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Myopic and non-myopic agent optimization in game theory, economics, biology and artificial intelligence. Kae Nemoto Quantum Information Science National Institute of Informatics, Japan Email: nemoto@nii.ac.jp. Michael J Gagen Institute of Molecular Bioscience University of Queensland

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## Myopic and non-myopic agent optimization in game theory, economics, biology and artificial intelligence

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**Myopic and non-myopic agent optimization in game theory,**economics, biology and artificial intelligence Kae Nemoto Quantum Information Science National Institute of Informatics, Japan Email: nemoto@nii.ac.jp Michael J Gagen Institute of Molecular Bioscience University of Queensland Email: m.gagen@imb.uq.edu.au**Overview: Functional Optimization in Strategic Economics**(and AI) Formalized by von Neumann and Morgenstern,Theory of Games and Economic Behavior (1944) Mathematics / Physics (minimize action)**Overview: Functional Optimization in Strategic Economics**(and AI) Formalized by von Neumann and Morgenstern,Theory of Games and Economic Behavior (1944) Strategic Economics (maximize expected payoff) Functionals: Fully general Not necessarily continuous Not necessarily differentiable Nb: Implicit Assumption of Continuity !!**Overview: Functional Optimization in Strategic Economics**(and AI) Strategic Economics (maximize expected payoff) von Neumann’s “myopic” assumption 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)**Overview: Functional Optimization in Strategic Economics**(and AI) Non-myopic Optimization No communications between players Correlations Constraints and forbidden regions**“Myopic” Economics (= Physics)**Non-myopic Optimization ∞ correlations & ∞ different trees constraint sets Myopic One Constraint = One Tree Overview: Functional Optimization in Strategic Economics (and AI) X Myopic “The” Game Tree lists All play options**Myopic = Missing Information!**Correlation = Information What Information? Nemoto: “It is not what they are doing, its what they are thinking!” • 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**Optimization and Correlations are Non-Commuting!**• Complex Systems Theory • Emergence of Complexity via correlated signals higher order structure**Prokaryotic gene**Eukaryotic gene Hidden layer networking mRNA mRNA & eRNA functions protein protein Mattick: RNA signals in molecular networks 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.**Optimization and Correlations are Non-Commuting!**• Economics • Selfish independent agents: “homo economicus” • Challenges: Japanese Development Economics, Toyota “Just-In-Time” Production System**o**i Optimization and Correlations are Non-Commuting! 1 Player Evolving / Learning Machines (neural and molecular networks) endogenously exploit correlations to alter own decision tree, dynamics and optima o = F(i) = F(t,d) = Ft (d) {F(x,y,z), … ,F(x,x,z),…} Functional Programming, Dataflow computation, re-write architectures, …**Iterated Prisoner’s Dilemma**Iterated Ultimatum Game Chain Store Paradox (Incumbent never fights new market entrants) Discrepancies: Myopic Agent Optimization and Observation Heuristic statistics**?**? Myopic Agent Optimization Strategic Form Normal Form Px Py Sum-Over-Histories or Path Integral formulation von Neumann and Morgenstern (1944): All possible information = All possible move combinations for all histories and all futures**Optimization**Probability of each path Payoff from each stage for each path Sum over all stages Sum over all paths to nth stage Myopic Agent Optimization**x1**y1 1-p p 0 ≤ p ≤ 1/2 • Myopic agents ( probability distributions) • uncorrelated • no additional constraints Backwards Induction & Minimax Myopic Agent Optimization**Fully general, notationally emphasized by:**Optimization Sum over all correlation strategies Payoff for each path Conditioned path probability Sum over all paths given strategy Probability of each strategy Constraint set of each strategy Non-Myopic Agent Optimization**Non-Myopic Agent Optimization in the Iterated Prisoner’s**Dilemma In 1950 Melvin Dresher and Merrill Flood devised a game later called the Prisoner’s Dilemma Two prisoners are in separate cells and must decide to cooperate or defect Cooperation Defect CKR: Common Knowledge of Rationality Payoff Matrix**max **Non-Myopic Agent Optimization in the Iterated Prisoner’s Dilemma Myopic agent assumption**=1 > 0 PN-1,x,HN-2(1) = 1**= 0 > 0 PNx,HN-1(1) = 1 Non-Myopic Agent Optimization in the Iterated Prisoner’s Dilemma Myopic agents: N max constraints Simultaneous solution Backwards Induction myopic agents always defect**2 max constraints**Non-Myopic Agent Optimization in the Iterated Prisoner’s Dilemma Correlated Constraints: (deriving Tit For Tat) < 0 P1x(1) = 0, so Pxcooperates < 0 P1y(1) = 0, so Pycooperates**Non-Myopic Agent Optimization in the Iterated Prisoner’s**Dilemma Families of correlation constraints: k, j index Change of notation: “dot N” = N, “dot dot N” = 2N, “dot dot N-2” = 2N-2, etc Optimize via game theory techniques Many constrained equilibria involving cooperation Cooperation is rational in IPD**Further Reading and Contacts**Kae Nemoto Email: nemoto@nii.ac.jp URL: http://www.qis.ex.nii.ac.jp/knemoto.html Michael J Gagen Email: m.gagen@imb.uq.edu.au URL: http://research.imb.uq.edu.au/~m.gagen/ See: 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)

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