Classifying Convergence Complexity of Nash Equilibria in Graphical Games Using Distributed Computing Theory

by   Juho Hirvonen, et al.

Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology. Yet, even though a player's payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of "natural" local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with a constant-round local algorithm. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of "time-constrained" inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood.


page 1

page 2

page 3

page 4


Tight Inapproximability for Graphical Games

We provide a complete characterization for the computational complexity ...

Pure Nash Equilibria and Best-Response Dynamics in Random Games

Nash equilibria are a central concept in game theory and have applicatio...

Approximating Nash Equilibrium in Random Graphical Games

Computing Nash equilibrium in multi-agent games is a longstanding challe...

Equilibrium Learning in Combinatorial Auctions: Computing Approximate Bayesian Nash Equilibria via Pseudogradient Dynamics

Applications of combinatorial auctions (CA) as market mechanisms are pre...

Memory Asymmetry Creates Heteroclinic Orbits to Nash Equilibrium in Learning in Zero-Sum Games

Learning in games considers how multiple agents maximize their own rewar...

On Sparse Discretization for Graphical Games

This short paper concerns discretization schemes for representing and co...

Graphical Potential Games

Potential games, originally introduced in the early 1990's by Lloyd Shap...

Please sign up or login with your details

Forgot password? Click here to reset