# The route to chaos in routing games: When is price of anarchy too optimistic?

@article{Chotibut2019TheRT, title={The route to chaos in routing games: When is price of anarchy too optimistic?}, author={Thiparat Chotibut and Fryderyk Falniowski and Michał Misiurewicz and Georgios Piliouras}, journal={arXiv: Computer Science and Game Theory}, year={2019} }

Routing games are amongst the most studied classes of games. Their two most well-known properties are that learning dynamics converge to equilibria and that all equilibria are approximately optimal. In this work, we perform a stress test for these classic results by studying the ubiquitous dynamics, Multiplicative Weights Update, in different classes of congestion games, uncovering intricate non-equilibrium phenomena. As the system demand increases, the learning dynamics go through period…

## 18 Citations

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## References

SHOWING 1-10 OF 96 REFERENCES

### Family of chaotic maps from game theory

- MathematicsDynamical Systems
- 2020

ABSTRACT From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself.…

### Adaptive game playing using multiplicative weights

- Computer Science
- 1999

A variant of the game-playing algorithm is proved to be optimal in a very strong sense and a new, simple proof of the min–max theorem, as well as a provable method of approximately solving a game.

### The Multiplicative Weights Update Method: a Meta-Algorithm and Applications

- Computer ScienceTheory Comput.
- 2012

A simple meta-algorithm is presented that unifies many of these disparate algorithms and derives them as simple instantiations of the meta-Algorithm.

### How bad is selfish routing?

- Computer ScienceProceedings 41st Annual Symposium on Foundations of Computer Science
- 2000

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 (subject to the condition that all traffic must be routed).

### Finite Regret and Cycles with Fixed Step-Size via Alternating Gradient Descent-Ascent

- Computer ScienceCOLT 2019
- 2019

This paper shows that in adversarial settings that agents' strategies are bounded and cycle when both are using the alternating gradient descent algorithm, and shows that an agent that uses gradient descent obtains bounded regret.

### Vortices Instead of Equilibria in MinMax Optimization: Chaos and Butterfly Effects of Online Learning in Zero-Sum Games

- EconomicsCOLT
- 2019

It is proved that no meaningful prediction can be made about the day-to-day behavior of online learning dynamics in zero-sum games, and Chaos is robust to all affine variants of zero- sum games, network variants with arbitrary large number of agents and even to competitive settings beyond these.

### Fast and Furious Learning in Zero-Sum Games: Vanishing Regret with Non-Vanishing Step Sizes

- Computer ScienceNeurIPS
- 2019

We show for the first time, to our knowledge, that it is possible to reconcile in online learning in zero-sum games two seemingly contradictory objectives: vanishing time-average regret and…

### Behavioral Game Theory: Experiments in Strategic Interaction

- Psychology
- 2003

Game theory, the formalized study of strategy, began in the 1940s by asking how emotionless geniuses should play games, but ignored until recently how average people with emotions and limited…