Dynamic Inefficiency: Anarchy without Stability

@inproceedings{Berger2011DynamicIA,
  title={Dynamic Inefficiency: Anarchy without Stability},
  author={Noam Berger and Michal Feldman and Ofer Neiman and Mishael Rosenthal},
  booktitle={SAGT},
  year={2011}
}
The price of anarchy [16] is by now a standard measure for quantifying the inefficiency introduced in games due to selfish behavior, and is defined as the ratio between the optimal outcome and the worst Nash equilibrium. However, this notion is well defined only for games that always possess a Nash equilibrium (NE). We propose the dynamic inefficiency measure, which is roughly defined as the average inefficiency in an infinite best-response dynamic. Both the price of anarchy [16] and the price… 
The Efficiency of Best-Response Dynamics
TLDR
A measure for quantifying the performance of different deviator rules is provided, which shows the inefficiency of a deviator rule S with respect to an initial strategy profile p is the ratio between the social cost of the worst equilibrium reachable by S from p and the socialcost of the best equilibrium reachables from p.
Best-Response Dynamics, Playing Sequences, and Convergence to Equilibrium in Random Games
We show that the playing sequence--the order in which players update their actions--is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we
On the convergence of the best-response algorithm in routing games
TLDR
It is proved that best-response operators are lipschitz continuous, which implies that a sufficient condition for the convergence of the best- Response dynamics is that the joint spectral radius of Jacobian matrices of best- response operators be strictly less than unity.
Mechanisms for Network Creation
  • Computer Science, Economics
  • 2018
TLDR
The mechanism approach is a true superset of both centralized network design and uncoordinated network creation games and to the best of the knowledge this is the first attempt to explore the realm inbetween those extremes.
Applications of game theory to distributed routing and delay tolerant networking. (Applications de la théorie des jeux à routage distribuée et mise en réseau à tolérance de retard)
TLDR
Nous proposons tout d'abord un mecanisme d'incitation base sur une recompense pour convaincre les noeuds mobiles de relayer les messages, and analysons l'influence of l'information donnee par the source aux relais sur le prix a payer pour transmettre le message.

References

SHOWING 1-10 OF 30 REFERENCES
Conflicting Congestion Effects in Resource Allocation Games
TLDR
The inefficiency of equilibria with respect to the minimax objective function is measured, and it is proved that there is no universal bound for the worst-case inefficiency (as quantified by the “price of anarchy” measure), however, the best- case inefficiency is bounded by 5/4, and this is tight.
Coordination mechanisms for selfish scheduling
Sink equilibria and convergence
TLDR
It is argued that there is a natural convergence process to sink equilibria in games where agents use pure strategies, and the price of sinking is an alternative measure of the social cost of a lack of coordination, which measures the worst case ratio between thevalue of a sink equilibrium and the value of the socially optimal solution.
On strategy-proofness and single peakedness
ConclusionThis paper investigates one of the possible weakening of the (too demanding) assumptions of the Gibbard-Satterthwaite theorem. Namely we deal with a class of voting schemes where at the
Efficient Coordination Mechanisms for Unrelated Machine Scheduling
TLDR
Three new coordination mechanisms for scheduling n selfish jobs on m unrelated machines are presented, one of which is the first that handles anonymous jobs and simultaneously guarantees that the induced game is a potential game and has bounded price of anarchy.
(Almost) optimal coordination mechanisms for unrelated machine scheduling
TLDR
A local ordering policy with the approximation ratio of Θ(log m) in equilibria is designed, and it is proved that this policy is optimal among all local ordering policies, and closes the gap between the known lower and upper bounds for this problem.
Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions
  • A. Vetta
  • Economics
    The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
TLDR
This work presents guarantees on the social performance of Nash equilibria on the basis of competitive versions of the facility location problem and k-median problem, a maximisation version of the traffic routing problem studied by Roughgarden and Tardos (2000), and multiple-item auctions.
Near-optimal network design with selfish agents
TLDR
This paper proves that there is a Nash equilibrium as cheap as the optimal network, and gives a polynomial time algorithm to find a (1+ε)-approximate Nash equilibrium that does not cost much more.
Convergence Time to Nash Equilibria
We study the number of steps required to reach a pure Nash Equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost.
How bad is selfish routing?
TLDR
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.
...
...