Strong Nash Equilibria in Games with the Lexicographical Improvement Property

We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Lexicographical Improvement Property (LIP) and show that it implies the existence of a generalized strong ordinal potential function. We use this characterization to derive existence, efficiency and fairness properties of strong Nash equilibria. We then study a class of games that generalizes congestion games with bottleneck objectives that we call bottleneck congestion games. We show that these games possess the LIP and thus the above mentioned properties. For bottleneck congestion games in networks, we identify cases in which the potential function associated with the LIP leads to polynomial time algorithms computing a strong Nash equilibrium. Finally, we investigate the LIP for infinite games. We show that the LIP does not imply the existence of a generalized strong ordinal potential, thus, the existence of SNE does not follow. Assuming that the function associated with the LIP is continuous, however, we prove existence of SNE. As a consequence, we prove that bottleneck congestion games with infinite strategy spaces and continuous cost functions possess a strong Nash equilibrium

Packing, Scheduling and Covering Problems in a Game-Theoretic Perspective

Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various fundamental aspects in networks optimization such as routing, resource allocation, congestion control, etc. Various combinatorial problems were already studied from the game theoretic standpoint, and we attempt to complement to this body of research. Specifically, we consider the bin packing problem both in the classic and parametric versions, the job scheduling problem and the machine covering problem in various machine models. We suggest new interpretations of such problems in the context of modern networks and study these problems from a game theoretic perspective by modeling them as games, and then concerning various game theoretic concepts in these games by combining tools from game theory and the traditional combinatorial optimization. In the framework of this research we introduce and study models that were not considered before, and also improve upon previously known results.Comment: PhD thesi

Fairness in Multi-Agent Sequential Decision-Making

We define a fairness solution criterion for multi-agent decision-making problems, where agents have local interests. This new criterion aims to maximize the worst performance of agents with consideration on the overall performance. We develop a simple linear programming approach and a more scalable game-theoretic approach for computing an optimal fairness policy. This game-theoretic approach formulates this fairness optimization as a two-player, zero-sum game and employs an iterative algorithm for finding a Nash equilibrium, corresponding to an optimal fairness policy. We scale up this approach by exploiting problem structure and value function approximation. Our experiments on resource allocation problems show that this fairness criterion provides a more favorable solution than the utilitarian criterion, and that our game-theoretic approach is significantly faster than linear programming

The Price of Fairness

In this paper we study resource allocation problems that involve multiple self-interested parties or players and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a “fair” allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We focus on two well-accepted, axiomatically justified notions of fairness, viz., proportional fairness and max-min fairness. For these notions we provide a tight characterization of the price of fairness for a broad family of problems.National Science Foundation (U.S.) (grant DMI- 0556106)National Science Foundation (U.S.) (grant EFRI-0735905

Attribute Equilibrium Dominance Reduction Accelerator (DCCAEDR) Based on Distributed Coevolutionary Cloud and Its Application in Medical Records

© 2013 IEEE. Aimed at the tremendous challenge of attribute reduction for big data mining and knowledge discovery, we propose a new attribute equilibrium dominance reduction accelerator (DCCAEDR) based on the distributed coevolutionary cloud model. First, the framework of N-populations distributed coevolutionary MapReduce model is designed to divide the entire population into N subpopulations, sharing the reward of different subpopulations' solutions under a MapReduce cloud mechanism. Because the adaptive balancing between exploration and exploitation can be achieved in a better way, the reduction performance is guaranteed to be the same as those using the whole independent data set. Second, a novel Nash equilibrium dominance strategy of elitists under the N bounded rationality regions is adopted to assist the subpopulations necessary to attain the stable status of Nash equilibrium dominance. This further enhances the accelerator's robustness against complex noise on big data. Third, the approximation parallelism mechanism based on MapReduce is constructed to implement rule reduction by accelerating the computation of attribute equivalence classes. Consequently, the entire attribute reduction set with the equilibrium dominance solution can be achieved. Extensive simulation results have been used to illustrate the effectiveness and robustness of the proposed DCCAEDR accelerator for attribute reduction on big data. Furthermore, the DCCAEDR is applied to solve attribute reduction for traditional Chinese medical records and to segment cortical surfaces of the neonatal brain 3-D-MRI records, and the DCCAEDR shows the superior competitive results, when compared with the representative algorithms

Game theoretic approaches to parallel machine scheduling

Tesis (Ingeniero Industrial)En un problema de programación de máquinas idénticas en paralelo que persigue minimizar dos criterios en particular, lapso y tiempo de terminación total, un mecanismo basado en la teoría de juegos es propuesto para solucionarlo. Se considera un juego bipersonal no-cooperativo de 2x2 en el que cada jugador busca minimizar alguno de estos criterios que propone el problema de producción. Cada escenario implica que los jugadores jueguen de manera simultanea y busquen minimizar los costos que están relacionados con los criterios a optimizar. El jugador que representa al trabajo tiene la opción de dejar al trabajo en su posición actual o moverlo a una posición previa, buscando minimizar su tiempo de terminación; mientras que el otro jugador, un agente controlador, toma la decisión de dejar al trabajo en la máquina actual o moverlo a otra, esperando balancear la carga de la máquina y minimizar el lapso. Como resultado de una serie de juegos repetidos entre estos agentes, el Frente de Pareto es construido, mostrando un conjunto de soluciones eficientes al problema.Universidad del Norte. Programa de Ingeniería Industrial