{"title":"Bernstein Polynomial Approximation of Fixation Probability in Finite Population Evolutionary Games","authors":"Jiyeon Park, Paul K. Newton","doi":"10.1007/s13235-023-00509-8","DOIUrl":"https://doi.org/10.1007/s13235-023-00509-8","url":null,"abstract":"We use the Bernstein polynomials of degree d as the basis for constructing a uniform approximation to the rate of evolution (related to the fixation probability) of a species in a two-component finite-population, well-mixed, frequency-dependent evolutionary game setting. The approximation is valid over the full range $$0 le w le 1$$ , where w is the selection pressure parameter, and converges uniformly to the exact solution as $$d rightarrow infty $$ . We compare it to a widely used non-uniform approximation formula in the weak-selection limit ( $$w sim 0$$ ) as well as numerically computed values of the exact solution. Because of a boundary layer that occurs in the weak-selection limit, the Bernstein polynomial method is more efficient at approximating the rate of evolution in the strong selection region ( $$w sim 1$$ ) (requiring the use of fewer modes to obtain the same level of accuracy) than in the weak selection regime.","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"181 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135842658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mixed Market Structure and R &D: A Differential Game Approach","authors":"Akihiko Yanase, N. Long","doi":"10.1007/s13235-023-00504-z","DOIUrl":"https://doi.org/10.1007/s13235-023-00504-z","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41513996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Learning, Mean Field Approximations, and Phase Transitions in Auction Models","authors":"J. P. Pinasco, N. Saintier, M. Kind","doi":"10.1007/s13235-023-00508-9","DOIUrl":"https://doi.org/10.1007/s13235-023-00508-9","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45027211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Deterministic Approximation of a Stochastic Imitation Dynamics with Memory","authors":"O. Aydogmus, Yun Kang","doi":"10.1007/s13235-023-00513-y","DOIUrl":"https://doi.org/10.1007/s13235-023-00513-y","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42662808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Review of Tipping Points and Precaution using HJB equations","authors":"A. de Zeeuw","doi":"10.1007/s13235-023-00505-y","DOIUrl":"https://doi.org/10.1007/s13235-023-00505-y","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49474864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Preface to the Special issue on “Group Formation and Farsightedness”","authors":"Francis Bloch, A. Mauleon, Vincent Vannetelbosch","doi":"10.1007/s13235-023-00506-x","DOIUrl":"https://doi.org/10.1007/s13235-023-00506-x","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"13 1","pages":"435 - 439"},"PeriodicalIF":1.5,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44515014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: Layered Networks, Equilibrium Dynamics, and Stable Coalitions","authors":"Jing Fu, Frank H. Page, Jean-Pierre Zigrand","doi":"10.1007/s13235-022-00483-7","DOIUrl":"https://doi.org/10.1007/s13235-022-00483-7","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"13 1","pages":"669-704"},"PeriodicalIF":1.5,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47241746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Does Spending More Always Ensure Higher Cooperation? An Analysis of Institutional Incentives on Heterogeneous Networks.","authors":"Theodor Cimpeanu, Francisco C Santos, The Anh Han","doi":"10.1007/s13235-023-00502-1","DOIUrl":"10.1007/s13235-023-00502-1","url":null,"abstract":"<p><p>Humans have developed considerable machinery used at scale to create policies and to distribute incentives, yet we are forever seeking ways in which to improve upon these, our institutions. Especially when funding is limited, it is imperative to optimise spending without sacrificing positive outcomes, a challenge which has often been approached within several areas of social, life and engineering sciences. These studies often neglect the availability of information, cost restraints or the underlying complex network structures, which define real-world populations. Here, we have extended these models, including the aforementioned concerns, but also tested the robustness of their findings to stochastic social learning paradigms. Akin to real-world decisions on how best to distribute endowments, we study several incentive schemes, which consider information about the overall population, local neighbourhoods or the level of influence which a cooperative node has in the network, selectively rewarding cooperative behaviour if certain criteria are met. Following a transition towards a more realistic network setting and stochastic behavioural update rule, we found that carelessly promoting cooperators can often lead to their downfall in socially diverse settings. These emergent cyclic patterns not only damage cooperation, but also decimate the budgets of external investors. Our findings highlight the complexity of designing effective and cogent investment policies in socially diverse populations.</p>","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":" ","pages":"1-20"},"PeriodicalIF":1.8,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10072037/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10093478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Evolution, Investment, and Bargaining","authors":"Jack Robles","doi":"10.1007/s13235-023-00499-7","DOIUrl":"https://doi.org/10.1007/s13235-023-00499-7","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"1 1","pages":"1-25"},"PeriodicalIF":1.5,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44187941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Evasion Differential Game of One Evader and Many Slow Pursuers","authors":"G. Ibragimov","doi":"10.1007/s13235-023-00501-2","DOIUrl":"https://doi.org/10.1007/s13235-023-00501-2","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"1 1","pages":"1-21"},"PeriodicalIF":1.5,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43804371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}