×

Direct reciprocity in structured populations. (English) Zbl 1355.91062

Summary: Reciprocity and repeated games have been at the center of attention when studying the evolution of human cooperation. Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Here we explore an open-ended, infinite strategy space, where every strategy that can be encoded by a finite state automaton is a possible mutant. Surprisingly, we find that direct reciprocity alone does not lead to high levels of cooperation. Instead we observe perpetual oscillations between cooperation and defection, with defection being substantially more frequent than cooperation. The reason for this is that “indirect invasions” remove equilibrium strategies: every strategy has neutral mutants, which in turn can be invaded by other strategies. However, reciprocity is not the only way to promote cooperation. Another mechanism for the evolution of cooperation, which has received as much attention, is assortment because of population structure. Here we develop a theory that allows us to study the synergistic interaction between direct reciprocity and assortment. This framework is particularly well suited for understanding human interactions, which are typically repeated and occur in relatively fluid but not unstructured populations. We show that if repeated games are combined with only a small amount of assortment, then natural selection favors the behavior typically observed among humans: high levels of cooperation implemented using conditional strategies.

MSC:

91D10 Models of societies, social and urban evolution
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] REV ECON STUD 38 pp 1– (1971) · Zbl 0274.90072 · doi:10.2307/2296617
[2] 54 pp 533– (1986) · Zbl 0615.90099 · doi:10.2307/1911307
[3] 56 pp 383– (1988) · Zbl 0637.90108 · doi:10.2307/1911077
[4] Axelrod, Science 211 (4489) pp 1390– (1981) · Zbl 1225.92037 · doi:10.1126/science.7466396
[5] The Behavioral and brain sciences 7 pp 115– (1984) · doi:10.1017/S0140525X00026479
[6] Nature; Physical Science (London) 327 pp 58– (1987) · doi:10.1038/327058a0
[7] Nature; Physical Science (London) 327 pp 15– (1987) · doi:10.1038/327015a0
[8] Nature; Physical Science (London) 355 pp 250– (1992) · doi:10.1038/355250a0
[9] Nowak, Nature; Physical Science (London) 364 (6432) pp 56– (1993) · doi:10.1038/364056a0
[10] PNAS 102 (31) pp 10797– (2005) · doi:10.1073/pnas.0502589102
[11] The American economic review 80 pp 274– (1990)
[12] 57 pp 278– (1992) · Zbl 0767.90095 · doi:10.1016/0022-0531(92)90037-I
[13] 28 pp 167– (1994) · Zbl 0877.90099 · doi:10.1016/0165-4896(94)90002-7
[14] The American economic review 101 pp 411– (2011) · doi:10.1257/aer.101.1.411
[15] Liberman, Personality and Social Psychology Bulletin 30 (9) pp 1175– (2004) · doi:10.1177/0146167204264004
[16] Bendor, PNAS 92 (8) pp 3596– (1995) · Zbl 0820.92016 · doi:10.1073/pnas.92.8.3596
[17] 39 pp 251– (1990)
[18] Animal Behaviour 39 pp 989– (1990) · doi:10.1016/S0003-3472(05)80966-2
[19] Clutton-Brock, Nature; Physical Science (London) 462 (7269) pp 51– (2009) · doi:10.1038/nature08366
[20] Hamilton, Journal of Theoretical Biology 7 (1) pp 1– (1964) · doi:10.1016/0022-5193(64)90038-4
[21] Eshel, PNAS 79 (4) pp 1331– (1982) · Zbl 0491.92024 · doi:10.1073/pnas.79.4.1331
[22] Nature; Physical Science (London) 359 pp 826– (1992) · doi:10.1038/359826a0
[23] Theoretical population biology 46 pp 363– (1994) · Zbl 0846.92027 · doi:10.1006/tpbi.1994.1032
[24] 149 pp 336– (1997) · doi:10.1086/285993
[25] Journal of evolutionary biology 13 pp 814– (2000) · doi:10.1046/j.1420-9101.2000.00219.x
[26] PNAS 103 (29) pp 10952– (2006) · doi:10.1073/pnas.0602530103
[27] Fletcher, Proceedings of the Royal Society B: Biological Sciences 276 (1654) pp 13– (2009) · doi:10.1098/rspb.2008.0829
[28] van Veelen, Journal of Theoretical Biology 259 (3) pp 589– (2009) · Zbl 1402.92324 · doi:10.1016/j.jtbi.2009.04.019
[29] Tarnita, Journal of Theoretical Biology 259 (3) pp 570– (2009) · Zbl 1402.91064 · doi:10.1016/j.jtbi.2009.03.035
[30] Nowak, Philosophical Transactions of the Royal Society B: Biological Sciences 365 (1537) pp 19– (2010) · doi:10.1098/rstb.2009.0215
[31] 74 pp 382– (2012) · Zbl 1279.91032 · doi:10.1016/j.geb.2011.05.010
[32] 14 pp 54– (2005) · doi:10.1002/evan.20046
[33] Palla, Nature; Physical Science (London) 446 (7136) pp 664– (2007) · doi:10.1038/nature05670
[34] Boyd, Journal of Theoretical Biology 132 (3) pp 337– (1988) · doi:10.1016/S0022-5193(88)80219-4
[35] Ohtsuki, Journal of Theoretical Biology 247 (3) pp 462– (2007) · doi:10.1016/j.jtbi.2007.03.018
[36] PNAS 108 (6) pp 2334– (2011) · doi:10.1073/pnas.1016008108
[37] PNAS 108 (48) pp 19193– (2011) · doi:10.1073/pnas.1108243108
[38] Oxford Surveys in Evolutionary Biology 2 pp 28– (1985)
[39] INT GAME THEORY REV 5 pp 211– (2003) · Zbl 1051.91076 · doi:10.1142/S0219198903001021
[40] Wedekind, PNAS 93 (7) pp 2686– (1996) · doi:10.1073/pnas.93.7.2686
[41] 144 pp 1135– (2009) · Zbl 1159.91336 · doi:10.1016/j.jet.2008.10.005
[42] The American economic review 102 pp 720– (2012) · doi:10.1257/aer.102.2.720
[43] Rand, Journal of Theoretical Biology 256 (1) pp 45– (2009) · Zbl 1400.91054 · doi:10.1016/j.jtbi.2008.09.015
[44] Dasgupta, Philosophical Transactions of the Royal Society B: Biological Sciences 364 (1533) pp 3301– (2009) · doi:10.1098/rstb.2009.0123
[45] J CONFLICT RESOLUTION 32 pp 367– (1988) · doi:10.1177/0022002788032002006
[46] Boyd, Journal of Theoretical Biology 136 (1) pp 47– (1989) · doi:10.1016/S0022-5193(89)80188-2
[47] J CONFLICT RESOLUTION 39 pp 183– (1995) · doi:10.1177/0022002795039001008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.