Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke
{"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":"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}
M. Kleshnina, Sabrina Streipert, Joel S. Brown, Kateřina Staňková
{"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 &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 &D to stimulate innovation is an increasing function of the initial CO2 concentration. However, the resource consumers can over-invest in R &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}
{"title":"Evolution of Risk-Taking Behaviour and Status Preferences in Anti-coordination Games","authors":"Manuel Staab","doi":"10.1007/s13235-023-00537-4","DOIUrl":"https://doi.org/10.1007/s13235-023-00537-4","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"2 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136023055","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":"Dynamics of Cournot and Bertrand Firms: Exploring Imitation and Replicator Processes","authors":"Hsiao-Chi Chen, Yunshyong Chow, Shi-Miin Liu","doi":"10.1007/s13235-023-00542-7","DOIUrl":"https://doi.org/10.1007/s13235-023-00542-7","url":null,"abstract":"","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"17 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103997","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}