Generalizations of Weighted Matroid Congestion Games: Pure Nash Equilibrium, Sensitivity Analysis, and Discrete Convex Function

2019 ◽  
pp. 594-614 ◽  
Author(s):  
Kenjiro Takazawa
Keyword(s):  
Sensitivity Analysis ◽  
Nash Equilibrium ◽  
Convex Function ◽  
Congestion Games ◽  
Pure Nash Equilibrium ◽  
Discrete Convex ◽  
Discrete Convex Function

scholarly journals The Minimum Tollbooth Problem in Atomic Network Congestion Games with Unsplittable Flows

2021 ◽  
Author(s):  
Julian Nickerl
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Congestion Games ◽  
Social Optimum ◽  
Network Congestion ◽  
Pure Nash Equilibrium ◽  
Positive Side ◽  
Minimum Number

AbstractThis work analyzes the minimum tollbooth problem in atomic network congestion games with unsplittable flows. The goal is to place tolls on edges, such that there exists a pure Nash equilibrium in the tolled game that is a social optimum in the untolled one. Additionally, we require the number of tolled edges to be the minimum. This problem has been extensively studied in non-atomic games, however, to the best of our knowledge, it has not been considered for atomic games before. By a reduction from the weighted CNF SAT problem, we show both the NP-hardness of the problem and the W[2]-hardness when parameterizing the problem with the number of tolled edges. On the positive side, we present a polynomial time algorithm for networks on series-parallel graphs that turns any given state of the untolled game into a pure Nash equilibrium of the tolled game with the minimum number of tolled edges.

Classes of Potential Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Resource Allocation ◽  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Potential Games ◽  
Congestion Games ◽  
Fictitious Play ◽  
Resource Allocation Problem ◽  
Distributed Resource Allocation ◽  
Symmetric Games ◽  
The Cost

This chapter discusses several classes of potential games that are common in the literature and how to derive the Nash equilibrium for such games. It first considers identical interests games and dummy games before turning to decoupled games and bilateral symmetric games. It then describes congestion games, in which all players are equal, in the sense that the cost associated with each resource only depends on the total number of players using that resource and not on which players use it. It also presents other potential games, including the Sudoku puzzle, and goes on to analyze the distributed resource allocation problem, the computation of Nash equilibria for potential games, and fictitious play. It concludes with practice exercises and their corresponding solutions, along with additional exercises.

scholarly journals Nash versus coarse correlation

2020 ◽  
Vol 23 (4) ◽  
pp. 1178-1204 ◽  
Author(s):  
Konstantinos Georgalos ◽  
Indrajit Ray ◽  
Sonali SenGupta
Keyword(s):  
Nash Equilibrium ◽  
Correlated Equilibrium ◽  
Individual Choice ◽  
Pure Nash Equilibrium ◽  
Expected Payoff ◽  
Equilibrium Payoff ◽  
Payoff Dominance ◽  
Dominated Strategies ◽  
Person Game ◽  
Nash Point

Abstract We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

EXISTENCE AND UNIQUENESS OF EQUILIBRIUM IN ASYMMETRIC CONTESTS WITH ENDOGENOUS PRIZES

2013 ◽  
Vol 15 (01) ◽  
pp. 1350005 ◽  
Author(s):  
SHUMEI HIRAI ◽  
FERENC SZIDAROVSZKY
Keyword(s):  
Nash Equilibrium ◽  
Existence And Uniqueness ◽  
Financial Constraints ◽  
Pure Nash Equilibrium ◽  
Asymmetric Contests ◽  
Uniqueness Of Equilibrium

This paper considers contests in which the efforts of the players determine the value of the prize. Players may have different valuations of the prize and different abilities to convert expenditures to productive efforts. In addition, players may face different financial constraints. This paper presents a proof for the existence and uniqueness of a pure Nash equilibrium in asymmetric contests with endogenous prizes.

Intermodal Hinterland Network Design Games

2020 ◽  
Vol 54 (5) ◽  
pp. 1272-1287
Author(s):  
Yann Bouchery ◽  
Marco Slikker ◽  
Jan C. Fransoo
Keyword(s):  
Nash Equilibrium ◽  
Network Design ◽  
Optimal Solution ◽  
Design Stage ◽  
Pure Nash Equilibrium ◽  
Design Problems ◽  
Distinctive Features ◽  
Multiple User ◽  
General Network ◽  
The Impact

Intermodal hinterland transportation is becoming increasingly critical for global container supply chains. Managing intermodal hinterland networks is challenging because multiple actors often interact in practice. The intermodal hinterland network design games that we propose enable assessing the impact of having noncooperative users in intermodal networks. The games fall into the class of network design games but have key distinctive features. We provide some general results as well as an instance without a pure Nash equilibrium for the general case. Subsequently, we focus on the special case with a single intermodal connection available. We show that a pure Nash equilibrium always exists but that this one is not always unique. We additionally identify key structural properties for this single-hub game. These properties enable us to identify all pure Nash equilibria and a system-optimal solution in polynomial time. We illustrate our results with an application related to the development of an extended gate in the Netherlands and derive a series of insights. Overall, the results show that the multiple user feature of intermodal hinterland networks is critical and needs to be accounted for at the network design stage. We believe that this latter statement holds for general network design problems with multiple users.

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