Maximizing Social Welfare Subject to Network Externalities: A Unifying Submodular Optimization Approach

We consider the problem of allocating multiple indivisible items to a set of networked agents to maximize the social welfare subject to network externalities. Here, the social welfare is given by the sum of agents' utilities and externalities capture the effect that one user of an item has on the item's value to others. We first provide a general formulation that captures some of the existing models as a special case. We then show that the social welfare maximization problem benefits some nice diminishing or increasing marginal return properties. That allows us to devise polynomial-time approximation algorithms using the Lovasz extension and multilinear extension of the objective functions. Our principled approach recovers or improves some of the existing algorithms and provides a simple and unifying framework for maximizing social welfare subject to network externalities

Nash Social Welfare in Selfish and Online Load Balancing

In load balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones, in order to execute a certain task. Each resource has a latency function, which depends on its workload, and a client's cost is the completion time of her chosen resource. Two fundamental variants of load balancing problems are {\em selfish load balancing} (aka. {\em load balancing games}), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and {\em online load balancing}, where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both selfish and online load balancing under the objective of minimizing the {\em Nash Social Welfare}, i.e., the geometric mean of the clients' costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal as it matches the performance of any possible online algorithm

Public transport network design for competitive service providers.

Chan, Yon Sim Eddie.Thesis submitted in: November 2008.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 89-92).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Background --- p.2Chapter 1.3 --- Literature Review --- p.5Chapter 2 --- Game Theoretic Models For Competing Operators --- p.10Chapter 2.1 --- Competitive Equilibrium Model --- p.12Chapter 2.1.1 --- Base Model Formulation --- p.12Chapter 2.1.2 --- Capacitated Model Formulation --- p.16Chapter 2.1.3 --- Solution Methods --- p.19Chapter 2.2 --- Net Profit Maximizing --- p.26Chapter 2.2.1 --- Equitable Route Assignment --- p.27Chapter 2.3 --- Congestion Game Model with Player- and Route-dependent Operating Cost --- p.31Chapter 2.3.1 --- Best-Response Algorithm --- p.34Chapter 2.3.2 --- Integer Programming Formulation --- p.41Chapter 2.3.3 --- Net Profit Maximizing --- p.43Chapter 3 --- Network Design --- p.45Chapter 3.1 --- Network Structure --- p.47Chapter 3.2 --- Comparison Between Two Network Structures --- p.49Chapter 3.2.1 --- Routes with Same Ridership --- p.49Chapter 3.2.2 --- Routes with Different Ridership --- p.65Chapter 3.2.3 --- Network with Player- and Route-specific Profit Function --- p.69Chapter 4 --- Elastic Demand --- p.71Chapter 4.1 --- Congestion Game Model with Service-Quality-Based Elastic Demand --- p.71Chapter 4.1.1 --- Network with Service-Quality-Based Elastic Demand --- p.82Chapter 5 --- Conclusion --- p.84Chapter 5.1 --- Future Work --- p.84Chapter 5.1.1 --- Impact of Network Design and structure --- p.84Chapter 5.1.2 --- Non-cooperative and Cooperative Games --- p.86Chapter 5.1.3 --- Joint game-theoretic model of both passenger and providers --- p.87Bibliography --- p.8

Network flow problems and congestion games : complexity and approximation results

This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006.Includes bibliographical references (p. 155-164).(cont.) We first address the complexity of finding an optimal minimum cost solution to a congestion game. We consider both network and general congestion games, and we examine several variants of the problem concerning the structure of the game and its associated cost functions. Many of the problem variants are NP-hard, though we do identify several versions of the games that are solvable in polynomial time. We then investigate existence and the price of anarchy of pure Nash equilibria in k-splittable congestion games with linear costs. A k-splittable congestion game is one in which each player may split its flow on at most k different paths. We identify conditions for the existence of equilibria by providing a series of potential functions. For the price of anarchy, we show an asymptotic lower bound of 2.4 for unweighted k-splittable congestion games and 2.401 for weighted k-splittable congestion games, and an upper bound of 2.618 in both cases.In this thesis we examine four network flow problems arising in the study of transportation, communication, and water networks. The first of these problems is the Integer Equal Flow problem, a network flow variant in which some arcs are restricted to carry equal amounts of flow. Our main contribution is that this problem is not approximable within a factor of 2n(1-epsilon]), for any fixed [epsilon] > 0, where n is the number of nodes in the graph. We extend this result to a number of variants on the size and structure of the arc sets. We next study the Pup Matching problem, a truck routing problem where two commodities ('pups') traversing an arc together in the network incur the arc cost only once. We propose a tighter integer programming formulation for this problem, and we address practical problems that arise with implementing such integer programming solutions. Additionally, we provide approximation and exact algorithms for special cases of the problem where the number of pups is fixed or the total cost in the network is bounded. Our final two problems are on the topic of congestion games, which were introduced in the area of communications networks.by Carol Meyers.Ph.D