4,240 research outputs found
Bayesian Quadratic Network Game Filters
A repeated network game where agents have quadratic utilities that depend on
information externalities -- an unknown underlying state -- as well as payoff
externalities -- the actions of all other agents in the network -- is
considered. Agents play Bayesian Nash Equilibrium strategies with respect to
their beliefs on the state of the world and the actions of all other nodes in
the network. These beliefs are refined over subsequent stages based on the
observed actions of neighboring peers. This paper introduces the Quadratic
Network Game (QNG) filter that agents can run locally to update their beliefs,
select corresponding optimal actions, and eventually learn a sufficient
statistic of the network's state. The QNG filter is demonstrated on a Cournot
market competition game and a coordination game to implement navigation of an
autonomous team
On Similarities between Inference in Game Theory and Machine Learning
In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoff-dominant but risk-dominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We first show that the standard update rule of mean field variational learning is analogous to a Cournot adjustment within game theory. By analogy with fictitious play, we then suggest an improved update rule, and show that this results in fictitious variational play, an improved mean field variational learning algorithm that exhibits better convergence in highly or strongly connected graphical models. Second, we use a recent advance in fictitious play, namely dynamic fictitious play, to derive a derivative action variational learning algorithm, that exhibits superior convergence properties on a canonical machine learning problem (clustering a mixture distribution)
- ā¦