# American Institute of Mathematical Sciences

ISSN:
2164-6066

eISSN:
2164-6074

All Issues

## Journal of Dynamics and Games

Open Access Articles

2021 doi: 10.3934/jdg.2021030 +[Abstract](903) +[HTML](359) +[PDF](406.64KB)
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This article shows how to apply results of chemical reaction network theory (CRNT) to prove uniqueness and stability of a positive equilibrium for pairs/groups distributional dynamics that arise in game theoretic models. Evolutionary game theory assumes that individuals accrue their fitness through interactions with other individuals. When there are two or more different strategies in the population, this theory assumes that pairs (groups) are formed instantaneously and randomly so that the corresponding pairs (groups) distribution is described by the Hardy–Weinberg (binomial) distribution. If interactions times are phenotype dependent the Hardy-Weinberg distribution does not apply. Even if it becomes impossible to calculate the pairs/groups distribution analytically we show that CRNT is a general tool that is very useful to prove not only existence of the equilibrium, but also its stability. In this article, we apply CRNT to pair formation model that arises in two player games (e.g., Hawk-Dove, Prisoner's Dilemma game), to group formation that arises, e.g., in Public Goods Game, and to distribution of a single population in patchy environments. We also show by generalizing the Battle of the Sexes game that the methodology does not always apply.

2021, 8(2): i-iv doi: 10.3934/jdg.2021016 +[Abstract](745) +[HTML](270) +[PDF](111.69KB)
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2020, 7(3): i-ii doi: 10.3934/jdg.2020011 +[Abstract](1451) +[HTML](449) +[PDF](91.92KB)
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2019, 6(2): i-i doi: 10.3934/jdg.2019006 +[Abstract](2745) +[HTML](873) +[PDF](84.66KB)
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2017, 4(3): 255-284 doi: 10.3934/jdg.2017015 +[Abstract](6502) +[HTML](2304) +[PDF](1062.5KB)
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The new digital economy has renewed interest in how digital agents can innovate. This follows the legacy of John von Neumann dynamical systems theory on complex biological systems as computation. The Gödel-Turing-Post (GTP) logic is shown to be necessary to generate innovation based structure changing Type 4 dynamics of the Wolfram-Chomsky schema. Two syntactic procedures of GTP logic permit digital agents to exit from listable sets of digital technologies to produce novelty and surprises. The first is meta-analyses or offline simulations. The second is a fixed point with a two place encoding of negation or opposition, referred to as the Gödel sentence. It is postulated that in phenomena ranging from the genome to human proteanism, the Gödel sentence is a ubiquitous syntactic construction without which escape from hostile agents qua the Liar is impossible and digital agents become entrained within fixed repertoires. The only recursive best response function of a 2-person adversarial game that can implement strategic innovation in lock-step formation of an arms race is the productive function of the Emil Post [58] set theoretic proof of the Gödel incompleteness result. This overturns the view of game theorists that surprise and innovation cannot be a Nash equilibrium of a game.

2016, 3(3): i-i doi: 10.3934/jdg.201603i +[Abstract](2300) +[PDF](78.9KB)
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The Journal of Dynamics and Games (JDG) is pleased to publish a series of special issues based on research and survey papers presented in the Dynamics and Games Hellenic-Latin meetings: Dynamics, Games and Science III, on the occasion of the 50th birthday of Alberto A. Pinto, Porto; 1st Hellenic-Portuguese meeting, Athens; XV Jornadas Latinoamericanas de Teoría Económica, Guanajuato.
These annual meetings in game theory and applications, with the help of the scientific committees that gather scientists from all around the world, join some of the most notable scientists with young researchers and PhD students. In these meetings the organization committees promote an exciting and friendly atmosphere that helps immensely the scientific interaction among the participants. In these JDG special issues, scientists from all over the world share their latest insights and important results, including the exploration of emerging and current cutting-edge theories and methods in the field.
We are very thankful to the invited editors of this series of special issues, Elvio Accinelli, Carlos Hervés Beloso, Ignacio Garcia-Jurado, Onésimo Hernandez-Lerma, Alberto A. Álvarez López, Jordi Massó, Alejandro Neme, Bruno Oliveira, Athanasios Yannacopoulos, Jorge Zubelli.
2016, 3(4): 335-354 doi: 10.3934/jdg.2016018 +[Abstract](2962) +[PDF](754.9KB)
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A qualitative criterion for a pursuer to intercept a target in a class of differential games is obtained in terms of future cones: Topological cones that contain all attainable trajectories of target or interceptor originating from an initial position. An interception solution exists after some initial time iff the future cone of the target lies within the future cone of the interceptor. The solution may be regarded as a kind of Nash equilibrium. This result is applied to two examples:
1. The game of Two Cars: The future cone condition is shown to be equivalent to conditions for interception obtained by Cockayne.
2. Satellite warfare: The future cone for a spacecraft or direct-ascent antisatellite weapon (ASAT) maneuvering in a central gravitational field is obtained and is shown to equal that for a spacecraft which maneuvers solely by means of a single velocity change at the cone vertex.
The latter result is illustrated with an analysis of the January 2007 interception of the FengYun-1C spacecraft.
2016, 3(2): i-i doi: 10.3934/jdg.201602i +[Abstract](2349) +[PDF](77.3KB)
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The Journal of Dynamics and Games (JDG) is pleased to publish a series of special issues based on research and survey papers presented in the Annual UECE - Lisbon Meetings - Game Theory and Applications.
These annual meetings in game theory and applications, with the help of the scientific committee that gathers scientists from all around the world, join some of the most notable scientists with young researchers and PhD students at ISEG, University of Lisbon. In these meetings the organization committee promotes an exciting and friendly atmosphere that helps immensely the scientific interaction among the participants.
In these JDG special issues, scientists from all over the world share their latest insights and important results, including the exploration of emerging and current cutting-edge theories and methods in the field.
We are very thankful to the invited editors of this series of special issues, Rabah Amir, Gabrielle Demange, Filomena Garcia, Joana Pais, Frank H. Page, Joana Resende and Myrna Wooders.
2015, 2(3&4): i-i doi: 10.3934/jdg.201534i +[Abstract](2521) +[PDF](95.5KB)
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The Journal of Dynamics and Games (JDG) is pleased to do publish these two special issues on Matching: Theory and Applications, dedicated to Marilda Sotomayor on the occasion of her 70th birthday.
Marilda Sotomayor's outstanding and innovative research in the field of matching models has made her renowned. In the paper On Marilda Sotomayor's extraordinary contribution to matching theory, published in these JDG special issues, Danilo Coelho and David Pérez-Castrillo briefly report on Marilda's outstanding contributions. In the paper, A survey on assignment markets, published in these JDG special issues, Marina Núñez and Carles Rafels do a survey on assignment games emphasizing the relevance in this research area of the book Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis, authored by Alvin Roth and Marilda Sotomayor. In the paper, Why do stable clearinghouses work so well? -- small sets of stable matchings in typical environments, and the limits on manipulation theorem of Demange, Gale and Sotomayor, published in these JDG special issues, Alvin Roth explains how an important theorem from Marilda's early work helps us understand today why stable matching clearinghouses work as well as they do.
In these JDG special issues, scientists from all over the world share their latest insights and important results, including the exploration of emerging and current cutting-edge theories and methods in the field.
We are very thankful to the invited editors, Ahmet Alkan, David Pérez Castrillo, John Wooders and, specially, Myrna Wooders for having prepared a premium work of a remarkable scientific and social value!
2014, 1(3): i-iv doi: 10.3934/jdg.2014.1.3i +[Abstract](3389) +[PDF](220.5KB)
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We have the immense pleasure of editing this special issue in honor of Sylvain Sorin. It follows the international conference GameS and StrategY in PariS,'' organized by the French school of mathematical game theory, that was also held in his honor. The conference took place at the Institut Henri Poincaré (IHP) in June 2012, included 21 plenary talks and attracted more than 150 participants.

2020 CiteScore: 0.6