems with Several Agents or with Stochastic Elements

Programa Oficial de Doutoramento en Estatística e Investigación Operativa. 5017V01[Abstract] This dissertation addresses sorne decision problems that arise in project management, cooperative game theory and vehicle route optimization. We start with the problem of allocating the delay costs of a project. In a stochastic context in which we assume that activity durations are random variables, we propose and study an allocation rule based on the Shapley value. In addition, we present an R package that allows a comprehensive control of the project, including the new rule. We propose and characterize new egalitarian solutions in the context of cooperative games with a coalitional structure. Also, using a necessary player property we introduce a new value for cooperative games, which we later extend and characterize within the framework of cooperative games with a coalitional structure. Finally, we present a two-step algorithm for solving multi-compartment vehicle route problems with stochastic demands. This algorithm obtains an initial solution through a constructive heuristic and then uses a tabu search to improve the solution. Using real data, we evaluate the performance of the algorithm.[Resumo] Nesta memoria abórdanse diversos problemas de decisión que xorden na xestión de proxectos, na teoría de xogos cooperativos e na optimización de rutas de vehículos. Empezamos estudando o problema da repartición dos custos de demora nun proxecto. Nun contexto estocástico no que supoñemos que as duracións das actividades son variables aleatorias, propoñemos e estudamos unha regra de repartición baseada no valor de Shapley. Ademais, presentamos un paquete de R que permite un control integral do proxecto, incluíndo a nova regra de repartición. A continuación, propoñemos e caracterizamos axiomaticamente novas solucións igualitarias no contexto dos xogos cooperativos cunha estrutura coalicional. E introducimos un novo valor, utilizando unha propiedade de xogadores necesarios, para xogos cooperativos, que posteriormente estendemos e caracterizamos dentro do marco dos xogos cooperativos cunha estrutura coalicional. Por último, presentamos un algoritmo en dous pasos para resolver problemas de rutas de vehículos con multi-compartimentos e demandas estocásticas. Este algoritmo obtén unha solución inicial mediante unha heurística construtiva e, a continuación, utiliza unha búsqueda tabú para mellorar a solución. Utilizando datos reais, levamos a cabo unha análise do comportamento do algoritmo.[Resumen] En esta memoria se abordan diversos problemas de decisión que surgen en la gestión de proyectos, en la teoría de juegos cooperativos y en la optimización de rutas de vehículos. Empezamos estudiando el problema del reparto de los costes de demora en un proyecto. En un contexto estocástico en el que suponemos que las duraciones de las actividades son variables aleatorias, proponemos y estudiamos una regla de reparto basada en el valor de Shapley. Además, presentamos un paquete de R que permite un control integral del proyecto, incluyendo la nueva regla de reparto. A continuación, proponemos y caracterizamos axiomáticamente nuevas soluciones igualitarias en el contexto de los juegos cooperativos con una estructura coalicional. E introducimos un nuevo valor, utilizando una propiedad de jugadores necesarios, para juegos cooperativos, que posteriormente extendemos y caracterizamos dentro del marco de los juegos cooperativos con una estructura coalicional. Por último, presentamos un algoritmo en dos pasos para resolver problemas de rutas de vehículos con multi-compartimentos y demandas estocásticas. Este algoritmo obtiene una solución inicial mediante una heurística constructiva y, a continuación, utiliza una búsqueda tabú para mejorar la solución. Utilizando datos reales, llevamos a cabo un análisis del comportamiento del algoritmo

Aggregate Energy Production in Wind Farms via Dynamic Robust Coalitional Games

This paper investigates the benefits of aggregating independent wind power producers. First, we quantify the expected joint profit in the case where such producers act as a single entity in a one-stage contract interval, and in a multi-stage contract interval with recourse. Second, we provide a constructive method to design stable allocation mechanisms in the case where the expected profit is changing with time. Third, we prove that the allocation policy stabilizes the coalition by correcting allocations in real-time in the case where the realized power output deviates from the contract size of the ahead market

Algorithmic and complexity aspects of simple coalitional games

Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network

07431 Abstracts Collection -- Computational Issues in Social Choice

From the 21st to the 26th of October 2007, the Dagstuhl Seminar 07431 on ``Computational Issues in Social Choice\u27\u27 was held at the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their recent research, and ongoing work and open problems were discussed. The abstracts of the talks given during the seminar are collected in this paper. The first section summarises the seminar topics and goals in general. Links to full papers are provided where available

The Present and Future of Game Theory

A broad nontechnical coverage of many of the developments in game theory since the 1950s is given together with some comments on important open problems and where some of the developments may take place. The nearly 90 references given serve only as a minimal guide to the many thousands of books and articles that have been written. The purpose here is to present a broad brush picture of the many areas of study and application that have come into being. The use of deep techniques flourishes best when it stays in touch with application. There is a vital symbiotic relationship between good theory and practice. The breakneck speed of development of game theory calls for an appreciation of both the many realities of conflict, coordination and cooperation and the abstract investigation of all of them.Game theory, Application and theory, Social sciences, Law, Experimental gaming, conflict, Coordination and cooperation