46 research outputs found
Polynomial Convergence of Bandit No-Regret Dynamics in Congestion Games
We introduce an online learning algorithm in the bandit feedback model that,
once adopted by all agents of a congestion game, results in game-dynamics that
converge to an -approximate Nash Equilibrium in a polynomial number
of rounds with respect to , the number of players and the number of
available resources. The proposed algorithm also guarantees sublinear regret to
any agent adopting it. As a result, our work answers an open question from
arXiv:2206.01880 and extends the recent results of arXiv:2306.15543 to the
bandit feedback model. We additionally establish that our online learning
algorithm can be implemented in polynomial time for the important special case
of Network Congestion Games on Directed Acyclic Graphs (DAG) by constructing an
exact -barycentric spanner for DAGs
Semi Bandit Dynamics in Congestion Games: Convergence to Nash Equilibrium and No-Regret Guarantees
In this work, we introduce a new variant of online gradient descent, which
provably converges to Nash Equilibria and simultaneously attains sublinear
regret for the class of congestion games in the semi-bandit feedback setting.
Our proposed method admits convergence rates depending only polynomially on the
number of players and the number of facilities, but not on the size of the
action set, which can be exponentially large in terms of the number of
facilities. Moreover, the running time of our method has polynomial-time
dependence on the implicit description of the game. As a result, our work
answers an open question from (Du et. al, 2022).Comment: ICML 202
Dynamics in atomic signaling games
We study an atomic signaling game under stochastic evolutionary dynamics.
There is a finite number of players who repeatedly update from a finite number
of available languages/signaling strategies. Players imitate the most fit
agents with high probability or mutate with low probability. We analyze the
long-run distribution of states and show that, for sufficiently small mutation
probability, its support is limited to efficient communication systems. We find
that this behavior is insensitive to the particular choice of evolutionary
dynamic, a property that is due to the game having a potential structure with a
potential function corresponding to average fitness. Consequently, the model
supports conclusions similar to those found in the literature on language
competition. That is, we show that efficient languages eventually predominate
the society while reproducing the empirical phenomenon of linguistic drift. The
emergence of efficiency in the atomic case can be contrasted with results for
non-atomic signaling games that establish the non-negligible possibility of
convergence, under replicator dynamics, to states of unbounded efficiency loss
Joint strategy fictitious play with inertia for potential games
We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion