Justina Gianatti, Francisco J. Silva, Ahmad Zorkot
{"title":"Approximation of deterministic mean field games under polynomial growth conditions on the data","authors":"Justina Gianatti, Francisco J. Silva, Ahmad Zorkot","doi":"10.3934/jdg.2023018","DOIUrl":"https://doi.org/10.3934/jdg.2023018","url":null,"abstract":"We consider a deterministic mean field game problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect to the state variable. In this framework, we construct a mean field game problem in discrete time and finite state space that approximates equilibria of the original game. Two numerical examples, solved with the fictitious play method, are presented.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010490","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":"Implicit coordination in an $ n $-player target selection game","authors":"S. Patek","doi":"10.3934/jdg.2022027","DOIUrl":"https://doi.org/10.3934/jdg.2022027","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85159429","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":"On two-player games with pure strategies on intervals $ [a, ; b] $ and comparisons with the two-player, two-strategy matrix case","authors":"Zahra Gambarova, D. Glycopantis","doi":"10.3934/jdg.2022015","DOIUrl":"https://doi.org/10.3934/jdg.2022015","url":null,"abstract":"<p style='text-indent:20px;'>We consider games of two-players with utility functions which are not necessarily linear on the product of convex and compact intervals of <inline-formula><tex-math id=\"M2\">begin{document}$ mathcal{R}^2 $end{document}</tex-math></inline-formula>. An issue is how far an analogy can be drawn with two-player, two-strategy matrix games with linear utility functions, where [0, 1] registers probabilities and equilibria are at the intersection of reaction functions. Now, the idea of <inline-formula><tex-math id=\"M3\">begin{document}$ delta $end{document}</tex-math></inline-formula> functions is exploited to construct mixed strategies to look for Nash equilibria (NE). \"Reaction\" functions are constructed and results are obtained graphically. They are related to topological theorems on NE. The games chosen make specific points in relation to existence conditions and properties of solutions. It is a distinguishing feature that an interval [a, b] now registers both pure and mixed strategies. For NE a choice has to be justified. Also \"reaction\" functions are more complicated and their intersection does not guarantee an equilibrium.</p>","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90480883","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":"The game-theoretical modelling of a dynamically evolving network: Revisiting the target sequence 111","authors":"","doi":"10.3934/jdg.2022026","DOIUrl":"https://doi.org/10.3934/jdg.2022026","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85704220","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":"Rumors' spread: A game theoretical approach with the replicator dynamics","authors":"E. Accinelli, L. Quintas, H. Muñiz","doi":"10.3934/jdg.2022020","DOIUrl":"https://doi.org/10.3934/jdg.2022020","url":null,"abstract":"In this paper we study a repeated game and the replicator dynamics to analyze the spread of a rumor in a society formed by two populations. One population is informed about a rumor and communicates the rumor to the other population. According to the preferences of each individual, this rumor is communicated in its original or in a modified form. We analyze the stability of dynamic equilibria. We conclude that there are three possibilities for the spread of a rumor. The rumor may end up being disseminated in its original version or being distorted by the diffusers throughout the society, or a part of the population remains in the long term spreading the rumor in its original form and another in a distorted way.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87235146","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":"Early warning indicators of epidemics on a coupled behaviour-disease model with vaccine hesitance and incomplete data","authors":"Brendon Phillips, C. Bauch","doi":"10.3934/jdg.2022024","DOIUrl":"https://doi.org/10.3934/jdg.2022024","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73159437","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}
Dai Zusai, Ryoji Sawa, Man-Wah Cheung, R. Lahkar, Jiabin Wu
{"title":"Tributes to Bill Sandholm","authors":"Dai Zusai, Ryoji Sawa, Man-Wah Cheung, R. Lahkar, Jiabin Wu","doi":"10.3934/jdg.2022009","DOIUrl":"https://doi.org/10.3934/jdg.2022009","url":null,"abstract":"In this paper, former students of Bill Sandholm provide summaries of Bill's academic contributions as a unifier of evolutionary game theory and also share their personal memories with Bill as a kind, friendly and dedicated mentor. The paper consists on five essays; first on the unification of EGT with the concept of revision protocols and his charming personality, second on stochastic dynamics, third on potential games, fourth on geometric aspects of Bill's analysis, especially on the projection dynamic, and fifth on applications to cultural evolution.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87683614","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}
Lonnie Turpin, Jr., K. Bruchhaus, Keith R. Credo, Gerard Ornas, Jr.
{"title":"Relative entropy and envy-free allocation","authors":"Lonnie Turpin, Jr., K. Bruchhaus, Keith R. Credo, Gerard Ornas, Jr.","doi":"10.3934/jdg.2022013","DOIUrl":"https://doi.org/10.3934/jdg.2022013","url":null,"abstract":"In this brief work, we study a basic environment consisting of a single receiver taking actions based on information (called signals) from multiple senders. The receiver is a rational Bayesian who uses optimization as a mechanism to convert the signals to actions. The conversions are gambles as the actions must be taken before signal reception. Formal comparisons of differences between the solution sets of both prior and posterior optimization frameworks and their respective probability distributions are given. The difference in probability distributions (denoted by relative entropy) presents a useful tool for modifying the receiver's level of risk. We then construct a simple scenario where the receiver acts as a proxy in a Shapely-Shubik-style game with two agents focusing on different objectives under a common risk level. Acting on their behalf, an envy-free allocation mechanism is presented to simultaneously satisfy each using the asymmetric assignment model when findings show the objectives require identical actions.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78803175","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":"On the symmetry relation between different characteristic functions for additively separable cooperative games","authors":"E. Gromova, K. Savin","doi":"10.3934/jdg.2022017","DOIUrl":"https://doi.org/10.3934/jdg.2022017","url":null,"abstract":"<p style='text-indent:20px;'>We analyze 4 characteristic functions <inline-formula><tex-math id=\"M1\">begin{document}$ V^alpha $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">begin{document}$ V^delta $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M3\">begin{document}$ V^zeta $end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id=\"M4\">begin{document}$ V^eta $end{document}</tex-math></inline-formula>, and give a necessary condition for these functions to satisfy the relation <inline-formula><tex-math id=\"M5\">begin{document}$ V^alpha - V^delta = V^zeta - V^eta $end{document}</tex-math></inline-formula> for all coalitions <inline-formula><tex-math id=\"M6\">begin{document}$ S $end{document}</tex-math></inline-formula>. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.</p>","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86912567","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":"Opening the source code: The threat of forking","authors":"A. Seidl, S. Wrzaczek","doi":"10.3934/jdg.2022010","DOIUrl":"https://doi.org/10.3934/jdg.2022010","url":null,"abstract":"Making software open source can have substantial positive effects on the quality and diffusion of a software and strengthen the sales of complementary products. However, it is a large concern of firms that a competitor might use the very same source code to start its own competitive project, a so-called fork. This paper analyzes whether the threat of forking prevents a firm to open its source code. We consider three different regimes: In the first regime a firm develops and sells software under a proprietary license, in the second regime, it uses an open source business model. The third regime is characterized by the competition of two related open source projects. The switching times between the regimes are optimally determined. We find that the optimal strategy substantially depends on the initial state value and the extent to which a competitor can make use of the firm's software quality. A small initial software quality can prevent a firm to open the code when it cannot afford competition, only with a competitive advantage open source is attractive then. For a large initial software quality, a firm would never open the code immediately, it would either wait or keep it proprietary forever.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78801695","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}