Bauso, D. and Norman, T.W.L. (2014) Approachability in Population Games. (Unpublished)
Abstract
This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a population of individuals with given distribution on actions. First, convergence conditions are revisited based on the common prior on the population distribution, and we define the notion of \emph{1st-moment approachability}. Second, we develop a model of two coupled partial differential equations (PDEs) in the spirit of mean-field game theory: one describing the best-response of every player given the population distribution (this is a \emph{Hamilton-Jacobi-Bellman equation}), the other capturing the macroscopic evolution of average payoffs if every player plays its best response (this is an \emph{advection equation}). Third, we provide a detailed analysis of existence, nonuniqueness, and stability of equilibria (fixed points of the two PDEs). Fourth, we apply the model to regret-based dynamics, and use it to establish convergence to Bayesian equilibrium under incomplete information.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Year The Author(s) |
Keywords: | math.OC; math.OC; 91A13 |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 28 Jan 2016 11:45 |
Last Modified: | 28 Jan 2016 11:45 |
Published Version: | http://arxiv.org/abs/1407.3910 |
Status: | Unpublished |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89660 |