Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&D Spillovers

In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical problems in engineering 2021, Vol.2021, p.1-19
Main Authors: Zhou, Wei, Chu, Tong, Wang, Xiao-Xue
Format: Article
Language:English
Subjects:
Adjustment
Behavior
Bifurcations
Competition
Competitive advantage
Cooperation
Costs
Decision making
Dynamic stability
Game theory
Games
Oligarchy
Organization theory
Product differentiation
Profits
R&D
Research & development
Stability analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c380t-590631a59c53a49f19a503faead2d4b4e05dcfdcbe71809518b5be259a3e453d3
cites cdi_FETCH-LOGICAL-c380t-590631a59c53a49f19a503faead2d4b4e05dcfdcbe71809518b5be259a3e453d3
container_end_page 19
container_issue
container_start_page 1
container_title Mathematical problems in engineering
container_volume 2021
creator Zhou, Wei
Chu, Tong
Wang, Xiao-Xue
description In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed. The effects of system parameters on the complex dynamical behaviors of the built game are analyzed. We find that the system can lose stability through a flip bifurcation or a Neimark–Sacker bifurcation. In addition, the coexistence of multiattractors is also discussed using the so-called basin of attraction. At the end of this research, the social welfare of the given duopoly game is also studied.
doi_str_mv 10.1155/2021/2096868
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2484145423</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2484145423</sourcerecordid><originalsourceid>FETCH-LOGICAL-c380t-590631a59c53a49f19a503faead2d4b4e05dcfdcbe71809518b5be259a3e453d3</originalsourceid><addsrcrecordid>eNp9kEtLAzEQgIMoWKs3f0BA8GJX89xujtJqFQqCrdRbmN1kNWW7qcnW0n9vSnv2MjMM3zz4ELqm5J5SKR8YYTQFlRd5cYJ6VOY8k1QMT1NNmMgo45_n6CLGJUmkpEUPLWYdlK5x3W6AJ40vocHjXQsrV8UBhtbgma9cai5sU0Ow2NcY8HzrszT3ZfEEVhZvWmMDfr8d49naNY3_tSFeorMammivjrmPPp6f5qOXbPo2eR09TrOKF6TLpCI5pyBVJTkIVVMFkvAaLBhmRCkskaaqTVXaIS2ISi-XsrRMKuBWSG54H90c9q6D_9nY2Oml34Q2ndRMFIIKKRhP1OBAVcHHGGyt18GtIOw0JXqvTu_V6aO6hN8d8G_XGti6_-k_e71sBQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2484145423</pqid></control><display><type>article</type><title>Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&amp;D Spillovers</title><source>Open Access: Wiley-Blackwell Open Access Journals</source><source>Publicly Available Content Database</source><creator>Zhou, Wei ; Chu, Tong ; Wang, Xiao-Xue</creator><contributor>Elsadany, Abdelalim ; Abdelalim Elsadany</contributor><creatorcontrib>Zhou, Wei ; Chu, Tong ; Wang, Xiao-Xue ; Elsadany, Abdelalim ; Abdelalim Elsadany</creatorcontrib><description>In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&amp;D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed. The effects of system parameters on the complex dynamical behaviors of the built game are analyzed. We find that the system can lose stability through a flip bifurcation or a Neimark–Sacker bifurcation. In addition, the coexistence of multiattractors is also discussed using the so-called basin of attraction. At the end of this research, the social welfare of the given duopoly game is also studied.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2021/2096868</identifier><language>eng</language><publisher>New York: Hindawi</publisher><subject>Adjustment ; Behavior ; Bifurcations ; Competition ; Competitive advantage ; Cooperation ; Costs ; Decision making ; Dynamic stability ; Game theory ; Games ; Oligarchy ; Organization theory ; Product differentiation ; Profits ; R&amp;D ; Research &amp; development ; Stability analysis</subject><ispartof>Mathematical problems in engineering, 2021, Vol.2021, p.1-19</ispartof><rights>Copyright © 2021 Wei Zhou et al.</rights><rights>Copyright © 2021 Wei Zhou et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-590631a59c53a49f19a503faead2d4b4e05dcfdcbe71809518b5be259a3e453d3</citedby><cites>FETCH-LOGICAL-c380t-590631a59c53a49f19a503faead2d4b4e05dcfdcbe71809518b5be259a3e453d3</cites><orcidid>0000-0002-4477-3940</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2484145423/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2484145423?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,4021,25751,27921,27922,27923,37010,44588,74896</link.rule.ids></links><search><contributor>Elsadany, Abdelalim</contributor><contributor>Abdelalim Elsadany</contributor><creatorcontrib>Zhou, Wei</creatorcontrib><creatorcontrib>Chu, Tong</creatorcontrib><creatorcontrib>Wang, Xiao-Xue</creatorcontrib><title>Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&amp;D Spillovers</title><title>Mathematical problems in engineering</title><description>In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&amp;D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed. The effects of system parameters on the complex dynamical behaviors of the built game are analyzed. We find that the system can lose stability through a flip bifurcation or a Neimark–Sacker bifurcation. In addition, the coexistence of multiattractors is also discussed using the so-called basin of attraction. At the end of this research, the social welfare of the given duopoly game is also studied.</description><subject>Adjustment</subject><subject>Behavior</subject><subject>Bifurcations</subject><subject>Competition</subject><subject>Competitive advantage</subject><subject>Cooperation</subject><subject>Costs</subject><subject>Decision making</subject><subject>Dynamic stability</subject><subject>Game theory</subject><subject>Games</subject><subject>Oligarchy</subject><subject>Organization theory</subject><subject>Product differentiation</subject><subject>Profits</subject><subject>R&amp;D</subject><subject>Research &amp; development</subject><subject>Stability analysis</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNp9kEtLAzEQgIMoWKs3f0BA8GJX89xujtJqFQqCrdRbmN1kNWW7qcnW0n9vSnv2MjMM3zz4ELqm5J5SKR8YYTQFlRd5cYJ6VOY8k1QMT1NNmMgo45_n6CLGJUmkpEUPLWYdlK5x3W6AJ40vocHjXQsrV8UBhtbgma9cai5sU0Ow2NcY8HzrszT3ZfEEVhZvWmMDfr8d49naNY3_tSFeorMammivjrmPPp6f5qOXbPo2eR09TrOKF6TLpCI5pyBVJTkIVVMFkvAaLBhmRCkskaaqTVXaIS2ISi-XsrRMKuBWSG54H90c9q6D_9nY2Oml34Q2ndRMFIIKKRhP1OBAVcHHGGyt18GtIOw0JXqvTu_V6aO6hN8d8G_XGti6_-k_e71sBQ</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Zhou, Wei</creator><creator>Chu, Tong</creator><creator>Wang, Xiao-Xue</creator><general>Hindawi</general><general>Hindawi Limited</general><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0002-4477-3940</orcidid></search><sort><creationdate>2021</creationdate><title>Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&amp;D Spillovers</title><author>Zhou, Wei ; Chu, Tong ; Wang, Xiao-Xue</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-590631a59c53a49f19a503faead2d4b4e05dcfdcbe71809518b5be259a3e453d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Adjustment</topic><topic>Behavior</topic><topic>Bifurcations</topic><topic>Competition</topic><topic>Competitive advantage</topic><topic>Cooperation</topic><topic>Costs</topic><topic>Decision making</topic><topic>Dynamic stability</topic><topic>Game theory</topic><topic>Games</topic><topic>Oligarchy</topic><topic>Organization theory</topic><topic>Product differentiation</topic><topic>Profits</topic><topic>R&amp;D</topic><topic>Research &amp; development</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhou, Wei</creatorcontrib><creatorcontrib>Chu, Tong</creatorcontrib><creatorcontrib>Wang, Xiao-Xue</creatorcontrib><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access Journals</collection><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Database‎ (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East &amp; Africa Database</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhou, Wei</au><au>Chu, Tong</au><au>Wang, Xiao-Xue</au><au>Elsadany, Abdelalim</au><au>Abdelalim Elsadany</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&amp;D Spillovers</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2021</date><risdate>2021</risdate><volume>2021</volume><spage>1</spage><epage>19</epage><pages>1-19</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&amp;D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed. The effects of system parameters on the complex dynamical behaviors of the built game are analyzed. We find that the system can lose stability through a flip bifurcation or a Neimark–Sacker bifurcation. In addition, the coexistence of multiattractors is also discussed using the so-called basin of attraction. At the end of this research, the social welfare of the given duopoly game is also studied.</abstract><cop>New York</cop><pub>Hindawi</pub><doi>10.1155/2021/2096868</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-4477-3940</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1024-123X
ispartof Mathematical problems in engineering, 2021, Vol.2021, p.1-19
issn 1024-123X
1563-5147
language eng
recordid cdi_proquest_journals_2484145423
source Open Access: Wiley-Blackwell Open Access Journals; Publicly Available Content Database
subjects Adjustment
Behavior
Bifurcations
Competition
Competitive advantage
Cooperation
Costs
Decision making
Dynamic stability
Game theory
Games
Oligarchy
Organization theory
Product differentiation
Profits
R&D
Research & development
Stability analysis
title Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&D Spillovers
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T14%3A17%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Stability,%20Global%20Dynamics,%20and%20Social%20Welfare%20of%20a%20Two-Stage%20Game%20under%20R&D%20Spillovers&rft.jtitle=Mathematical%20problems%20in%20engineering&rft.au=Zhou,%20Wei&rft.date=2021&rft.volume=2021&rft.spage=1&rft.epage=19&rft.pages=1-19&rft.issn=1024-123X&rft.eissn=1563-5147&rft_id=info:doi/10.1155/2021/2096868&rft_dat=%3Cproquest_cross%3E2484145423%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c380t-590631a59c53a49f19a503faead2d4b4e05dcfdcbe71809518b5be259a3e453d3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2484145423&rft_id=info:pmid/&rfr_iscdi=true