Abstract
Congestion games possess the property of emitting at least one pure Nash equilibrium and have a rich history of practical use in transport modelling. In this paper we approach the problem of modelling equilibrium within congestion games using a decentralised multi-player probabilistic approach via stochastic bandit feedback. Restricting the strategies available to players under the assumption of bounded rationality, we explore an online multiplayer exponential weights algorithm for unweighted atomic routing games and compare this with a \(\epsilon \)-greedy algorithm.
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- 1.
\((a_i; a_{-i})\) is commonly used to refer to player i’s strategy given the strategy profile \(\mathbf {a}=(a_1,\cdots ,a_i, \cdots ,a_N)\).
- 2.
In general an unweighted traffic rate routes the same quantity \(k_i =k \quad \forall i \in \mathcal {N}\).
- 3.
The source code is available at https://github.com/samtoneill/congestionbanditgames.
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O’Neill, S., Bagdasar, O., Liotta, A. (2020). An Online Learning Approach to a Multi-player N-armed Functional Bandit. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_41
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DOI: https://doi.org/10.1007/978-3-030-40616-5_41
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