Pub Date : 2016-03-28DOI: 10.1142/S0219198915500164
D. Sheetal
This paper analyzes zero sum game involving hybrid controls using viscosity solution theory where both players use discrete as well as continuous controls. We study two problems, one in finite horizon and other in infinite horizon. In both cases, we allow the cost functionals to be unbounded with certain growth, hence the corresponding lower and upper value functions defined in Elliot–Kalton sense can be unbounded. We characterize the value functions as the unique viscosity solution of the associated lower and upper quasi variational inequalities in a suitable function class. Further we find a condition under which the game has a value for both games. The major difficulties arise due to unboundedness of value function. In infinite horizon case we prove uniqueness of viscosity solution by converting the unbounded value function into bounded ones by suitable transformation. In finite horizon case an argument is based on comparison with a supersolution.
{"title":"Viscosity Solutions of Hybrid Game Problems with Unbounded Cost Functionals","authors":"D. Sheetal","doi":"10.1142/S0219198915500164","DOIUrl":"https://doi.org/10.1142/S0219198915500164","url":null,"abstract":"This paper analyzes zero sum game involving hybrid controls using viscosity solution theory where both players use discrete as well as continuous controls. We study two problems, one in finite horizon and other in infinite horizon. In both cases, we allow the cost functionals to be unbounded with certain growth, hence the corresponding lower and upper value functions defined in Elliot–Kalton sense can be unbounded. We characterize the value functions as the unique viscosity solution of the associated lower and upper quasi variational inequalities in a suitable function class. Further we find a condition under which the game has a value for both games. The major difficulties arise due to unboundedness of value function. In infinite horizon case we prove uniqueness of viscosity solution by converting the unbounded value function into bounded ones by suitable transformation. In finite horizon case an argument is based on comparison with a supersolution.","PeriodicalId":45451,"journal":{"name":"International Game Theory Review","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2016-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219198915500164","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64369951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-12-01DOI: 10.1142/S0219198907001643
José Méndez Naya, Luciano Méndez Naya
The effects of tariff wars on welfare are analysed for the case of trade between two countries with outputs of the traded good given exogenously. Assuming mild conditions, it is shown that if there are non-zero tariffs for which welfare-maximizing equilibrium holds, then free trade is not strictly preferable when the countries' outputs are equal, and if they are not equal is strictly disadvantageous to the country with the smaller output. Therefore, the main result of the paper is that free trade is not sustainable in an asymmetric context nor in a symmetric situation.
{"title":"TARIFF RETALIATION AND THE FREE TRADE ARGUMENT","authors":"José Méndez Naya, Luciano Méndez Naya","doi":"10.1142/S0219198907001643","DOIUrl":"https://doi.org/10.1142/S0219198907001643","url":null,"abstract":"The effects of tariff wars on welfare are analysed for the case of trade between two countries with outputs of the traded good given exogenously. Assuming mild conditions, it is shown that if there are non-zero tariffs for which welfare-maximizing equilibrium holds, then free trade is not strictly preferable when the countries' outputs are equal, and if they are not equal is strictly disadvantageous to the country with the smaller output. Therefore, the main result of the paper is that free trade is not sustainable in an asymmetric context nor in a symmetric situation.","PeriodicalId":45451,"journal":{"name":"International Game Theory Review","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219198907001643","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64369542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-09-01DOI: 10.1142/S0219198903001008
R. Amir, J. Bergin, T. Knudsen
{"title":"PREFACE TO THE SPECIAL ISSUE EVOLUTIONARY GAME THEORY 2000","authors":"R. Amir, J. Bergin, T. Knudsen","doi":"10.1142/S0219198903001008","DOIUrl":"https://doi.org/10.1142/S0219198903001008","url":null,"abstract":"","PeriodicalId":45451,"journal":{"name":"International Game Theory Review","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219198903001008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64369422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-09-01DOI: 10.1142/S0219198903001057
Carlos Alós-Ferrer
This paper examines the stability of mixed-strategy Nash equilibria of sym- metric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered and combined with different assumptions about the speed of adjustment. It is found that specific refinements of mixed Nash equi- libria serve to identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 x 2 case, both im- itation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.
{"title":"Finite Population Dynamics and Mixed Equilibria","authors":"Carlos Alós-Ferrer","doi":"10.1142/S0219198903001057","DOIUrl":"https://doi.org/10.1142/S0219198903001057","url":null,"abstract":"This paper examines the stability of mixed-strategy Nash equilibria of sym- metric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered and combined with different assumptions about the speed of adjustment. It is found that specific refinements of mixed Nash equi- libria serve to identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 x 2 case, both im- itation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.","PeriodicalId":45451,"journal":{"name":"International Game Theory Review","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219198903001057","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64369470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.4135/9789353885694.n19
{"title":"The NDA, THE UPA and TWO Types of Chicken","authors":"","doi":"10.4135/9789353885694.n19","DOIUrl":"https://doi.org/10.4135/9789353885694.n19","url":null,"abstract":"","PeriodicalId":45451,"journal":{"name":"International Game Theory Review","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89136115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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