Journal of Dynamics and Games (JDG)

Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations

Pages: 255 - 284, Volume 4, Issue 3, July 2017      doi:10.3934/jdg.2017015

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Sheri M. Markose - Economics Department, University of Essex, Wivenhoe Park, Colchester, United Kingdom (email)

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.

Keywords:  Type 4 dynamics, Gödel incompleteness, Gödel sentence, off-line simulation, strategic innovation, novelty, surprises, Red Queen arms race, creative and productive sets, productive function, surprise Nash equilibrium.
Mathematics Subject Classification:  Primary: 03D20, 68Q05, 91A40; Secondary: 0300, 92D15.

Received: April 2016;      Revised: April 2017;      Available Online: July 2017.