Cournot games with limited demand: from multiple equilibria to stochastic equilibrium
We construct Cournot games with limited demand, resulting into capped sales volumes according to the respective production shares of the players. We show that such games admit three distinct equilibrium regimes, including an intermediate regime that allows for a range of possible equilibria. When in...
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/161255 |
| _version_ | 1826110504251162624 |
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| author | Polak, Ido Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Polak, Ido Privault, Nicolas |
| author_sort | Polak, Ido |
| collection | NTU |
| description | We construct Cournot games with limited demand, resulting into capped sales volumes according to the respective production shares of the players. We show that such games admit three distinct equilibrium regimes, including an intermediate regime that allows for a range of possible equilibria. When information on demand is modeled by a delayed diffusion process, we also show that this intermediate regime collapses to a single equilibrium while the other regimes approximate the deterministic setting as the delay tends to zero. Moreover, as the delay approaches zero, the unique equilibrium achieved in the stochastic case provides a way to select a natural equilibrium within the range observed in the no lag setting. Numerical illustrations are presented when demand is modeled by an Ornstein–Uhlenbeck process and price is an affine function of output. |
| first_indexed | 2024-10-01T02:35:31Z |
| format | Journal Article |
| id | ntu-10356/161255 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:35:31Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1612552022-08-22T07:56:06Z Cournot games with limited demand: from multiple equilibria to stochastic equilibrium Polak, Ido Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Game Theory Multiple Equilibria We construct Cournot games with limited demand, resulting into capped sales volumes according to the respective production shares of the players. We show that such games admit three distinct equilibrium regimes, including an intermediate regime that allows for a range of possible equilibria. When information on demand is modeled by a delayed diffusion process, we also show that this intermediate regime collapses to a single equilibrium while the other regimes approximate the deterministic setting as the delay tends to zero. Moreover, as the delay approaches zero, the unique equilibrium achieved in the stochastic case provides a way to select a natural equilibrium within the range observed in the no lag setting. Numerical illustrations are presented when demand is modeled by an Ornstein–Uhlenbeck process and price is an affine function of output. Ministry of Education (MOE) This research was supported by the Singapore MOE Tier 2 Grant MOE2016-T2-1- 036. 2022-08-22T07:56:06Z 2022-08-22T07:56:06Z 2020 Journal Article Polak, I. & Privault, N. (2020). Cournot games with limited demand: from multiple equilibria to stochastic equilibrium. Applied Mathematics and Optimization, 81(1), 195-220. https://dx.doi.org/10.1007/s00245-018-9481-1 0095-4616 https://hdl.handle.net/10356/161255 10.1007/s00245-018-9481-1 2-s2.0-85042106236 1 81 195 220 en MOE2016-T2-1- 036 Applied Mathematics and Optimization © 2018 Springer Science+Business Media, LLC, part of Springer Nature. All rights reserved. |
| spellingShingle | Science::Mathematics Game Theory Multiple Equilibria Polak, Ido Privault, Nicolas Cournot games with limited demand: from multiple equilibria to stochastic equilibrium |
| title | Cournot games with limited demand: from multiple equilibria to stochastic equilibrium |
| title_full | Cournot games with limited demand: from multiple equilibria to stochastic equilibrium |
| title_fullStr | Cournot games with limited demand: from multiple equilibria to stochastic equilibrium |
| title_full_unstemmed | Cournot games with limited demand: from multiple equilibria to stochastic equilibrium |
| title_short | Cournot games with limited demand: from multiple equilibria to stochastic equilibrium |
| title_sort | cournot games with limited demand from multiple equilibria to stochastic equilibrium |
| topic | Science::Mathematics Game Theory Multiple Equilibria |
| url | https://hdl.handle.net/10356/161255 |
| work_keys_str_mv | AT polakido cournotgameswithlimiteddemandfrommultipleequilibriatostochasticequilibrium AT privaultnicolas cournotgameswithlimiteddemandfrommultipleequilibriatostochasticequilibrium |