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On the Inefficiency of Equilibria in Congestion Games [chapter]

José R. Correa, Andreas S. Schulz, Nicolás E. Stier-Moses
2005 Lecture Notes in Computer Science  
We general previous proofs by introducing for a given class of cost functions (polynomials of a certain degree) Theorem: General Separable Functions Assume polynomials with positive coefficients: For  ... 
doi:10.1007/11496915_13 fatcat:afoqmzxhxzck5nm2got3mslixy

On the Inefficiency of Equilibria in Linear Bottleneck Congestion Games [chapter]

Bart de Keijzer, Guido Schäfer, Orestis A. Telelis
2010 Lecture Notes in Computer Science  
We study the inefficiency of equilibrium outcomes in bottleneck congestion games. These games model situations in which strategic players compete for a limited number of facilities.  ...  We derive upper and (asymptotically) matching lower bounds on the (strong) price of anarchy of linear bottleneck congestion games for a natural load balancing social cost objective (i.e., minimize the  ...  In this paper we study the inefficiency of stable outcomes in bottleneck congestion games.  ... 
doi:10.1007/978-3-642-16170-4_29 fatcat:as24hxaribgrdaheofijwcvgny

On the Inefficiency Ratio of Stable Equilibria in Congestion Games [chapter]

Arash Asadpour, Amin Saberi
2009 Lecture Notes in Computer Science  
The current paper studies the inefficiency of the equilibria that are most stable in the presence of noise.  ...  Both of these notions focus on extreme cases: one is defined as the inefficiency ratio of the worst-case equilibrium and the other as the best one.  ...  Introduction The inefficiency of equilibria in noncooperative games has been studied vastly in the algorithmic game theory community during the last decade.  ... 
doi:10.1007/978-3-642-10841-9_54 fatcat:y4mdkjvgyvaptojxr7qxmkxlpi

Bounding the inefficiency of equilibria in nonatomic congestion games

Tim Roughgarden, Éva Tardos
2004 Games and Economic Behavior  
Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma.  ...  In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a "best possible" outcome.  ...  Cost Functions In this section we undertake a deeper study of the inefficiency of equilibria in nonatomic congestion games.  ... 
doi:10.1016/j.geb.2003.06.004 fatcat:togl3qwagnfs5mycsrnug2vswa

On the characterization and computation of Nash equilibria on parallel networks with horizontal queues

Walid Krichene, Jack Reilly, Saurabh Amin, Alexandre Bayen
2012 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)  
The article expands studies on routing games which traditionally model congestion with latency functions that increase with the flow on a particular link.  ...  We study inefficiencies in parallel networks with horizontal queues due to the selfish behavior of players, by comparing social optima to Nash equilibria.  ...  Routing games and Nash equilibria Routing games (or congestion games) form an important class of non-atomic games that is used to model the interaction of players who are sharing resources on a network  ... 
doi:10.1109/cdc.2012.6426543 dblp:conf/cdc/KricheneRAB12 fatcat:7cvnnygrgnflvcehpwlgyykdjq

Bounding the Inefficiency of Route Control in Intelligent Transport Systems [article]

Charlotte Roman, Paolo Turrini
2021 arXiv   pre-print
Then we find the inefficiency of the routing equilibria by calculating the Price of Anarchy for polynomial cost functions.  ...  We formulate an associated network control game, consisting of multiple actors seeking to optimise the social welfare of their assigned subpopulations in an underlying nonatomic congestion game.  ...  Conclusion We studied multiple agents optimising the routing of subpopulations in a nonatomic congestion game.  ... 
arXiv:2104.00357v1 fatcat:jv3qhhncm5gmtpouxct5qi57ni

The price of anarchy in games of incomplete information

Tim Roughgarden
2012 Proceedings of the 13th ACM Conference on Electronic Commerce - EC '12  
We outline a recently developed theory for bounding the inefficiency of equilibria in games of incomplete information, with applications to auctions and routing games.  ...  of the commons and in games with congestion effects; from uninternalized positive externalities with a public good or with network effects; from a failure to coordinate in team games; and so on.  ...  Now that the study of equilibrium inefficiency has grown in scope and considers strategically interesting auctions and mechanisms, there is presently a well-motivated focus on the price of anarchy in games  ... 
doi:10.1145/2229012.2229078 dblp:conf/sigecom/Roughgarden12 fatcat:325pi75qrzfsthmvwh5em6jhqe

The price of anarchy in games of incomplete information

Tim Roughgarden
2012 ACM SIGecom Exchanges  
We outline a recently developed theory for bounding the inefficiency of equilibria in games of incomplete information, with applications to auctions and routing games.  ...  of the commons and in games with congestion effects; from uninternalized positive externalities with a public good or with network effects; from a failure to coordinate in team games; and so on.  ...  Now that the study of equilibrium inefficiency has grown in scope and considers strategically interesting auctions and mechanisms, there is presently a well-motivated focus on the price of anarchy in games  ... 
doi:10.1145/2325713.2325716 fatcat:2jdxa7z2i5ehxpylyorwhfwhyq

The Price of Anarchy in Games of Incomplete Information

Tim Roughgarden
2015 ACM Transactions on Economics and Computation  
We outline a recently developed theory for bounding the inefficiency of equilibria in games of incomplete information, with applications to auctions and routing games.  ...  of the commons and in games with congestion effects; from uninternalized positive externalities with a public good or with network effects; from a failure to coordinate in team games; and so on.  ...  Now that the study of equilibrium inefficiency has grown in scope and considers strategically interesting auctions and mechanisms, there is presently a well-motivated focus on the price of anarchy in games  ... 
doi:10.1145/2737816 fatcat:jcqvxmvfizhgtmml3g2ve5b4sa

Computing approximate pure Nash equilibria in congestion games

Ioannis Caragiannis, Angelo Fanelli, Nick Gravin, Alexander Skopalik
2012 ACM SIGecom Exchanges  
In this letter, we discuss recent positive algorithmic results for approximate pure Nash equilibria in congestion games.  ...  Among other solution concepts, the notion of the pure Nash equilibrium plays a central role in Game Theory.  ...  Potential functions provide only inefficient proofs of existence of pure Nash equilibria.  ... 
doi:10.1145/2325713.2325718 fatcat:zmmykpbbrbc7vb4bky7njejb6e

On Stackelberg routing on parallel networks with horizontal queues

Walid Krichene, Jack Reilly, Saurabh Amin, Alexandre Bayen
2012 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)  
Ahstract-In order to address inefficiencies of Nash equilib ria for congestion networks with horizontal queues, we study the Stackelberg routing game on parallel networks: assuming a coordinator has control  ...  We study Stackelberg routing for a new class of latency functions, which models congestion on horizontal queues.  ...  n(xn, mn) (2) n = l In order to study the inefficiency of Nash equilibria, and the improvement of performance that the Stackelberg routing game can achieve, we focus our attention on best Nash equilibria  ... 
doi:10.1109/cdc.2012.6426526 dblp:conf/cdc/KricheneRAB12a fatcat:huo4pajr4vb3lklg6kcpgmwqim

Passive transmission rights will not do the job

Shmuel S. Oren
1997 Electricity Journal  
In fact there is no accepted 6 theory even to tell us that the outcome will necessarily be one of the game's Nash equilibria. 11 This ambiguity in game theory is illustrated by the experimental results  ...  For simplicity we begin in the context of the one-line game with only two generators who produce q1 and q2.  ... 
doi:10.1016/s1040-6190(97)80527-1 fatcat:ecz2cts7orgtlc64aphmtyy53i

Dynamic Traffic Models in Transportation Science (Dagstuhl Seminar 18102)

Roberto Cominetti, Tobias Harks, Carolina Osorio, Britta Peis, Michael Wagner
2018 Dagstuhl Reports  
In view of the above, this interdisciplinary seminar brought together leading scientists in the areas traffic simulations, algorithmic game theory and dynamic traffic assignment as well as people from  ...  On the other hand, within the past few years, the theory of dynamic traffic assignments in terms of equilibrium existence and equilibrium computation has not matured to the point matching the model complexity  ...  The Inefficiency of Wardrop Routing with Uncertain Demand We discussed the complexity theoretic characterization of mixed Nash equilibria in Potential or Congestion Games.  ... 
doi:10.4230/dagrep.8.3.21 dblp:journals/dagstuhl-reports/CominettiHOP18 fatcat:rywgmshsizharnoomv4ymii5tq

Weighted Congestion Games: Price of Anarchy, Universal Worst-Case Examples, and Tightness [chapter]

Kshipra Bhawalkar, Martin Gairing, Tim Roughgarden
2010 Lecture Notes in Computer Science  
We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions.  ...  We also prove a new result about unweighted congestion games: the worst-case price of anarchy in symmetric games is, as the number of players goes to infinity, as large as in their more general asymmetric  ...  Congestion games have played a starring role in recent research on quantifying the inefficiency of game-theoretic equilibria.  ... 
doi:10.1007/978-3-642-15781-3_2 fatcat:eae6kjcrv5hgjptnycrqlusmi4

Tight inefficiency bounds for perception-parameterized affine congestion games

Pieter Kleer, Guido Schäfer
2018 Theoretical Computer Science  
We introduce a new model of congestion games that captures several extensions of the classical congestion game introduced by Rosenthal in 1973.  ...  We derive tight bounds on the price of anarchy and the price of stability for a large range of parameters. Our bounds provide a complete picture of the inefficiency of equilibria for these games.  ...  We thank the anonymous referees for their very useful comments.  ... 
doi:10.1016/j.tcs.2018.04.025 fatcat:7zogde56hngdxm633m5apy4nya
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