Myopic and non-myopic agent optimization in game theory, economics, biology and artificial intelligence Michael J Gagen Institute of Molecular Bioscience University of Queensland Email: [email protected]Kae Nemoto Quantum Information Science National Institute of Informatics, Japan Email: [email protected]
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Myopic and non-myopic agent optimization in game theory, economics, biology and artificial intelligence Michael J Gagen Institute of Molecular Bioscience.
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Myopic and non-myopic agent optimization in game theory, economics, biology and
Overview: Functional Optimization in Strategic Economics (and AI)
Mathematics / Physics (minimize action)
Formalized by von Neumann and Morgenstern, Theory of Games and Economic Behavior (1944)
Overview: Functional Optimization in Strategic Economics (and AI)
Strategic Economics (maximize expected payoff)
Formalized by von Neumann and Morgenstern, Theory of Games and Economic Behavior (1944)
Functionals: Fully general
Not necessarily continuous
Not necessarily differentiable
Nb: Implicit Assumption of Continuity !!
von Neumann’s “myopic” assumption
Overview: Functional Optimization in Strategic Economics (and AI)
Strategic Economics (maximize expected payoff)
Evidence:
von Neumann & Nash used fixed point theorems in probability simplex equivalent to a convex subset of a real vector space
von Neumann and Morgenstern, Theory of Games and Economic Behavior (1944)J. F. Nash, Equilibrium points in n-person games. PNAS, 36(1):48–49 (1950)
Non-myopic Optimization
Correlations Constraints and forbidden regions
Overview: Functional Optimization in Strategic Economics (and AI)
No communications between players
∞ correlations & ∞ different trees constraint sets
Non-myopic Optimization
Overview: Functional Optimization in Strategic Economics (and AI)
Myopic “The” Game Tree lists All play options
Myopic One Constraint = One Tree
“Myopic” Economics (= Physics)
Myopic = Missing Information!
Correlation = Information
Chess:
“Chunking” or pattern recognition in human chess play
Experts: Performance in speed chess doesn’t degrade much Rapidly direct attention to good moves Assess less than 100 board positions per move Eye movements fixate only on important positions Re-produce game positions after brief exposure better than novices, but random positions only as well as novices
Learning Strategy = Learning information to help win game
Nemoto: “It is not what they are doing, its what they are thinking!”
What Information?
Optimization and Correlations are Non-Commuting!
Complex Systems Theory
Emergence of Complexity via correlated signals higher order structure
Optimization and Correlations are Non-Commuting!
Life Sciences (Evolutionary Optimization)
Selfish Gene Theory
Mayr: Incompatibility between biology and physicsRosen: “Correlated” Components in biology, rather than “uncorrelated” partsMattick: Biology informs information science
6 Gbit DNA program more complex than any human program, implicating RNA as correlating signals allowing multi-tasking and developmental control of complex organisms.
Mattick: RNA signals in molecular networksProkaryotic gene
mRNA
protein
Eukaryotic gene
mRNA & eRNA
protein
networking functions
Hidden layer
Optimization and Correlations are Non-Commuting!
Economics
Selfish independent agents: “homo economicus”
Challenges: Japanese Development Economics,Toyota “Just-In-Time” Production System
Cooperative equilibria in the finite iterated prisoner's dilemma, K. Nemoto and M. J. Gagen, EconPapers:wpawuwpga/0404001 (http://econpapers.hhs.se/paper/wpawuwpga/0404001.htm)