{"id":{"repo_id":"brazil-uerj","oai_identifier":"oai:pantheon.ufrj.br:11422/5997"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-uerj/oai:pantheon.ufrj.br:11422/5997","repository":{"repo_id":"brazil-uerj","name":"Brazil UERJ","base_url":"https://pantheon.ufrj.br/oai/request"},"display":{"title":"Modeling and analysis of market share dynamics in a duopoly subject to affine feedback advertising policies and delays","abstract":"Presents extensions of the Vidale-Wolfe and Lanchester models for market share duopoly dynamics. The novelties in the proposed extensions are the explicit introduction of a set of undecided clients into existing models, which consider only the sets of clients of the two competing firms, as well as the use of decentralized affine feedback advertising policies. It is shown that, under the proposed class of advertising policies, the extended Vidale-Wolfe and Lanchester models, despite having different dynamics, have equilibria in identical locations, with the same stability properties. The introduction of a third set of undecided clients also motivates the introduction of a more elaborate model of market share dynamics based on the replicator-mutator model from evolutionary game theory. This is done by identifying strategies with the entries of a preference matrix consisting of the choice preferences of firms by clients and the mutation matrix representing transition probabilities from one set of clients to another. The proposed model is analysed with respect to equilibria and their stability properties, as well as parametric sensitivity, under the proposed advertising policies. All proposed models are analysed for stability, the presence of oscillations, existence of Hopf bifurcations when implementation or adoption delays are introduced. The extended models of Vidale-Wolfe and Lanchester are robust to implementation delays, while for adoption delays, bifurcations can occur. The proposed replicator-mutator model is robust for both types of delays.","abstract_html":"Presents extensions of the Vidale-Wolfe and Lanchester models for market share duopoly dynamics. The novelties in the proposed extensions are the explicit introduction of a set of undecided clients into existing models, which consider only the sets of clients of the two competing firms, as well as the use of decentralized affine feedback advertising policies. It is shown that, under the proposed class of advertising policies, the extended Vidale-Wolfe and Lanchester models, despite having different dynamics, have equilibria in identical locations, with the same stability properties. The introduction of a third set of undecided clients also motivates the introduction of a more elaborate model of market share dynamics based on the replicator-mutator model from evolutionary game theory. This is done by identifying strategies with the entries of a preference matrix consisting of the choice preferences of firms by clients and the mutation matrix representing transition probabilities from one set of clients to another. The proposed model is analysed with respect to equilibria and their stability properties, as well as parametric sensitivity, under the proposed advertising policies. All proposed models are analysed for stability, the presence of oscillations, existence of Hopf bifurcations when implementation or adoption delays are introduced. The extended models of Vidale-Wolfe and Lanchester are robust to implementation delays, while for adoption delays, bifurcations can occur. The proposed replicator-mutator model is robust for both types of delays.","abstract_has_math":false,"creators":["Aliaga Aliaga, Walter"],"institution":"Universidade Federal do Rio de Janeiro","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Bhaya, Amit"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-09","date_published":"2017-09","updated_at":"2026-07-24T01:16:18Z","subjects":["Sistemas dinâmicos","Modelos matemáticos"],"languages":["eng"],"rights":["Acesso Aberto"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11422/5997","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Bhaya, Amit"]},{"key":"dc:creator","label":"Author","values":["Aliaga Aliaga, Walter"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-12-17T14:07:16Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-16T03:01:39Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-09"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal do Rio de Janeiro"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"]},{"key":"dc:type","label":"Dc Type","values":["Tese"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Sistemas dinâmicos","Modelos matemáticos"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Acesso Aberto"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11422/5997"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Presents extensions of the Vidale-Wolfe and Lanchester models for market share duopoly dynamics. The novelties in the proposed extensions are the explicit introduction of a set of undecided clients into existing models, which consider only the sets of clients of the two competing firms, as well as the use of decentralized affine feedback advertising policies. It is shown that, under the proposed class of advertising policies, the extended Vidale-Wolfe and Lanchester models, despite having different dynamics, have equilibria in identical locations, with the same stability properties. The introduction of a third set of undecided clients also motivates the introduction of a more elaborate model of market share dynamics based on the replicator-mutator model from evolutionary game theory. This is done by identifying strategies with the entries of a preference matrix consisting of the choice preferences of firms by clients and the mutation matrix representing transition probabilities from one set of clients to another. The proposed model is analysed with respect to equilibria and their stability properties, as well as parametric sensitivity, under the proposed advertising policies. All proposed models are analysed for stability, the presence of oscillations, existence of Hopf bifurcations when implementation or adoption delays are introduced. The extended models of Vidale-Wolfe and Lanchester are robust to implementation delays, while for adoption delays, bifurcations can occur. The proposed replicator-mutator model is robust for both types of delays."]},{"key":"dc:title","label":"Title","values":["Modeling and analysis of market share dynamics in a duopoly subject to affine feedback advertising policies and delays"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bhaya, Amit"],"dc:creator":["Aliaga Aliaga, Walter"],"dc:date.accessioned":["2018-12-17T14:07:16Z"],"dc:date.available":["2026-05-16T03:01:39Z"],"dc:date.issued":["2017-09"],"dc:description.abstract":["Presents extensions of the Vidale-Wolfe and Lanchester models for market share duopoly dynamics. The novelties in the proposed extensions are the explicit introduction of a set of undecided clients into existing models, which consider only the sets of clients of the two competing firms, as well as the use of decentralized affine feedback advertising policies. It is shown that, under the proposed class of advertising policies, the extended Vidale-Wolfe and Lanchester models, despite having different dynamics, have equilibria in identical locations, with the same stability properties. The introduction of a third set of undecided clients also motivates the introduction of a more elaborate model of market share dynamics based on the replicator-mutator model from evolutionary game theory. This is done by identifying strategies with the entries of a preference matrix consisting of the choice preferences of firms by clients and the mutation matrix representing transition probabilities from one set of clients to another. The proposed model is analysed with respect to equilibria and their stability properties, as well as parametric sensitivity, under the proposed advertising policies. All proposed models are analysed for stability, the presence of oscillations, existence of Hopf bifurcations when implementation or adoption delays are introduced. The extended models of Vidale-Wolfe and Lanchester are robust to implementation delays, while for adoption delays, bifurcations can occur. The proposed replicator-mutator model is robust for both types of delays."],"dc:identifier.uri":["http://hdl.handle.net/11422/5997"],"dc:language":["eng"],"dc:publisher":["Universidade Federal do Rio de Janeiro"],"dc:publisher.department":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"],"dc:rights":["Acesso Aberto"],"dc:subject":["Sistemas dinâmicos","Modelos matemáticos"],"dc:title":["Modeling and analysis of market share dynamics in a duopoly subject to affine feedback advertising policies and delays"],"dc:type":["Tese"]},"updated_at":"2026-07-24T01:16:18Z"}