Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/313393 
Year of Publication: 
2022
Citation: 
[Journal:] Optimization Letters [ISSN:] 1862-4480 [Volume:] 17 [Issue:] 6 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 1379-1412
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
We develop a Nash equilibrium problem representing a perfectly competitive market wherein all players are subject to the same source of uncertainty with an unknown probability distribution. Each player—depending on her individual access to and confidence over empirical data—builds an ambiguity set containing a family of potential probability distributions describing the uncertain event. The ambiguity set of different players is not necessarily identical, yielding a market with potentially heterogeneous ambiguity aversion. Built upon recent developments in the field of Wasserstein distributionally robust chance-constrained optimization, each ambiguity-averse player maximizes her own expected payoff under the worst-case probability distribution within her ambiguity set. Using an affine policy and a conditional value-at-risk approximation of chance constraints, we define a tractable Nash game. We prove that under certain conditions a unique Nash equilibrium point exists, which coincides with the solution of a single optimization problem. Numerical results indicate that players with comparatively lower consumption utility are highly exposed to rival ambiguity aversion.
Subjects: 
Distributionally robust equilibrium problem
Nash game
Wasserstein ambiguity set
Heterogeneous ambiguity aversion
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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