• Corpus ID: 208267951

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

  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},
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… 

Follow-the-Regularized-Leader Routes to Chaos in Routing Games

It is established that, even in simple linear non-atomic congestion games with two parallel links and any fixed learning rate, unless the game is fully symmetric, increasing the population size or the scale of costs causes learning dynamics to becomes unstable and eventually chaotic.

The Evolution of Uncertainty of Learning in Games

This work uses the popular measure of differential entropy to quantify the evolution of uncertainty in learning-in-games systems and shows that the differential entropy of these learning- in-game systems increases linearly with time, formalizing their increased unpredictability over time.

Alternating Mirror Descent for Constrained Min-Max Games

This paper proposes and analyzes the alternating mirror descent algorithm, in which each player takes turns to take action following the mirror descent algorithms for constrained optimization, and establishes an O(K−2/3) bound on its average regret after K iterations.

Scaling Mean Field Games by Online Mirror Descent

We address the scaling of equilibrium computation in Mean Field Games (MFGs) by using Online Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash equilibrium under a

Nash, Conley, and Computation: Impossibility and Incompleteness in Game Dynamics

Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players’ behavior is a discrete-time or continuous-time rule


We study the dynamics of simple congestion games with two resources where a continuum of agents behaves according to a version of Experience-Weighted Attraction (EWA) algorithm. The dynamics is

Unpredictable dynamics in congestion games: memory loss can prevent chaos

We study the dynamics of simple congestion games with two resources where a continuum of agents behaves according to a version of Experience-Weighted Attraction (EWA) algorithm. The dynamics is

Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos

This paper introduces a natural multi-agent version of performative prediction, where multiple decision makers try to predict the same outcome, and proves that such competition can result in interesting phenomena by proving the possibility of phase transitions from stability to instability and eventually chaos.

Lyapunov Exponents for Diversity in Differentiable Games

Theoretical motivation for the method is given by leveraging machinery from the field of dynamical systems, and it is empirically evaluated by finding diverse solutions in the iterated prisoners’ dilemma and relevant machine learning problems including generative adversarial networks.

Evolutionary Dynamics and Phi-Regret Minimization in Games

It is proved here that the well-studied evolutionary learning algorithm of replicator dynamics (RD) seamlessly minimizes the strongest possible form of Φ-regret in generic 2 × 2 games, without any modification of the underlying algorithm itself.



Family of chaotic maps from game theory

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

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

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

Worst-case Equilibria

How bad is selfish routing?

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

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

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

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

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

Chaos on the Interval