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Distributionally robust equilibrium for continuous games: Nash and Stackelberg models

Distributionally robust equilibrium for continuous games: Nash and Stackelberg models
Distributionally robust equilibrium for continuous games: Nash and Stackelberg models
We develop several distributionally robust equilibrium models, following the recent research surge of robust game theory, in which some or all of the players in the games lack of complete information on the true probability distribution of underlying uncertainty but they need to make a decision prior to the realization of such uncertainty. We start with a distributionally robust Nash equilibrium model where each player uses partial information to construct a set of distributions and chooses an optimal decision on the basis of the worst distribution rather than the worst scenario to hedge the risk arising from ambiguity of the true probability distribution. We investigate the existence of equilibrium, develop a numerical scheme for its computation, and consider special cases where the distributionally robust Nash equilibrium model can be reformulated as an ordinary deterministic Nash equilibrium. We then extend our modeling scheme to two possible frameworks of distributionally robust Stackelberg setting: a distributionally robust follower model and a distributionally robust leader model. These two frameworks are employed to study an innovative problem of hierarchical competition in a supply chain where a buyer not only invests in its own capacity to supply an end-product market under demand uncertainty but also outsources a certain amount of market supplies to multiply competing suppliers who invest in capacity for obtaining the buyer’s orders. In this application, we show that the buyer has more incentives to invest in capacity whereas the suppliers have less to do so when those suppliers are confronted with more demand uncertainty in the end-product market over the buyer.
0377-2217
631-643
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Yang, Shu-jung S
c7b91fda-ee4f-4ef6-aa45-0bb9c378e5fc
Zhang, Jin
684cb039-53b8-41c5-ae32-fce01f855a14
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Yang, Shu-jung S
c7b91fda-ee4f-4ef6-aa45-0bb9c378e5fc
Zhang, Jin
684cb039-53b8-41c5-ae32-fce01f855a14

Liu, Yongchao, Xu, Huifu, Yang, Shu-jung S and Zhang, Jin (2018) Distributionally robust equilibrium for continuous games: Nash and Stackelberg models. European Journal of Operational Research, 265 (2), 631-643. (doi:10.1016/j.ejor.2017.07.050).

Record type: Article

Abstract

We develop several distributionally robust equilibrium models, following the recent research surge of robust game theory, in which some or all of the players in the games lack of complete information on the true probability distribution of underlying uncertainty but they need to make a decision prior to the realization of such uncertainty. We start with a distributionally robust Nash equilibrium model where each player uses partial information to construct a set of distributions and chooses an optimal decision on the basis of the worst distribution rather than the worst scenario to hedge the risk arising from ambiguity of the true probability distribution. We investigate the existence of equilibrium, develop a numerical scheme for its computation, and consider special cases where the distributionally robust Nash equilibrium model can be reformulated as an ordinary deterministic Nash equilibrium. We then extend our modeling scheme to two possible frameworks of distributionally robust Stackelberg setting: a distributionally robust follower model and a distributionally robust leader model. These two frameworks are employed to study an innovative problem of hierarchical competition in a supply chain where a buyer not only invests in its own capacity to supply an end-product market under demand uncertainty but also outsources a certain amount of market supplies to multiply competing suppliers who invest in capacity for obtaining the buyer’s orders. In this application, we show that the buyer has more incentives to invest in capacity whereas the suppliers have less to do so when those suppliers are confronted with more demand uncertainty in the end-product market over the buyer.

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EJOR-D-16-00583-R2 - Accepted Manuscript
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Accepted/In Press date: 18 July 2017
e-pub ahead of print date: 22 July 2017
Published date: 1 March 2018

Identifiers

Local EPrints ID: 413319
URI: http://eprints.soton.ac.uk/id/eprint/413319
ISSN: 0377-2217
PURE UUID: 87143eee-43a8-43de-9b6b-d0f60a3f7450
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 21 Aug 2017 16:31
Last modified: 20 Feb 2021 05:02

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Contributors

Author: Yongchao Liu
Author: Huifu Xu ORCID iD
Author: Shu-jung S Yang
Author: Jin Zhang

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