Local Nash Equilibrium in Social Networks
Identifieur interne : 000318 ( France/Analysis ); précédent : 000317; suivant : 000319Local Nash Equilibrium in Social Networks
Auteurs : Yichao Zhang [France, République populaire de Chine] ; M. A. Aziz-Alaoui [France] ; Cyrille Bertelle [France] ; Jihong Guan [République populaire de Chine]Source :
- Scientific Reports [ 2045-2322 ] ; 2014.
English descriptors
- KwdEn :
- MESH :
Abstract
Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures.
Url:
DOI: 10.1038/srep06224
PubMed: 25169150
PubMed Central: 4148661
Affiliations:
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PMC:4148661Le document en format XML
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Lebon</institution>, 76600 Le Havre, France</nlm:aff><country xml:lang="fr">France</country><wicri:regionArea>, 76600 Le Havre</wicri:regionArea><placeName><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region><settlement type="city">Le Havre</settlement></placeName></affiliation><affiliation wicri:level="1"><nlm:aff id="a2"><institution>Department of Computer Science and Technology, Tongji University</institution>, 4800 Cao'an Road, Shanghai 201804, China</nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>, 4800 Cao'an Road, Shanghai 201804</wicri:regionArea><wicri:noRegion>Shanghai 201804</wicri:noRegion></affiliation></author><author><name sortKey="Aziz Alaoui, M A" sort="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M" first="M. A." last="Aziz-Alaoui">M. A. Aziz-Alaoui</name><affiliation wicri:level="3"><nlm:aff id="a1"><institution>Normandie Univ, France; ULH, LMAH, F-76600 Le Havre; FR-CNRS-3335, ISCN, 25 rue Ph. Lebon</institution>, 76600 Le Havre, France</nlm:aff><country xml:lang="fr">France</country><wicri:regionArea>, 76600 Le Havre</wicri:regionArea><placeName><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region><settlement type="city">Le Havre</settlement></placeName></affiliation></author><author><name sortKey="Bertelle, Cyrille" sort="Bertelle, Cyrille" uniqKey="Bertelle C" first="Cyrille" last="Bertelle">Cyrille Bertelle</name><affiliation wicri:level="3"><nlm:aff id="a3"><institution>Normandie Univ, France; ULH, LITIS, F-76600 Le Havre; FR-CNRS-3638, ISCN, 25 rue Ph. Lebon</institution>, 76600 Le Havre, France</nlm:aff><country xml:lang="fr">France</country><wicri:regionArea>, 76600 Le Havre</wicri:regionArea><placeName><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region><settlement type="city">Le Havre</settlement></placeName></affiliation></author><author><name sortKey="Guan, Jihong" sort="Guan, Jihong" uniqKey="Guan J" first="Jihong" last="Guan">Jihong Guan</name><affiliation wicri:level="1"><nlm:aff id="a2"><institution>Department of Computer Science and Technology, Tongji University</institution>, 4800 Cao'an Road, Shanghai 201804, China</nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>, 4800 Cao'an Road, Shanghai 201804</wicri:regionArea><wicri:noRegion>Shanghai 201804</wicri:noRegion></affiliation></author></analytic><series><title level="j">Scientific Reports</title><idno type="eISSN">2045-2322</idno><imprint><date when="2014">2014</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Cooperative Behavior</term><term>Game Theory</term><term>Humans</term><term>Interpersonal Relations</term><term>Models, Statistical</term><term>Social Networking</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Cooperative Behavior</term><term>Game Theory</term><term>Humans</term><term>Interpersonal Relations</term><term>Models, Statistical</term><term>Social Networking</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Schelling, T C" uniqKey="Schelling T">T. C. Schelling</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ward, H" uniqKey="Ward H">H. Ward</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chiappori, P" uniqKey="Chiappori P">P. Chiappori</name></author><author><name sortKey="Levitt, S" uniqKey="Levitt S">S. Levitt</name></author><author><name sortKey="Groseclose, T" uniqKey="Groseclose T">T. 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Zhou</name></author><author><name sortKey="Wang, W" uniqKey="Wang W">W. Wang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Szolnoki, A" uniqKey="Szolnoki A">A. Szolnoki</name></author><author><name sortKey="Perc, M" uniqKey="Perc M">M. Perc</name></author><author><name sortKey="Danku, Z" uniqKey="Danku Z">Z. Danku</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pinheiro, F L" uniqKey="Pinheiro F">F. L. Pinheiro</name></author><author><name sortKey="Santos, F C" uniqKey="Santos F">F. C. Santos</name></author><author><name sortKey="Pacheco, J M" uniqKey="Pacheco J">J. M. Pacheco</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhang, Y" uniqKey="Zhang Y">Y. Zhang</name></author><author><name sortKey="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M">M. A. Aziz-Alaoui</name></author><author><name sortKey="Bertelle, C" uniqKey="Bertelle C">C. Bertelle</name></author><author><name sortKey="Zhou, S" uniqKey="Zhou S">S. Zhou</name></author><author><name sortKey="Wang, W" uniqKey="Wang W">W. Wang</name></author></analytic></biblStruct></listBibl></div1></back></TEI><affiliations><list><country><li>France</li><li>République populaire de Chine</li></country><region><li>Haute-Normandie</li><li>Région Normandie</li></region><settlement><li>Le Havre</li></settlement></list><tree><country name="France"><region name="Région Normandie"><name sortKey="Zhang, Yichao" sort="Zhang, Yichao" uniqKey="Zhang Y" first="Yichao" last="Zhang">Yichao Zhang</name></region><name sortKey="Aziz Alaoui, M A" sort="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M" first="M. A." last="Aziz-Alaoui">M. A. Aziz-Alaoui</name><name sortKey="Bertelle, Cyrille" sort="Bertelle, Cyrille" uniqKey="Bertelle C" first="Cyrille" last="Bertelle">Cyrille Bertelle</name></country><country name="République populaire de Chine"><noRegion><name sortKey="Zhang, Yichao" sort="Zhang, Yichao" uniqKey="Zhang Y" first="Yichao" last="Zhang">Yichao Zhang</name></noRegion><name sortKey="Guan, Jihong" sort="Guan, Jihong" uniqKey="Guan J" first="Jihong" last="Guan">Jihong Guan</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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