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 2164-6066

eISSN:
 2164-6074

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Volume 5, 2018

Volume 4, 2017

Volume 3, 2016

Volume 2, 2015

Volume 1, 2014

Journal of Dynamics & Games

Open Access Articles

Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations
Sheri M. Markose
2017, 4(3): 255-284 doi: 10.3934/jdg.2017015 +[Abstract](922) +[HTML](588) +[PDF](1062.5KB)
Abstract:

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.

Preface
Alberto Adrego Pinto and Michel Benaim
2016, 3(3): i-i doi: 10.3934/jdg.201603i +[Abstract](244) +[PDF](78.9KB)
Abstract:
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.
Interception in differential pursuit/evasion games
John A. Morgan
2016, 3(4): 335-354 doi: 10.3934/jdg.2016018 +[Abstract](296) +[PDF](754.9KB)
Abstract:
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.
Preface
Alberto Adrego Pinto and Michel Benaim
2016, 3(2): i-i doi: 10.3934/jdg.201602i +[Abstract](287) +[PDF](77.3KB)
Abstract:
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.
Preface
Alberto Adrego Pinto and Michel Benaïm
2015, 2(3&4): i-i doi: 10.3934/jdg.201534i +[Abstract](373) +[PDF](95.5KB)
Abstract:
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!

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