Dynamic Games and Applications最新文献

{"title":"Strategy Complexity of Reachability in Countable Stochastic 2-Player Games.","authors":"Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke","doi":"10.1007/s13235-024-00575-6","DOIUrl":"10.1007/s13235-024-00575-6","url":null,"abstract":"<p><p>We study countably infinite stochastic 2-player games with reachability objectives. Our results provide a complete picture of the memory requirements of <math><mi>ε</mi></math> -optimal (resp. optimal) strategies. These results depend on the size of the players' action sets and on whether one requires strategies that are uniform (i.e., independent of the start state). Our main result is that <math><mi>ε</mi></math> -optimal (resp. optimal) Maximizer strategies requires infinite memory if Minimizer is allowed infinite action sets. This lower bound holds even under very strong restrictions. Even in the special case of infinitely branching turn-based reachability games, even if all states allow an almost surely winning Maximizer strategy, strategies with a step counter plus finite private memory are still useless. Regarding <i>uniformity</i>, we show that for Maximizer there need not exist memoryless (i.e., positional) uniformly <math><mi>ε</mi></math> -optimal strategies even in the special case of finite action sets or in finitely branching turn-based games. On the other hand, in games with finite action sets, there always exists a uniformly <math><mi>ε</mi></math> -optimal Maximizer strategy that uses just one bit of public memory.</p>","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"15 3","pages":"980-1036"},"PeriodicalIF":1.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12222464/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144576787","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":"Hyper Diversity, Species Richness, and Community Structure in ESS and Non-ESS Communities.","authors":"Kailas Shankar Honasoge, Tania L S Vincent, Gordon G McNickle, Roel Dobbe, Kateřina Staňková, Joel S Brown, Joseph Apaloo","doi":"10.1007/s13235-025-00646-2","DOIUrl":"10.1007/s13235-025-00646-2","url":null,"abstract":"<p><p>In mathematical models of eco-evolutionary dynamics with a quantitative trait, two species with different strategies can coexist only if they are separated by a valley or peak of the adaptive landscape. A community is ecologically and evolutionarily stable if each species' trait sits on global, equal fitness peaks, forming a <i>saturated</i> ESS community. However, the adaptive landscape may allow communities with fewer (<i>undersaturated</i>) or more (<i>hypersaturated</i>) species than the ESS. Non-ESS communities at ecological equilibrium exhibit <i>invasion windows</i> of strategies that can successfully invade. <i>Hypersaturated</i> communities can arise through <i>mutual invasibility</i> where each non-ESS species' strategy lies in another's invasion window. Hypersaturation in ESS communities with more than 1 species remains poorly understood. We use the <i>G</i>-function approach to model niche coevolution and Darwinian dynamics in a Lotka-Volterra competition model. We confirm that up to 2 species can coexist in a hypersaturated community with a single-species ESS if the strategy is scalar-valued, or 3 species if the strategy is bivariate. We conjecture that at most <math><mrow><mi>n</mi> <mo>·</mo> <mfenced><mrow><mi>s</mi> <mo>+</mo> <mn>1</mn></mrow> </mfenced> </mrow> </math> species can form a hypersaturated community, where <math><mi>n</mi></math> is the number of ESS species at the strategy's dimension <math><mi>s</mi></math> . For a scalar-valued 2-species ESS, 4 species coexist by \"straddling\" the would-be ESS traits. When our model has a 5-species ESS, we can get 7 or 8, but not 9 or 10, species coexisting in the hypersaturated community. In a bivariate model with a single-species ESS, an infinite number of 3-species hypersaturated communities can exist. We offer conjectures and discuss their relevance to ecosystems that may be non-ESS due to invasive species, climate change, and human-altered landscapes.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s13235-025-00646-2.</p>","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"15 4","pages":"1424-1444"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12460531/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145186436","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":"Stability of the Darwinian Dynamics: Effect of Intraspecific Competition and Human Intervention.","authors":"Mohammadreza Satouri, Jafar Rezaei, Kateřina Staňková","doi":"10.1007/s13235-025-00629-3","DOIUrl":"10.1007/s13235-025-00629-3","url":null,"abstract":"<p><p>We analyze the stability of a game-theoretic model of a polymorphic eco-evolutionary system in the presence of human intervention. The goal is to understand how the intensity of this human intervention and competition within the system impact its stability, with cancer treatment as a case study. In this case study, the physician applies anti-cancer treatment, while cancer, consisting of treatment-sensitive and treatment-resistant cancer cells, responds by evolving more or less treatment-induced resistance, according to Darwinian evolution. We analyze how the existence and stability of the cancer eco-evolutionary equilibria depend on the treatment dose and rate of competition between cancer cells of the two different types. We also identify initial conditions for which the resistance grows unbounded. In addition, we adopt the level-set method to find viscosity solutions of the corresponding Hamilton-Jacobi equation to estimate the basins of attraction of the found eco-evolutionary equilibria and simulate typical eco-evolutionary dynamics of cancer within and outside these estimated basins. While we illustrate our results on the cancer treatment case study, they can be generalized to any situation where a human aims at containing, eradicating, or saving Darwinian systems, such as in managing antimicrobial resistance, fisheries management, and pest management. The obtained results help our understanding of the impact of human interventions and intraspecific competition on the possibility of containing, eradicating, or saving evolving species. This will help us with our ability to control such systems.</p>","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"15 4","pages":"1467-1493"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12460579/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145186790","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":"Stackelberg Stochastic Differential Games in Feedback Information Pattern with Applications","authors":"Qi Huang, Jingtao Shi","doi":"10.1007/s13235-023-00549-0","DOIUrl":"https://doi.org/10.1007/s13235-023-00549-0","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"12 2","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139380777","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":"Asymmetric Replicator Dynamics on Polish Spaces: Invariance, Stability, and Convergence","authors":"Karl D. Lewis, A. J. Shaiju","doi":"10.1007/s13235-023-00546-3","DOIUrl":"https://doi.org/10.1007/s13235-023-00546-3","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"83 12","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957881","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":"Partially-Observed Bilinear Nonzero-Sum Stochastic Differential Game with Affine-Quadratic Discounted Payoff and Application to Competitive Advertising","authors":"Wang Tao, Cheng-Ke Zhang, Lu Yang","doi":"10.1007/s13235-023-00535-6","DOIUrl":"https://doi.org/10.1007/s13235-023-00535-6","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"40 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139009877","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":"Game Theory for Managing Evolving Systems: Challenges and Opportunities of Including Vector-Valued Strategies and Life-History Traits","authors":"M. Kleshnina, Sabrina Streipert, Joel S. Brown, Kateřina Staňková","doi":"10.1007/s13235-023-00544-5","DOIUrl":"https://doi.org/10.1007/s13235-023-00544-5","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"1 4","pages":"1130 - 1155"},"PeriodicalIF":1.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138625390","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":"Evolutionary Games and Applications: Fifty Years of ‘The Logic of Animal Conflict’","authors":"Christian Hilbe, M. Kleshnina, Kateřina Staňková","doi":"10.1007/s13235-023-00545-4","DOIUrl":"https://doi.org/10.1007/s13235-023-00545-4","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"22 9","pages":"1035 - 1048"},"PeriodicalIF":1.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138624125","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":"Competition and Recall in Selection Problems","authors":"Gensbittel Fabien, Pizarro Dana, Jérôme Renault","doi":"10.1007/s13235-023-00539-2","DOIUrl":"https://doi.org/10.1007/s13235-023-00539-2","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"53 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933019","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 Dynamic Game of Strategic Carbon Taxation and Energy Pricing with Green Technology Innovation","authors":"Xiao-Bing Zhang","doi":"10.1007/s13235-023-00541-8","DOIUrl":"https://doi.org/10.1007/s13235-023-00541-8","url":null,"abstract":"Abstract This paper uses a dynamic game to investigate the strategic interactions between carbon taxation by a coalition of resource consumers and (wellhead) energy pricing by a producers’ cartel under the possibility of innovation in a cheap carbon-free technology. The timing of innovation is uncertain, but can be affected by the amount spent on R &amp;D. The results show that the expectation of possible innovation decreases both the initial carbon tax and producer price, resulting in higher initial resource extraction and carbon emissions. Though this ’green paradox’ effect triggered by possible innovation also will appear in the cooperative case (without strategic interactions), the presence of strategic interactions between resource producers and consumers can somewhat restrain such an effect. For both the resource consumers and a global planner, the optimal R &amp;D to stimulate innovation is an increasing function of the initial CO2 concentration. However, the resource consumers can over-invest in R &amp;D relative to the investment level that a global planner would choose.","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934426","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}