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DNA computing capabilities for game theory

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Abstract

Problems in game theory can be used for benchmark DNA computations. Large numbers of game strategies and chance events can be assembledinto finite state machines. These many machines perform, in parallel,distinct plays of a game. Strategies can be exposed to selection and breeding.The computational capabilities of DNA are matched with aspects of game theory, but the most interesting problems are yet to be treated.

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References

  • Ackermann J, Wlotzka B and McCaskill JS (1999) In vitro DNA-based predator-prey system with oscillatory kinetics. Bulletin of Mathematical Biology 60(2): 329–354

    Google Scholar 

  • Alspach B (1998) Poker computations. http: //www.math.sfu.ca/~alspach/computations.html.

  • Aumann RJ and Hart S (eds.) (1992) Handbook of Game Theory with Economic Applications, Handbooks in Economics. Elsevier Science Publishers New York

    Google Scholar 

  • Bäck T, Fogel DB and Michalewicz Z (eds) (1997) Handbook of Evolutionary Computation. Institute of Physics Publishing, Philadelphia, PA

    Google Scholar 

  • Barone L and While L (1998) Evolving adaptive play for simplified poker. In: 1998 IEEE International Conference on Computational Intelligence (ICEC '98), pp. 108–113. IEEE publications

  • Barone L and While L (1999) An adaptive learning model for simplified poker using evolutionary algorithms. In: 1999 Congress on Evolutionary Computation (CEC '99), pp. 153–160. IEEE publications

  • Benenson Y, Paz-Elizur T, Adar R, Keinan E, Livneh Z and Shapiro E (2001) Programmable and autonomous computing machine made of biomolecules. Nature 414(1): 430–434

    Google Scholar 

  • Bi H, Chen J, Deaton R, Garzon M, Rubin H and Wood DH (2002) A PCR-based protocol for in vitro selection of non-crosshybridizing oligonucleotides. In (Hagiya and Ohuchi, to appear), Springer-Verlag

  • Billings D (1995) Computer poker. M.Sc. Research Essay

  • Billings D, Peña L, Schaeffer J and Szafron D (2002) The challenge of poker. Artificial Intelligence 134(1-2): 201–240. Special Issue on Games, Computers and Artificial Intelligence

    Google Scholar 

  • Breaker RR, Banerji A and Joyce GF (1994) Continuous in vitro evolution of bacteriophage RNA polymerase promoters. Biochemistry 33(39): 11980–11986

    Google Scholar 

  • Chen J, Antipov E, Lemieux B, Cedeño W and Wood DH (2000) In vitro selection for a One Max DNA Genetic Algorithm. In: Gifford D and Winfree E (eds) DNA Based Computers V: DIMACS Workshop, June 14-15, 1999, Vol. 54 of DIMACS series in Discrete Mathematics and Theoretical Computer Science, pp. 23–37. American Mathematical Society, Providence, RI

    Google Scholar 

  • Chen J and Wood DH (2000) Computation with biomolecules. Proceedings of the National Academy of Sciences, USA 97(4): 1328–1330. Invited commentary

    Google Scholar 

  • Conitzer V and Sandholm T (2002) Complexity results about Nash equilibria. Technical Report CMU-CS-02-135, Carnegie Mellon University Computer Science Department, Pittsburgh, PA

    Google Scholar 

  • Cressman R (1992) The Stability Concept of Evolutionary Game Theory (A Dynamic Approach), Vol. 94 of Lecture Notes in Biomathematics. Springer-Verlag, New York

    Google Scholar 

  • Cressman R (2003) Evolutionary Dynamics and Extensive Form Games. The MIT Press, Cambridge, MA

    Google Scholar 

  • Deaton RJ and Garzon MH (2001) Fuzzy logic with biomolecules. Soft Computing 5(1): 2–9. Special issue on Biomolecular Approaches to Soft Computing

    Google Scholar 

  • Garzon M and Deaton R (1999) Biomolecular computing and programming. Transactions on Evolutionary Computation 3(3): 236–250

    Google Scholar 

  • Garzon M and Oehmen C (2002) Biomolecular computation in virtual test tubes. In: (Jonoska and Seeman, 2002), pp. 117–128. Springer

  • Gilboa I and Zemel E (1989) Nash and correlated equilibria: Some complexity considerations. Games and Economic Behavior 1: 80–93

    Google Scholar 

  • Gintis H (2000) Game Theory Evolving. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Hagiya M (2002) Perspecitves on molecular computing. New Generation Computing 17: 131–151

    Google Scholar 

  • Hagiya M and Ohuchi A (eds) (to appear) DNA Computing, 8th International Workshop on DNA-Based Computers, DNA8, Hokkaido University, Japan, June 10-13, 2002. Revised Papers, Vol. 2568 of Lecture Notes in Computer Science. Springer-Verlag, Berlin

    Google Scholar 

  • Han M, Gao X, Su JZ and Nie S (2001) Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules. Nature Biochemistry 19: 631–635

    Google Scholar 

  • Heller M, Edman C and Esener S (1998) Electric field assisted self-assembly of DNA structures: A potential nanofabrication technology. Sixth Foresight Conference on Molecular Nanotechnology.

  • Heller MJ (2001) Microelectronic array devices: New designs for DNA diagnostic, biomedical research, and pharmacogenomic applications. In: Lab-on-a-Chip and Microarrays. Newton Upper Falls, MA. Abstract only

  • Herrera F, Lozano M and Verdegay J (1994) Generating fuzzy rules from examples using genetic algorithms. Proc. IPMU'94 (5th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems), pp. 675–680

  • Jonoska N and Seeman N (eds) (2002) DNA Computing: 7th InternationalWorkshop on DNABased Computers, DNA7, Tampa, FL, USA, June 10-13, 2001. Revised Papers, Vol. 2340 of Lecture Notes in Computer Science. Springer

  • Kain RY (1972) Automata Theory: Machines and Languages. McGraw Hill, New York

    Google Scholar 

  • Kendall G and Willdig M (2001) An investigation of an adaptive poker player. In: Australian Joint Conference on Artificial Intelligence, pp. 189–200

  • Klir G and Folger T (1988) Fuzzy Sets, Uncertainty and Information. Prentice Hall International

  • Koller D and Pfeffer A (1997) Representations and solutions for game-theoretic problems. Artificial Intelligence 94(1-2): 167–215

    Google Scholar 

  • Komiya K, Sakamoto K, Gouzo H, Yokoyama S, Arita M, Nishikawa A and Hagiya M (2000) Successive state transitions with I/O interface by molecules. In: (Winfree and Gifford, 2000), pp. 21–30. American Mathematical Society, Providence, RI

    Google Scholar 

  • Komiya K, Sakamoto K, Gouzo H, Yokoyama S, Arita M, Nishikawa A and Hagiya M (2000) Successive state transitions with I/O interface by molecules. In: Condon A and Rozenberg G (eds.), DNA Computing: Revised papers / 6th International Workshop on DNA Based Computers, DNA 2000, Vol. 2054 of Lecture Notes in Computer Science, pp. 17–26, Springer-Verlag, Berlin

    Google Scholar 

  • Kuhn HW (1953) Extensive games and the problem of information. In: Kuhn HW and Tucker AW (eds), Contributions to the Theory of Games II, Annals of Mathematical Studies, pp. 193–216. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Lawrence S and Giles C (1999) Accessibility of information on the web. Nature 400: 107-109

    Google Scholar 

  • McCaskill JS (2001) Optically programming DNA computing in microflow reactors. Biosystems 59(2): 125–138

    Google Scholar 

  • McCaskill JS, Penchovsky R, Gohlke M, Ackermann J and Rucker T (2000) Steady flow micro-reactor module for pipelined DNA computation. In: (Winfree and Gifford, 2000), pp. 239–246, American Mathematical Society, Providence, RI

    Google Scholar 

  • Mills AP Jr., Turberfield M, Turberfield AJ, Yurke B and Platzman PM (2001) Experimental aspects of DNA neural network computation. Soft Computing 5(1): 10–18. Special issue on Biomolecular Approaches to Soft Computing

    Google Scholar 

  • micro.htm.

  • Nash JF Jr. (1950) Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, USA 36: 48–49

    Google Scholar 

  • Nishikawa A, Yamamura M and Hagiya M (2001) DNA computation simulator based on abstract bases. Soft Computing 5(1): 25–38. Special issue on Biomolecular Approaches to Soft Computing

    Google Scholar 

  • Nash JF Jr. (1996) Motovation and interpretation. In: Nash JF Jr. (ed) Essays on Game Theory, pp. 31–33. Edward Edgar Publishing, Limited, Cheltenham, UK. Previously unpublished appendix from Ph. D. Thesis

    Google Scholar 

  • Nash JF Jr. and Shapley LS (1950) A simple three-person poker game. In: Kuhn HW and Tucker AW(eds) Contributions to the Theory of Games I, Annals of Mathematical Studies, pp. 105–116. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Osborne M and Rubinstein A (1994) A Course in Game Theory. MIT Press, Boston, MA

    Google Scholar 

  • Papadimitriou CH (2001) Algorithms, games, and the Internet. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing: STOC'01, July 6-8, 2001, Hersonissos, Crete, Greece, pp. 749–753. ACM Press, New York

    Google Scholar 

  • Pena-Reyes CA and Sipper M (2001) Fuzzy CoCo: Balancing accuracy and interpretability of fuzzy models by means of coevolution. IEEE Transactions on Fuzzy Systems 9(5): 727–737

    Google Scholar 

  • Reif JH (2002) The emerging discipline of biomolecular computation in the US. New Generation Computing 20(3): 217–236

    Google Scholar 

  • Rose JA, Deaton RJ, Hagiya M and Suyama A (2001) The fidelity of the tag-antitag system. In: (Jonoska and Seeman, 2002), pp. 138–149, Springer

  • SantaLucia J Jr. (1998) A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proceedings of the National Academy of Sciences, USA 95(4): 1460–1465

    Google Scholar 

  • Schmitt T and Lehman N (1999) Non-unity molecular heritability demonstrated by continuous evolution in vitro. Chemistry and Biology 12(6): 857–869

    Google Scholar 

  • Stemmer WPC (1995) The evolution of molecular computation. Science 270: 1510–1510

    Google Scholar 

  • van Noort D, Gast FU and McCaskill JS (2002) DNA computing in microreactors. In: (Jonoska and Seeman, 2002), pp. 128–137. Springer

  • Vartanian JP, Henry M and WainHobson S (1996) Hypermutagenic PCR involving all four transitions and a sizeable proportion of transversions. Nucleic Acids Research 24(14): 2627–2631

    Google Scholar 

  • von Neumann J and Morgenstern O (1944) Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Wetmur JG (1999) Physical chemistry of nucleic acid hybridization. In: DNA Based Computers III: DIMACS Workshop, June 23-25, 1997, Vol. 48 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 1–14, American Mathematical Society, Providence

    Google Scholar 

  • html/Papers/whiplash.ps.

    Google Scholar 

  • Winfree E and Gifford DK (eds) (2000) DNA based computers V: DIMACS workshop, June 14-15, 1999, Vol. 54 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, Providence, RI

  • Wood DH, Bi H, Kimbrough SO, Wu D and Chen J (2001a) DNA starts to learn poker. In: (Jonoska and Seeman, 2002), pp. 92–103. Springer

  • Wood DH, Chen J, Antipov E, Lemieux B and Cedeño W(2001b) A design for DNA computation of the OneMax problem. Soft Computing 5(1): 19–24. Special issue on Biomolecular Approaches to Soft Computing

    Google Scholar 

  • Wood DH, Clelland CLT and Bancroft C (2003) Universal biochip readout of directed Hamiltonian path problems. In: (Hagiya and Ohuchi, pear). Springer-Verlag

  • Wurmbach E, Yuen T, Ebersole BJ and Sealfon SC (2001) Gonadotropin-releasing hormone receptor-coupled gene network organization. Journal of Biological Chemistry 276(50): 47195–47201

    Google Scholar 

  • Yokomori T (2002) Molecular computing paradigm - toward freedom from Turing's charm. Natural Computing 1: 333–390

    Google Scholar 

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Wood, D.H. DNA computing capabilities for game theory. Natural Computing 2, 85–108 (2003). https://doi.org/10.1023/A:1023332711880

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