Stability in games with continua of equilibria

Sebastian Bervoets and Mathieu Faure ()

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Abstract: The stability of Nash equilibria has often been studied by examining the asymptotic behavior of the best-response dynamics. This is generally done in games where interactions are global and equilibria are isolated. In this paper, we analyze stability in contexts where interactions are local and where there are continua of equilibria. We focus on the public good game played on a network, where the set of equilibria is known to depend on the network structure (Bramoullé and Kranton, 2007), and where, as we show, continua of equilibria often appear. We provide necessary and sufficient conditions for a component of Nash equilibria to be asymptotically stable vis-à-vis the best-response dynamics. Interestingly, we demonstrate that these conditions relate to the structure of the network in a simple way. We also provide corresponding results for several dynamical systems related to the best response.

Keywords: Best-response dynamics; Public good games; Stability (search for similar items in EconPapers)
Date: 2019-01
New Economics Papers: this item is included in nep-gth, nep-mic and nep-net
Note: View the original document on HAL open archive server: https://amu.hal.science/hal-02021221
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Citations: View citations in EconPapers (16)

Published in Journal of Economic Theory, 2019, 179, pp.131-162. ⟨10.1016/j.jet.2018.10.011⟩

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Journal Article: Stability in games with continua of equilibria (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02021221

DOI: 10.1016/j.jet.2018.10.011

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