Pub Date : 2023-06-24DOI: 10.1007/s13235-023-00509-8
Jiyeon Park, Paul K. Newton
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.
我们使用d度的Bernstein多项式作为在双组分有限种群、混合良好、频率依赖的进化博弈设置中构建物种进化速率(与固定概率相关)的统一近似的基础。该近似在整个范围内都是有效的$$0 le w le 1$$，其中w是选择压力参数，并均匀收敛到精确解$$d rightarrow infty $$。我们将其与在弱选择极限($$w sim 0$$)中广泛使用的非均匀近似公式以及精确解的数值计算值进行比较。由于在弱选择极限中存在边界层，伯恩斯坦多项式方法在强选择区域($$w sim 1$$)(需要使用更少的模式来获得相同的精度水平)中近似进化速率比在弱选择区域更有效。
{"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}
Pub Date : 2023-06-22DOI: 10.1007/s13235-023-00504-z
Akihiko Yanase, N. Long
{"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}
Pub Date : 2023-06-12DOI: 10.1007/s13235-023-00508-9
J. P. Pinasco, N. Saintier, M. Kind
{"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}
Pub Date : 2023-06-02DOI: 10.1007/s13235-023-00513-y
O. Aydogmus, Yun Kang
{"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}
Pub Date : 2023-05-24DOI: 10.1007/s13235-023-00505-y
A. de Zeeuw
{"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}
Pub Date : 2023-05-22DOI: 10.1007/s13235-023-00506-x
Francis Bloch, A. Mauleon, Vincent Vannetelbosch
{"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}
Pub Date : 2023-04-26DOI: 10.1007/s13235-022-00483-7
Jing Fu, Frank H. Page, Jean-Pierre Zigrand
{"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}
Pub Date : 2023-04-04DOI: 10.1007/s13235-023-00502-1
Theodor Cimpeanu, Francisco C Santos, The Anh Han
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.
{"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}
Pub Date : 2023-03-29DOI: 10.1007/s13235-023-00499-7
Jack Robles
{"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}
Pub Date : 2023-03-28DOI: 10.1007/s13235-023-00501-2
G. Ibragimov
{"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}
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