This article recalls the recent work on a linear programming formulation of infinite horizon risk-sensitive control via its equivalence with a single controller game, using a classic work of Vrieze. This is then applied to a constrained risk-sensitive control problem with a risk-sensitive cost and risk-sensitive constraint. This facilitates a Lagrange multiplier based resolution thereof. In the process, this leads to an unconstrained linear program and its dual, parametrized by a parameter that is a surrogate for Lagrange multiplier. This also opens up the possibility of a primal - dual type numerical scheme wherein the linear program is a subroutine within the subgradient ascent based update rule for the Lagrange multiplier. This equivalent unconstrained risk-sensitive control formulation does not seem obvious without the linear programming equivalents as intermediaries. We also discuss briefly other related algorithmic possibilities for future research.
{"title":"Risk-sensitive control, single controller games and linear programming","authors":"V. Borkar","doi":"10.3934/jdg.2023024","DOIUrl":"https://doi.org/10.3934/jdg.2023024","url":null,"abstract":"This article recalls the recent work on a linear programming formulation of infinite horizon risk-sensitive control via its equivalence with a single controller game, using a classic work of Vrieze. This is then applied to a constrained risk-sensitive control problem with a risk-sensitive cost and risk-sensitive constraint. This facilitates a Lagrange multiplier based resolution thereof. In the process, this leads to an unconstrained linear program and its dual, parametrized by a parameter that is a surrogate for Lagrange multiplier. This also opens up the possibility of a primal - dual type numerical scheme wherein the linear program is a subroutine within the subgradient ascent based update rule for the Lagrange multiplier. This equivalent unconstrained risk-sensitive control formulation does not seem obvious without the linear programming equivalents as intermediaries. We also discuss briefly other related algorithmic possibilities for future research.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"36 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139313159","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}
{"title":"Network games and solutions from decomposition techniques","authors":"J. Sánchez-Pérez","doi":"10.3934/jdg.2023009","DOIUrl":"https://doi.org/10.3934/jdg.2023009","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"66 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72559820","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}
Clarissa Astuto, Jan Haskovec, Peter Markowich, Simone Portaro
We study self-regulating processes modeling biological transportation networks as presented in [15]. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result under the assumption of positivity of the diffusivity $ D $. We explore systematically various scenarios and gain insights into the behavior of $ D $ and its impact on the studied system. This involves analyzing the system with a signed measure distribution of sources and sinks. Finally, we perform several numerical tests in which the solution $ D $ touches zero, confirming the previous hints of local existence in particular cases.
我们研究了模拟生物运输网络的自调节过程，如[15]所示。我们特别关注Dirichlet和Neumann边界条件的一维设置。我们证明了在扩散系数为正的假设下的一个存在唯一性结果。我们系统地探索各种场景，并深入了解$ D $的行为及其对所研究系统的影响。这包括用源和汇的有符号测量分布来分析系统。最后，我们进行了几个解$ D $为零的数值测试，在特定情况下证实了前面的局部存在性提示。
{"title":"Self-regulated biological transportation structures with general entropy dissipations, part Ⅰ: The 1D case","authors":"Clarissa Astuto, Jan Haskovec, Peter Markowich, Simone Portaro","doi":"10.3934/jdg.2023022","DOIUrl":"https://doi.org/10.3934/jdg.2023022","url":null,"abstract":"We study self-regulating processes modeling biological transportation networks as presented in [15]. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result under the assumption of positivity of the diffusivity $ D $. We explore systematically various scenarios and gain insights into the behavior of $ D $ and its impact on the studied system. This involves analyzing the system with a signed measure distribution of sources and sinks. Finally, we perform several numerical tests in which the solution $ D $ touches zero, confirming the previous hints of local existence in particular cases.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135709289","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}
{"title":"Optimal economic policy and growth in an open economy","authors":"E. Casares, M. García-Salazar","doi":"10.3934/jdg.2023008","DOIUrl":"https://doi.org/10.3934/jdg.2023008","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"61 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77076684","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}
Agenda setting is a key feature of political systems. We propose a novel approach to contrast the respective power of candidates and parties when bargaining over agenda, which consists in comparing the simulations of four institutional models: single term with candidates proposing, single term with parties proposing, two-term with candidates proposing and two-term with parties proposing. Valences of candidates and preferences for alternation of voters are two important components of the analysis. Simulations establish that two-term schemes are inefficient, while term limits is a second order component of the agenda setting bargaining, while the offering side is the main component.
{"title":"Empowering of candidates and parties in single term vs re-election schemes","authors":"Fernanda Herrera López, David Cantala","doi":"10.3934/jdg.2023019","DOIUrl":"https://doi.org/10.3934/jdg.2023019","url":null,"abstract":"Agenda setting is a key feature of political systems. We propose a novel approach to contrast the respective power of candidates and parties when bargaining over agenda, which consists in comparing the simulations of four institutional models: single term with candidates proposing, single term with parties proposing, two-term with candidates proposing and two-term with parties proposing. Valences of candidates and preferences for alternation of voters are two important components of the analysis. Simulations establish that two-term schemes are inefficient, while term limits is a second order component of the agenda setting bargaining, while the offering side is the main component.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135157751","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}
This paper presents a quantitative approach to hedging financial risks associated with changes in international oil prices for companies that import crude oil. The authors utilize the Geometric Brownian Motion model to capture the dynamic behavior of prices over time. To determine the optimal use of Call-options, the authors formulate a linear problem that minimizes the Conditional Value-at-Risk of the distribution of losses relative to the expected budget. The solution to this problem is obtained through a combination of Linear Programming optimization and Monte Carlo simulation. It enables the identification of the best Call-option offer that minimizes the risk of financial losses while staying within budget constraints. The validity of the proposed methodology is demonstrated through detailed examples that showcase its capabilities.
{"title":"Appraising the convenience of a call-based dynamical hedging strategy for an oil-company","authors":"Claudio RISSO, Juan Piccini, Bernardo Zimberg","doi":"10.3934/jdg.2023015","DOIUrl":"https://doi.org/10.3934/jdg.2023015","url":null,"abstract":"This paper presents a quantitative approach to hedging financial risks associated with changes in international oil prices for companies that import crude oil. The authors utilize the Geometric Brownian Motion model to capture the dynamic behavior of prices over time. To determine the optimal use of Call-options, the authors formulate a linear problem that minimizes the Conditional Value-at-Risk of the distribution of losses relative to the expected budget. The solution to this problem is obtained through a combination of Linear Programming optimization and Monte Carlo simulation. It enables the identification of the best Call-option offer that minimizes the risk of financial losses while staying within budget constraints. The validity of the proposed methodology is demonstrated through detailed examples that showcase its capabilities.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306276","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}
Alexander Von Moll, Zachariah Fuchs, Daigo Shishika, Dipankar Maity, Michael Dorothy, Meir Pachter
In this paper, a zero-sum differential game is formulated and solved in which a mobile Evader seeks to escape from within a circle at whose origin lies a stationary, turn-constrained Turret. The scenario is a variant of the famous Lady in the Lake game in which the shore-constrained Pursuer has been replaced with the Turret. As in the former, it is assumed that the Turret's maximum angular rate is greater than the linear velocity of the Evader. Since two outcomes are possible, a Game of Kind arises - either the Evader wins by reaching the perimeter of the circle, or the Turret wins by aligning with the latter's position. A barrier surface partitions the state space into two regions corresponding to these two outcomes and a Game of Degree is solved within each region. The solutions to the Games of Degree are comprised of the Value functions (i.e., the equilibrium value of the cost/utility as a function of the state) and the saddle-point equilibrium control policies for the two players. Like the Lady in the Lake game, the equilibrium policy of the Evader is not uniquely defined where it has angular rate advantage over the Turret. Unlike the Lady in the Lake game, the losing region for the Evader is present for all speed ratios, and there is an additional semi-permeable surface separating center- and shore-bound Evader trajectories. The solution depends heavily upon the speed ratio of the agents; in particular, there are two speed ratio regimes with distinctive solution structures.
{"title":"Turret escape differential game","authors":"Alexander Von Moll, Zachariah Fuchs, Daigo Shishika, Dipankar Maity, Michael Dorothy, Meir Pachter","doi":"10.3934/jdg.2023012","DOIUrl":"https://doi.org/10.3934/jdg.2023012","url":null,"abstract":"In this paper, a zero-sum differential game is formulated and solved in which a mobile Evader seeks to escape from within a circle at whose origin lies a stationary, turn-constrained Turret. The scenario is a variant of the famous Lady in the Lake game in which the shore-constrained Pursuer has been replaced with the Turret. As in the former, it is assumed that the Turret's maximum angular rate is greater than the linear velocity of the Evader. Since two outcomes are possible, a Game of Kind arises - either the Evader wins by reaching the perimeter of the circle, or the Turret wins by aligning with the latter's position. A barrier surface partitions the state space into two regions corresponding to these two outcomes and a Game of Degree is solved within each region. The solutions to the Games of Degree are comprised of the Value functions (i.e., the equilibrium value of the cost/utility as a function of the state) and the saddle-point equilibrium control policies for the two players. Like the Lady in the Lake game, the equilibrium policy of the Evader is not uniquely defined where it has angular rate advantage over the Turret. Unlike the Lady in the Lake game, the losing region for the Evader is present for all speed ratios, and there is an additional semi-permeable surface separating center- and shore-bound Evader trajectories. The solution depends heavily upon the speed ratio of the agents; in particular, there are two speed ratio regimes with distinctive solution structures.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135550570","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}
{"title":"Dynamic stability of the set of Nash equilibria in stable stochastic games","authors":"Divya Murali, A. Shaiju","doi":"10.3934/jdg.2023004","DOIUrl":"https://doi.org/10.3934/jdg.2023004","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"52 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74790398","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}
{"title":"Cooperation in problems of common-pool resources","authors":"Jesús Erubiel Ordaz-Cuevas, J. Sánchez-Pérez","doi":"10.3934/jdg.2023010","DOIUrl":"https://doi.org/10.3934/jdg.2023010","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"299 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79669193","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}
Joshua Sin, John W. Bonnes, Luke C. Brown, David M. Ambrose
Time-dependent mean field games are a coupled system of a forward parabolic and backward parabolic partial differential equation. Stationary solutions are of interest, and then naturally the forward-backward structure in time becomes irrelevant. Forward-forward mean field games have been introduced with the rationale that they may be used to straightforwardly compute such stationary solutions. We perform some numerical simulations to find that typically stationary solutions of mean field games are unstable to the forward-forward evolution, i.e. frequently only trivial solutions can be found in this way. We then ask whether there are situations in which one would have reason to believe that the stationary solutions would be stable, and we use the exchange-of-stability phenomenon in bifurcation theory to give a class of examples for which the forward-forward solutions do converge to nontrivial stationary solutions as time increases.
{"title":"Existence and computation of stationary solutions for congestion-type mean field games via bifurcation theory and forward-forward problems","authors":"Joshua Sin, John W. Bonnes, Luke C. Brown, David M. Ambrose","doi":"10.3934/jdg.2023014","DOIUrl":"https://doi.org/10.3934/jdg.2023014","url":null,"abstract":"Time-dependent mean field games are a coupled system of a forward parabolic and backward parabolic partial differential equation. Stationary solutions are of interest, and then naturally the forward-backward structure in time becomes irrelevant. Forward-forward mean field games have been introduced with the rationale that they may be used to straightforwardly compute such stationary solutions. We perform some numerical simulations to find that typically stationary solutions of mean field games are unstable to the forward-forward evolution, i.e. frequently only trivial solutions can be found in this way. We then ask whether there are situations in which one would have reason to believe that the stationary solutions would be stable, and we use the exchange-of-stability phenomenon in bifurcation theory to give a class of examples for which the forward-forward solutions do converge to nontrivial stationary solutions as time increases.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135755084","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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