The price of stability for network design with fair cost allocation

TL;DR: The price of anarchy of pure Nash equilibria in congestion games with linear latency functions is considered and some of the results are extended to latency functions that are polynomials of bounded degree.

TL;DR: This talk will give an overview of recent progress in many of the traditional algorithmic questions in networks from the perspective of game theory, and show strong ties to certain algorithmic techniques.

TL;DR: It is proved that optimizing over correlated equilibria is NP-hard in all of the other classes of games that this work considers, including anonymous games and graphical games of bounded tree-width.

TL;DR: This work develops a polynomial-time algorithm for finding correlated equilibria (a well-studied notion of rationality due to Aumann that generalizes the Nash equilibrium) in a broad class of succinctly representable multiplayer games, encompassing essentially all known kinds.

TL;DR: This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service, from which max-min fairness of rates emerges as a limiting special case.

Abstract: THE CAPABILITIES AND EFFICIENT OPERATION OF SEVERAL TYPES OF TRANSPORTATION SYSTEMS ARE STUDIED. FOR HIGHWAY TRAFFIC THE MAIN EMPHASIS IS ON CONGESTION AND ITS CONSEQUENCES. QUEUING MODELS ARE USED TO DETERMINE FLUCTUATIONS IN WAITING TIME FOR TWO CASES, THE FLOW OF CARS THROUGH AN INTERSECTION AND THE PASSING OF SLOWER CARS BY FASTER CARS ON A TWO-LANE HIGHWAY. THE RESULTS OF THESE STUDIES ARE INCORPORATED INTO A NON-LINEAR MODEL OF HIGHWAY TRAFFIC BEHAVIOR ON A ROAD NETWORK. THE CAPACITIES ARE EXPRESSED BY THE RELATIONSHIP BETWEEN TRAFFIC FLOWS ON ALL ROUTES AND THE COSTS ENCOUNTERED ON EACH AS A RESULT OF THESE FLOWS. HIGHWAY TRAFFIC DEMANDS ARE THE RESULT OF A GREAT MANY INDIVIDUAL DECISIONS ABOUT DESTINATION, ROUTES, AND PREFERRED SPEEDS. THE ANALOGY BETWEEN HIGHWAY TRAFFIC EQUILIBRIUM AND THE MARKET RESPONSE MODELS USED BY ECONOMISTS IS GIVEN. IF THE INDIVIDUALLY INCURRED COST OF TRANSPORTATION IS REGARDED AS THE "PRICE" IN THE TRANSPORTATION "MARKET," THE ECONOMIST'S DEMAND CURVE BECOMES APPLICABLE. FOR A SINGLE ROAD IT GIVES THE FLOW OF TRAFFIC DEMANDED FOR ANY GIVEN COST ENCOUNTERED ON THAT ROAD. GENERALLY, THE HIGHER THE COST, THE SMALLER THE FLOW. CONSIDERING A ROAD NETWORK THE DEMAND FUNCTION GIVES THE FLOWS ON EACH ROUTE IN RESPONSE TO A SET OF TRANSPORTATION COSTS ALONG THESE ROUTES. EQUILIBRIUM EXISTS IF THE FLOWS ON ALL ROADS RESULTING FROM THESE COSTS ARE THE SAME AS THE FLOWS THAT PRODUCE THESE SAME COSTS. THIS CONCEPT IS APPLIED TO A STUDY OF TRAFFIC EQUILIBRIUM AND USE OF THE ANALYSIS IN THE PREDICTION OF TRAFFIC FLOWS IS DISCUSSED. THE ANALYSIS OF DEMAND AND OF EQUILIBRIUM RECOGNIZES THAT FREEDOM OF CHOICE IS PART OF THE SERVICE RENDERED BY THE ROAD NETWORK. TOLLS FROM THE USERS OF CONGESTED ROADS AT RATES THAT WOULD MEASURE THE COST TO OTHERS CAUSED BY THE AVERAGE ROAD USER WOULD ENCOURAGE BETTER USE OF THE HIGHWAY SYSTEM. THERE ARE OBSERVATIONS ON HOW CLOSELY MAXIMUM EFFICIENCY CAN BE APPROACHED BY PROPER CHOICE OF RATES ON PRESENT TOLL ROADS AND BY OTHER WAYS OF PENALIZING ADDITIONS TO TRAFFIC CONGESTION. BECAUSE OF THE NONLINEAR RELATIONSHIP BETWEEN USE AND COST, SUCH PRICING DOES NOT NECESSARILY PRODUCE REVENUES EQUAL TO THE TOTAL COST OF OPERATING AND FINANCING THE INDIVIDUAL FACILITY. SOME OBSERVATIONS ON THE QUESTION OF CRITERIA FOR EXTENSIONS OR IMPROVEMENTS OF THE NETWORK TO RELIEVE CONGESTION ARE GIVEN. /AUTHOR/

TL;DR: In this paper, the authors propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system and derive upper and lower bounds for this ratio in a model in which several agents share a very simple network.

TL;DR: The degradation in network performance due to unregulated traffic is quantified and it is proved that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency.