DeepAI AI Chat
Log In Sign Up

Exact Price of Anarchy for Weighted Congestion Games with Two Players

03/03/2022
by   Joran van den Bosse, et al.
0

This paper gives a complete analysis of worst-case equilibria for various versions of weighted congestion games with two players and affine cost functions. The results are exact price of anarchy bounds which are parametric in the weights of the two players, and establish exactly how the primitives of the game enter into the quality of equilibria. Interestingly, some of the worst-cases are attained when the players' weights only differ slightly. Our findings also show that sequential play improves the price of anarchy in all cases, however, this effect vanishes with an increasing difference in the players' weights. Methodologically, we obtain exact price of anarchy bounds by a duality based proof mechanism, based on a compact linear programming formulation that computes worst-case instances. This mechanism yields duality-based optimality certificates which can eventually be turned into purely algebraic proofs.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/09/2020

Convergence of Large Atomic Congestion Games

We study the convergence of sequences of atomic unsplittable congestion ...
03/08/2019

Price of Anarchy in Stochastic Atomic Congestion Games with Affine Costs

We consider an atomic congestion game with stochastic demand in which ea...
07/16/2019

The Impact of Tribalism on Social Welfare

We explore the impact of mutual altruism among the players belonging to ...
07/13/2021

The Anarchy-Stability Tradeoff in Congestion Games

This work focuses on the design of incentive mechanisms in congestion ga...
07/10/2020

Partial Altruism is Worse than Complete Selfishness in Nonatomic Congestion Games

We seek to understand the fundamental mathematics governing infrastructu...
08/22/2017

Game Efficiency through Linear Programming Duality

The efficiency of a game is typically quantified by the price of anarchy...
07/03/2019

Pricing in Resource Allocation Games Based on Duality Gaps

We consider a basic resource allocation game, where the players' strateg...