Advertisement

Theory in Biosciences

, Volume 134, Issue 1–2, pp 17–46 | Cite as

Non-cooperative game theory in biology and cooperative reasoning in humans

  • Alihan Kabalak
  • Elena Smirnova
  • Jürgen JostEmail author
Original Paper

Abstract

The readiness for spontaneous cooperation together with the assumptions that others share this cooperativity has been identified as a fundamental feature that distinguishes humans from other animals, including the great apes. At the same time, cooperativity presents an evolutionary puzzle because non-cooperators do better in a group of cooperators. We develop here an analysis of the process leading to cooperation in terms of rationality concepts, game theory and epistemic logic. We are, however, not attempting to reconstruct the actual evolutionary process. We rather want to provide the logical structure underlying cooperation in order to understand why cooperation is possible and what kind of reasoning and beliefs would lead to cooperative decision-making. Game theory depends on an underlying common belief in non-cooperative rationality of the players, and cooperativity similarly can utilize a common belief in cooperative rationality as its basis. We suggest a weaker concept of rational decision-making in games that encompasses both types of decision-making. We build this up in stages, starting from simple optimization, then using anticipation of the reaction of others, to finally arrive at reflexive and cooperative reasoning. While each stage is more difficult than the preceding, importantly, we also identify a reduction of complexity achieved by the consistent application of higher stage reasoning.

Keywords

Game theory Rationality Cooperation Complexity reduction 

Notes

Acknowledgments

We are grateful to Martin Kell, Oliver Pfante, Nils Bertschinger, Eckehard Olbrich and Michael Tomasello for several insightful discussions. We also thank two anonymous referees for their helpful comments and suggestions.

References

  1. Aumann R, Brandenburger A (1995) Epistemic conditions for Nash equilibrium. Econometrica 63(5):1161–1180CrossRefGoogle Scholar
  2. Aumann R (1999) Interactive epistemology II: probability. Int J Game Theory 28(3):301–314CrossRefGoogle Scholar
  3. Axelrod R, Hamilton WD (1981) The evolution of cooperation. Science 211:1390–1396PubMedCrossRefGoogle Scholar
  4. Axelrod R (1997) The evolution of strategies in the iterated prisoner’s dilemma. In: Bicchieri C, Jeffrey R, Skyrms B (eds) The dynamics of norms. Cambridge University Press, Cambridge, pp 1–16Google Scholar
  5. Battigalli P (1997) On rationalizability in extensive games. J Econ Theory 74:40–61CrossRefGoogle Scholar
  6. Battigalli P, Siniscalchi M (2002) Strong belief and forward induction reasoning. J Econ Theory 106(2):356–391CrossRefGoogle Scholar
  7. Battigalli P, Dufwenberg M (2007) Guilt in games. Am Econ Rev 97(2):170–176CrossRefGoogle Scholar
  8. Behne T, Liszkowski U, Carpenter M, Tomasello M (2012) Twelve-month-olds comprehension and production of pointing. Br J Dev Psychol 30:359–375PubMedCrossRefGoogle Scholar
  9. Bernheim B (1984) Rationalizable strategic behavior. Econometrica 52(4):1007–1028CrossRefGoogle Scholar
  10. Boesch C, Boesch H (1989) Hunting behavior of wild chimpanzees in the Tai National Park. Am J Phys Anthropol 78:547–573PubMedCrossRefGoogle Scholar
  11. Boesch C (1994) Cooperative hunting in wild chimpanzees. Anim Behav 48:653–667CrossRefGoogle Scholar
  12. Boesch C (2005) Joint cooperative hunting among wild chimpanzees: taking natural observations seriously. Behav Brain Sci 28:692693CrossRefGoogle Scholar
  13. Bradfield J, Stirling C (2007) Modal mu-calculi. In: Studies in logic and practical reasoning, vol 3, pp 72156Google Scholar
  14. Bräuer J, Call J, Tomasello M (2005) All Great Ape species follow gaze to distant locations and around barriers. J Comp Psychol 119–2:145–154CrossRefGoogle Scholar
  15. Camaioni L, Perucchini P, Bellagamba F, Colonnesi C (2004) The role of declarative pointing in developing a theory of mind. Infancy 5–3:291–308CrossRefGoogle Scholar
  16. Carpenter M, Tomasello M, Striano T (2005) Role reversal imitation in 12 and 18 month olds and children with autism. Infancy 8:253–278CrossRefGoogle Scholar
  17. Cäsar C, Zuberbühler K, Young RJ, Byrne RW (2013) Titi monkey call sequences vary with predator location and type. Biol Lett 9(5). doi:  10.1098/rsbl.2013.0535
  18. Chellas B (1984) Modal logic: an introduction. Cambridge University Press, CambridgeGoogle Scholar
  19. Cheney D, Seyfarth R (1990) How monkeys see the world: Inside the mind of another species. University of Chicago Press, ChicagoGoogle Scholar
  20. Cochet H, Vauclair J (2010) Pointing gesture in young children: hand preference and language development. Gesture 10(2–3):129–149CrossRefGoogle Scholar
  21. Cochet H, Vauclair J (2010) Pointing gestures produced by toddlers from 15 to 30 months: different functions, hand shapes and laterality patterns. Infant Behav Dev 33:431–441PubMedCrossRefGoogle Scholar
  22. Cubitt R, Sugden R (2003) Common knowledge. Salience and convention: a reconstruction of David Lewis’ game theory. Econ Philos 19(2):175–210CrossRefGoogle Scholar
  23. Ditmarsch H, Van der Hoek W, Kooi B (2007) Dynamic epistemic logic. Springer, New YorkCrossRefGoogle Scholar
  24. Fagin R, Halpern J (1988) Belief, awareness and limited reasoning. Artif Intell 34:39–76CrossRefGoogle Scholar
  25. Fagin R, Halpern J, Moses Y, Vardi M (1995) Reasoning about knowledge. MIT Press, CambridgeGoogle Scholar
  26. Franco F, Butterworth G (1996) Pointing and social awareness: declaring and requesting in the second year. J Child Lang 23:307–336PubMedCrossRefGoogle Scholar
  27. Fudenberg D, Tirole J (1991) Game theory. MIT Press, CambridgeGoogle Scholar
  28. Fukuyama F (1996) Trust: human nature and the reconstitution of social order: the social virtues and the creation of prosperity. Free press, New YorkGoogle Scholar
  29. Gigerenzer G, Todd P (1999) Simple heuristics that make us smart. Oxford University Press, OxfordGoogle Scholar
  30. Gintis H (2000) Strong reciprocity and human sociality. J Theor Biol 206:169–179PubMedCrossRefGoogle Scholar
  31. Gintis H, Bowles S, Boyd R, Fehr E (eds) (2005) Moral sentiments and material interests. MIT Press, CambridgeGoogle Scholar
  32. Gould SJ (2002) The structure of evolutionary theory. Harvard University Press, CambridgeGoogle Scholar
  33. Gould SJ, Vrba S (1982) Exaptation—a missing term in the science of form. Paleobiology 8:4–15Google Scholar
  34. Grice HP (1957) Meaning. Philos Rev 66:377–388CrossRefGoogle Scholar
  35. Halpern J (2003) Reasoning about uncertainty. MIT Press, CambridgeGoogle Scholar
  36. Hamilton W (1964) The genetical evolution of social behaviour, I. J Theor Biol 7:1–16PubMedCrossRefGoogle Scholar
  37. Hare B, Call J, Tomasello M (2006) Chimpanzees deceive a human competitor by hiding. Cognition 101:495–514PubMedCrossRefGoogle Scholar
  38. Hauser M (1996) The evolution of communication. MIT Press, CambridgeGoogle Scholar
  39. Heifetz A, Meier M, Schipper B (2006) Interactive unawareness. J Econ Theory 130:78–94CrossRefGoogle Scholar
  40. Jensen K, Call J, Tomasello M (2007) Chimpanzees are rational maximizers in an ultimatum game. Science 318:107–109PubMedCrossRefGoogle Scholar
  41. Johnstone P (1995) Sexual selection, honest advertisement and the handicap principle: reviewing the evidence. Biol Rev 70:1–65PubMedCrossRefGoogle Scholar
  42. Jost J (2004) External and internal complexity of complex adaptive systems. Theory Biosci 123:69–88PubMedCrossRefGoogle Scholar
  43. Jost J (2005) Formal aspects of the emergence of institutions, structure and dynamics. J Anthropol Relat Sci 1(1). https://escholarship.org/uc/item/6p64s9j0
  44. Jost J (2006) Temporal correlation based learning in neuron models. Theory Biosci 125:37–53PubMedCrossRefGoogle Scholar
  45. Kirchhof J, Hammerschmidt K (2007) Functionally referential alarm calls in Tamarins (Saguinis fusicollis and Saguinis mystax)—evidence from playback experiments. Ethology 112:346–354CrossRefGoogle Scholar
  46. Kokolakis A, Smith C, Evans C (2010) Aerial alarm calling by male fowl (Gallus gallus) reveals subtle new mechanisms of risk management. Anim Behav 79(6):1373–1380CrossRefGoogle Scholar
  47. Kozen D (1983) Results on the propositional \(\mu\)-calculus. Theor Comput Sci 27:333–354CrossRefGoogle Scholar
  48. Lewis D (1969) Convention: a philosophical study. Harvard University Press, CambridgeGoogle Scholar
  49. Lewis D (2001) Counterfactuals. Wiley, New YorkGoogle Scholar
  50. Lorini E, Longin D, Gaudou B, Herzig A (2009) The logic of acceptance: grounding institutions on agents’ attitudes. J Log Comput 19(6):901–940 (Oxford University Press)CrossRefGoogle Scholar
  51. Lorini E, Schwarzentruber F (2010) A modal logic of epistemic games. Games 1:478–526CrossRefGoogle Scholar
  52. Luhmann N (1987) Soziale systeme. Suhrkamp, Frankfurt/MGoogle Scholar
  53. Macedonia JM (1990) What is communicated in the antipredator calls of lemurs: evidence from antipredator call playbacks to Ringtailed and Ruffled Lemurs. Ethology 86:177–190CrossRefGoogle Scholar
  54. Maschler M, Solan E, Zamir S (2013) Game theory. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  55. Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  56. Morgan R, Hunt S (1994) The commitment-trust theory of relationship marketing. J Market 58:20–38CrossRefGoogle Scholar
  57. Nash J (1951) Non-cooperative games. Ann Math 54(2):286–295CrossRefGoogle Scholar
  58. von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, PrincetonGoogle Scholar
  59. Olson M (1965) The logic of collective action. Harvard University Press, CambridgeGoogle Scholar
  60. Ostrom E (1990) Governing the commons. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  61. Pearce D (1984) Rationalizable strategic behavior and the problem of perfection. Econometrica 52:1029–1050CrossRefGoogle Scholar
  62. Povinelli DJ, Reaux JE, Bierschwale DT, Allain AD, Simon BB (1997) Exploitation of pointing as a referential gesture in young children, but not adolescent chimpanzees. Cogn Dev 12:423–461CrossRefGoogle Scholar
  63. Rainey HJ, Zuberbühler K, Slater PJB (2004) Hornbills can distinguish between primate alarm calls. Proc R Soc Lond B 271:205–207CrossRefGoogle Scholar
  64. Savage LJ (1954) The foundations of statistics. Wiley, New YorkGoogle Scholar
  65. Searle J (2001) Rationality in action. MIT Press, CambridgeGoogle Scholar
  66. Seyfarth R, Cheney D, Marler P (1980) Vervet monkey alarm calls: semantic communication in a free-ranging primate. Anim Behav 28:10701094Google Scholar
  67. Seyfarth R, Cheney D (2003) Signalers and receivers in animal communication. Annu Rev Psychol 54:145173CrossRefGoogle Scholar
  68. Shannon C (1998) The mathematical theory of communication, 1949, reproduced. In: Shannon C, Weaver W, Blahut R, Hajek B (eds) The mathematical theory of communication. University of Illinois Press, pp 29–125Google Scholar
  69. Shettleworth S (2010) Cognition, evolution, and behavior. Oxford University Press, OxfordGoogle Scholar
  70. Simon HA (1955) A behavioral model of rational choice. Q J Econ 69(1):99118CrossRefGoogle Scholar
  71. Simon HA (1956) Rational choice and the structure of environments. Psych Rev 63:129138CrossRefGoogle Scholar
  72. Skyrms B (2010) Signals: evolution, learning, and information. Oxford University Press, OxfordCrossRefGoogle Scholar
  73. Slanina F (2010) Essentials of econophysics modelling. Oxford University Press, OxfordGoogle Scholar
  74. Slobodchikoff CN, Kiriazis J, Fischer C, Creef E (1991) Semantic information distinguishing individual predators in the alarm calls of Gunnison’s Prairie Dogs. Anim Behav 42:713–719CrossRefGoogle Scholar
  75. Smith C, Taylor A, Evans C (2011) Tactical multimodal signalling in birds: facultative variation in signal modality reveals sensitivity to social costs. Anim Behav 82:521–527CrossRefGoogle Scholar
  76. Southgate V, van Maanen C, Csibra G (2007) Infant pointing: communication to cooperate or communication to learn? Child Dev 78–3:735–740CrossRefGoogle Scholar
  77. Sperber D, Wilson D (1995) Relevance: communication and cognition. Blackwell, OxfordGoogle Scholar
  78. Stalnaker R (1996) Knowledge, belief and counterfactual reasoning in games. Econ Philos 12:133–163CrossRefGoogle Scholar
  79. Struhsaker T (1967) Auditory communication among vervet monkeys (Cercopithecus aethiops). In: Altmann SA (ed) Social communication among primates. University of Chicago Press, Chicago, pp. 281324Google Scholar
  80. Sugden R (2003) The logic of team reasoning. Philos Explor 6(3):165–181. doi:  10.1080/10002003098538748 CrossRefGoogle Scholar
  81. Tomasello M (2006) Why don’t apes point? In: Enfield NJ, Levinson SC (eds) Roots of human sociality: culture, cognition and interaction. berg, Oxford, pp 506–524Google Scholar
  82. Tomasello M (2008) Origins of human communication. MIT Press, CambridgeGoogle Scholar
  83. Tomasello M (2011) Human culture in evolutionary perspective. In: Gelfand M (ed) Advances in culture and psychology. Oxford University Press, Oxford, pp 5–51Google Scholar
  84. Tomasello M, Hare B, Agnetta B (1999) Chimpanzees follow gaze direction geometrically. Anim Behav 58:769–777PubMedCrossRefGoogle Scholar
  85. Tomasello M, Zuberbuehler K (2002) Primate vocal and gestural communication. In: Bekoff M, Allen C, Burghardt G (eds) The cognitive animal: empirical and theoretical perspectives on animal cognition. MIT Press, CambridgeGoogle Scholar
  86. Tomasello M, Carpenter M, Call J, Behne T, Moll H (2005) In search of the uniquely human. Behav Brain Sci 28:721727Google Scholar
  87. Tomasello M, Carpenter M (2007) Shared intentionality. Dev Sci 10(1):121125CrossRefGoogle Scholar
  88. Trivers R (1971) The evolution of reciprocal altruism. Q Rev Biol 46:35–57CrossRefGoogle Scholar
  89. Tuomela R (2005) We-intentions revisited. Philos Stud 125:327–369CrossRefGoogle Scholar
  90. Vygotsky LS (1962) Thought and language. MIT Press, CambridgeCrossRefGoogle Scholar
  91. Workman L, Reader W (2004) Evolutionary psychology. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  92. Zahavi A (1977) Reliability in communication systems and the evolution of altruism. In: Stonehouse B, Perrins C (eds) Evolutionary ecology. Mac Millan, London, pp 253–259Google Scholar
  93. Zuberbuehler K, Cheney D, Seyfarth R (1999) Conceptual semantics in a nonhuman primate. J Comp Psychol 113:3342Google Scholar
  94. Zuberbuehler K (2000) Referential labeling in Diana monkeys. Anim Behav 59:917–927CrossRefGoogle Scholar
  95. Zuberbuehler K (2001) Predator-specific alarm calls in Campbell’s monkeys, Cercopithecus campbelli. Behav Ecol Sociobiol 50:414–422CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.German DepartmentLeibniz Universität HannoverHannoverGermany
  3. 3.Santa Fe Institute for the Sciences of ComplexitySanta FeUSA

Personalised recommendations