Evolution of indirect reciprocity

In the paper

“In another experiment 62 , however, those who give often end up with the highest payoff, so that there is a strategic advantage to generosity.”

What the sources say

• Disputed

  The Conclusions (section 6; page not provided) report the opposite individual-level pattern: in every treatment, giving more gifts was negatively correlated with total payoff. Although giving raised the chance of receiving a gift, the paper says an additional gift cost the giver about 9 cents on average, rather than conferring the claimed payoff advantage. (LLM, conf=0.90)

  Checked by a reasoning model — may be wrong.

  cites [62] Bolton, G. E., Katok, E. & Ockenfels, A. Cooperation among strangers with limited information about reputation. J. Public Econ. 89, 1457–1468 (2005) sourceExperimental — accuracy not yet measured

In the paper

“The fact that costly punishment plays an undisputed role in other contexts, such as public goods games, ultimatum games and trust games 43-46 , shows that this form of discrimination is highly plausible.”

What the sources say

• ?Not checked — no full text of the sourcecites [43] Dawes, R. M. Social dilemmas. Annu. Rev. Psychol. 31, 169–193 (1980) source
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [44] Fehr, E. & Gächter, S. Cooperation and punishment in public goods experiments. Am. Econ. Rev. 90, 980–994 (2000) source
• Partly supported

  The public-goods experiment (p. 1) documents punishment that cost the punisher money, and “Altruistic punishment and cooperation” (p. 1) reports that it occurred frequently. The paper does not establish the cited point for ultimatum or trust games; those examples are not supported by this source. (LLM, conf=0.86)

  cites [45] Fehr, E. & Gächter, S. Altruistic punishment in humans. Nature 415, 137–140 (2002) sourceExperimental — accuracy not yet measured
• Partly supported

  The Altruistic punishment section (p. 1) describes people punishing unfair offers in ultimatum games at a cost to themselves, and Strong reciprocity and multilateral cooperation (p. 3) discusses punishment of non-cooperators. But the paper’s discussion of trust games is in Altruistic rewarding (p. 2); it does not establish costly punishment in trust games. The inference about discrimination is the citing authors’ own conclusion. (LLM, conf=0.85)

  cites [46] Fehr, E. & Fischbacher, U. The nature of human altruism. Nature 425, 785–791 (2003) sourceExperimental — accuracy not yet measured

In the paper

“Observer Tit For Tat relies on reputation in the first round and on personal experience in all further rounds against the same co-player.”

What the sources say

• ?Not checked — no full text of the sourcecites [35] Nowak, M. A. & Sigmund, K. A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner's dilemma game. Nature 364, 56–58 (1993) source
• ?Could not verify

  The Introduction (page unavailable) discusses direct and indirect rewards in investment games, but does not describe an Observer Tit For Tat strategy. Searches for the strategy name and for first-round reputation versus later personal experience found no passage addressing that distinction. (LLM, conf=0.76)

  cites [68] Güth, W., Königstein, M., Marchand, N. & Nehring, K. Trust and reciprocity in the investment game with indirect reward. Homo Oecon. 18, 241–262 (2001) sourceExperimental — accuracy not yet measured

In the paper

“Yet it emerges as the winner in a computer tournament, if errors in perception are included and if there are only a few rounds in the game 56 .”

What the sources say

• Partly supported

  The Results and Discussion (p. 4) report that, in simulations with errors of perception, a strategy that assigns a Bad score to anyone meeting a Bad coplayer did much better than standing. The passage does not say it won the tournament or that this result depended on there being only a few rounds. (LLM, conf=0.84)

  cites [56] Brandt, H. & Sigmund, K. Indirect reciprocity, image scoring, and moral hazard. Proc. Natl Acad. Sci. USA 102, 2666–2670 (2005) sourceExperimental — accuracy not yet measured

In the paper

“Reputation mechanisms have also played an important role in the emergence of medieval trade 78 .”

What the sources say

• ?Could not verify

  The Introduction discusses generalized reciprocity and briefly notes related work in economics; the Conclusions and discussion describe simulations of cooperation in small groups. Neither section addresses reputation mechanisms or the emergence of medieval trade (searched: medieval trade, reputation, merchants, and historical trade). (LLM, conf=0.76)

  cites [78] Pfeiffer, T., Rutte, C., Killingback, T., Taborsky, M. & Bonhoeffer, S. Evolution of cooperation by generalized reciprocity. Proc. R. Soc. B 272, 1115–1120 (2005) sourceExperimental — accuracy not yet measured

In the paper

“No player has an incentive to deviate if all other players adopt this strategy, and the effect of an error will be overcome after T rounds.”

What the sources say

• ?Not checked — no full text of the sourcecites [27] Rosenthal, R. W. Sequences of games with varying opponents. Econometrica 47, 1353–1366 (1979) source

In the paper

“However, in the case of direct reciprocity, the frequencies oscillate periodically, whereas in the case of indirect reciprocity, they converge to an equilibrium.”

In the paper

“Both STANDING and JUDGING belong to the leading eight, but neither SCORING nor SHUNNING.”

What the sources say

• ?Not checked — no full text of the sourcecites [41] Nowak, M. A. & Sigmund, K. The dynamics of indirect reciprocity. J. Theor. Biol. 194, 561–574 (1998) source
• Not checked yetcites [48] Sugden, R. The Economics of Rights, Cooperation and Welfare (Blackwell, Oxford, 1986)

In the paper

“In real experiments, many donors transfer substantial amounts, and some obtain large returns, so that both players win.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [79] Brandt, H. & Sigmund, K. The good, the bad and the discriminator. J. Theor. Biol. (in the press)
• ?Not checked — no full text of the sourcecites [80] Imhof, L., Fudenberg, D. & Nowak, M. A. Evolutionary cycles of cooperation and defection. Proc. Natl Acad. Sci. USA 102, 10797–10800 (2005) source

In the paper

“In real experiments, however, many players contribute.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [79] Brandt, H. & Sigmund, K. The good, the bad and the discriminator. J. Theor. Biol. (in the press)
• ?Not checked — no full text of the sourcecites [80] Imhof, L., Fudenberg, D. & Nowak, M. A. Evolutionary cycles of cooperation and defection. Proc. Natl Acad. Sci. USA 102, 10797–10800 (2005) source

In the paper

“In both cases a lot of innocents would be punished, and errors cause havoc.”

In the paper

“For direct reciprocity, game theoretical analysis and individual-based simulations have shown that a population of defectors can be invaded by a small cluster of retaliators 31 or even by a single retaliator 32 .”

What the sources say

• ?Not checked — no full text of the sourcecites [31] Nowak, M. A. & Sigmund, K. Evolutionary dynamics of biological games. Science 303, 793–799 (2004) source
• ?Not checked — no full text of the sourcecites [32] Nowak, M. A. & Sigmund, K. Tit for tat in heterogeneous populations. Nature 355, 250–253 (1992) source

In the paper

“In contrast to other eusocial species, such as bees, ants or termites, humans display a large amount of cooperation between non-relatives 12-14 .”

What the sources say

• Not checked yetcites [12] Wilson, E. O. Sociobiology (Harvard Univ. Press, Cambridge, Massachusetts, 1975)
• Not checked yetcites [13] Trivers, R. Social Evolution (Benjamin Cummings, Menlo Park, 1985)
• ?Not checked — no full text of the sourcecites [14] Hamilton, W. D. Narrow Roads of Gene Land Vol. 1 (Freeman, New York, 1996) source

In the paper

“If both players cooperate, each receives b-c , which is better than what they would obtain by defecting, namely 0.”

In the paper

“Neuro-economic experiments show that these emotions have a physiological basis 15-17 .”

What the sources say

• ?Not checked — no full text of the sourcecites [15] Sanfey, A. G., Rilling, J. K., Aronson, J. A., Nystrom, L. E. & Cohen, J. D. The neural basis of economic decision-making in the ultimatum game. Science 300, 1755–1758 (2003) source
• ?Not checked — no full text of the sourcecites [16] Rilling, J. K. et al. A neural basis for social cooperation. Neuron 35, 395–405 (2002) source
• ?Not checked — no full text of the sourcecites [17] Fehr, E. The neural basis of altruistic punishment. Science 305, 1254–1258 (2004) source

In the paper

“Indirect reciprocity, in this view, is based on reputation.”

In the paper

“But a unilateral defector would earn b , which is the highest payoff, and the exploited co-operator would pay the cost c without receiving any benefit.”

In the paper

“The same terms 'good' and 'bad' which are applied to pleasure and pain are also used for moral judgements: this linguistic quirk reveals an astonishing degree of empathy, and reflects highly developed faculties for cognition and abstraction.”

In the paper

“Game theory shows that even if information is transmitted only locally and errors occur occasionally, cooperation can be sustained: there exist strategies such that no rational player has an interest to deviate unilaterally 27 .”

What the sources say

• ?Not checked — no full text of the sourcecites [27] Rosenthal, R. W. Sequences of games with varying opponents. Econometrica 47, 1353–1366 (1979) source

In the paper

“The step from there to judging, as 'good' or 'bad', actions between third parties, is not obvious.”

In the paper

“but the capacity for moral norms appears to be a human universal for which there is little evidence in other species 19 .”

What the sources say

• Not checked yetcites [19] Brown, D. E. Human Universals (McGraw-Hill, New York, 1991)

In the paper

“The evolution of cooperation by indirect reciprocity leads to reputation building, morality judgement and complex social interactions with ever increasing cognitive demands.”

In the paper

“But a trigger strategy prescribing each person to cooperate until the first defection is personally experienced, and thenceforth to defect, hurts the original wrong-doer only after many rounds. A strategy triggered by the first defection in the population leaves cooperation at the mercy of the first wrong move.”

In the paper

“The so-called folk theorem on repeated games states that if the probability for future rounds is sufficiently high, cooperation can be sustained by so-called trigger strategies, which switch to relentless defection as soon as the co-player defects once 25 .”

What the sources say

• ?Not checked — no full text of the sourcecites [25] Fudenberg, D. & Maskin, E. The folk theorem in repeated games with discounting or with incomplete information. Econometrica 50, 533–554 (1986) source

In the paper

“In order to analyse these questions, an even simpler model was proposed, based on a binary score, taking only the values 'good' or 'bad', depending on what the co-player did when last observed 39-41 .”

What the sources say

• ?Not checked — no full text of the sourcecites [39] Leimar, O. & Hammerstein, P. Evolution of cooperation through indirect reciprocation. Proc. R. Soc. Lond. B 268, 745–753 (2001) source
• ?Not checked — no full text of the sourcecites [40] Panchanathan, K. & Boyd, R. A tale of two defectors: The importance of standing for evolution of indirect reciprocity. J. Theor. Biol. 224, 115–126 (2003) source
• ?Not checked — no full text of the sourcecites [41] Nowak, M. A. & Sigmund, K. The dynamics of indirect reciprocity. J. Theor. Biol. 194, 561–574 (1998) source

In the paper

“Such a form of altruistic punishment is good for the community, but costly for the punisher, and thus can be viewed as a social dilemma 42 .”

What the sources say

• ?Not checked — no full text of the sourcecites [42] Ohtsuki, H. & Iwasa, Y. How should we define goodness? Reputation dynamics in indirect reciprocity. J. Theor. Biol. 231, 107–120 (2004) source

In the paper

“Alternatively, if the discriminating strategy distinguishes between justified and unjustified defection, the population can converge to discriminators only, which cannot be invaded by unconditional strategies 39 .”

What the sources say

• ?Not checked — no full text of the sourcecites [39] Leimar, O. & Hammerstein, P. Evolution of cooperation through indirect reciprocation. Proc. R. Soc. Lond. B 268, 745–753 (2001) source

In the paper

“In this scenario, a population consisting only of conditional and unconditional altruists is not subject to random drift, but selection leads to a well defined, stable mix of the two types.”

What the sources say

• ?Not checked — no full text of the sourcecites [39] Leimar, O. & Hammerstein, P. Evolution of cooperation through indirect reciprocation. Proc. R. Soc. Lond. B 268, 745–753 (2001) source
• ?Not checked — no full text of the sourcecites [49] Ohtsuki, H. & Iwasa, Y. The leading eight: social norms that can maintain cooperation by indirect reciprocity. J. Theor. Biol.(in the press) source
• ?Not checked — no full text of the sourcecites [50] Lotem, A., Fishman, M. A. & Stone, L. Evolution of cooperation between individuals. Nature 400, 226–227 (1999) source
• ?Not checked — no full text of the sourcecites [51] Lotem, A., Fishman, M. A. & Stone, L. Evolution of unconditional altruism through signalling benefits. Proc. R. Soc. Lond. B 270, 199–205 (2002) source
• ?Not checked — no full text of the sourcecites [52] Fishman, M. A., Lotem, A. & Stone, L. Heterogeneity stabilises reciprocal altruism interaction. J. Theor. Biol. 209, 87–95 (2001) source

In the paper

“A discriminating donor using this assessment rule refuses help to a 'bad' recipient, and therefore becomes 'bad', which reduces the chance of being helped in turn.”

In the paper

“This can be viewed as a basic system of moral assessment.”

In the paper

“Therefore, both the lack of information and the prevalence of unconditional altruists may, surprisingly, stabilise cooperation.”

In the paper

“Punishing a player with a bad score creates another player with a bad score; but this 'passing the buck along' can stop in two ways, by encountering either a discriminator who is uninformed, or an undiscriminating altruist.”

In the paper

“In a population consisting entirely of discriminators, undiscriminating co-operators fare just as well and thus spread by neutral drift.”

What the sources say

• ?Not checked — no full text of the sourcecites [39] Leimar, O. & Hammerstein, P. Evolution of cooperation through indirect reciprocation. Proc. R. Soc. Lond. B 268, 745–753 (2001) source
• ?Not checked — no full text of the sourcecites [49] Ohtsuki, H. & Iwasa, Y. The leading eight: social norms that can maintain cooperation by indirect reciprocity. J. Theor. Biol.(in the press) source
• ?Not checked — no full text of the sourcecites [50] Lotem, A., Fishman, M. A. & Stone, L. Evolution of cooperation between individuals. Nature 400, 226–227 (1999) source
• ?Not checked — no full text of the sourcecites [51] Lotem, A., Fishman, M. A. & Stone, L. Evolution of unconditional altruism through signalling benefits. Proc. R. Soc. Lond. B 270, 199–205 (2002) source
• ?Not checked — no full text of the sourcecites [52] Fishman, M. A., Lotem, A. & Stone, L. Heterogeneity stabilises reciprocal altruism interaction. J. Theor. Biol. 209, 87–95 (2001) source

In the paper

“Various assumptions on the distribution of the number of rounds lead to a bi-stable system, where depending on the initial state, the population converges either to the fixation of defectors, or to a stable mix of altruists which cannot be invaded by defectors 52,53 .”

What the sources say

• ?Not checked — no full text of the sourcecites [52] Fishman, M. A., Lotem, A. & Stone, L. Heterogeneity stabilises reciprocal altruism interaction. J. Theor. Biol. 209, 87–95 (2001) source
• ?Not checked — no full text of the sourcecites [53] Fishman, M. A. Indirect reciprocity among imperfect individuals. J. Theor. Biol. 225, 285–292 (2003) source

In the paper

“Only eight of them lead to cooperation and, at the same time, are evolutionarily stable: a homogeneous population of players using such a strategy cannot be invaded by players using other strategies 41 .”

What the sources say

• ?Not checked — no full text of the sourcecites [41] Nowak, M. A. & Sigmund, K. The dynamics of indirect reciprocity. J. Theor. Biol. 194, 561–574 (1998) source

In the paper

“More generally, it seems that decisions often depend on both the donor's payoff and the recipient's score, but such strategies have not been analysed so far.”

In the paper

“Indirect reciprocity is situated somewhere between direct reciprocity and public goods.”

In the paper

“The widespread tendency to judge actions between third parties, and the readiness for cooperation combined with altruistic punishment (also known as strong reciprocity 69 ) has been neatly captured in an experiment involving three players 70,71 .”

What the sources say

• ?Not checked — no full text of the sourcecites [69] Pollock, G. B. & Dugatkin, L. A. Reciprocity and the evolution of reputation. J. Theor. Biol. 159, 25–37 (1992) source
• ?Not checked — no full text of the sourcecites [70] Gintis, H. Game Theory Evolving: A Problem-Centered Introduction to Modeling Stategic Interaction (Princeton Univ. Press, Princeton, 2000)
• ?Not checked — no full text of the sourcecites [71] Fehr, E. & Fischbacher, U. Social norms and human cooperation. Trends Cogn. Sci. 8, 185–190 (2004) source

In the paper

“In order to eliminate confounding effects, players usually do not interact face-to-face, but they are given some information about the past actions of their potential recipients.”

In the paper

“Gossip might be a way of achieving consensus, but can also be used for spreading false rumours and manipulating co-players.”

In the paper

“Many experiments have shown that players who have just received a donation are more likely to give a donation in turn.”

In the paper

“They know that their recipients will never be their donors on future occasions, and thus that there is no scope for direct reciprocity.”

In the paper

“Richard Alexander claimed that indirect reciprocity originates from direct reciprocity in the presence of interested audiences 2 .”

What the sources say

• Not checked yetcites [2] Alexander, R. D. The Biology of Moral Systems (Aldine de Gruyter, New York, 1987)

In the paper

“This indicates that they expect their refusal to lower their score in the co-players' eyes, and that they do not rely on the community's understanding.”

In the paper

“In this series of experiments, there is a significant positive correlation between the number of gifts given and received, but a slightly negative correlation between the number of gifts given and the total payoff obtained.”

In the paper

“Often there is evidence for a dual motivation players give donations if the recipient's score is high or their own score is low 35 .”

What the sources say

• ?Not checked — no full text of the sourcecites [35] Nowak, M. A. & Sigmund, K. A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner's dilemma game. Nature 364, 56–58 (1993) source

In the paper

“As expected, donations occur more frequently if the cost-to-benefit ratio is lower, or the starting account higher.”

In the paper

“In such small populations, random drift can strongly affect evolution.”

In the paper

“The discrepancy could be due to the larger number of rounds - the advantage showed up only after a dozen of rounds - or to the fact that players were informed not only about the recipients' last move but their whole history of giving.”

In the paper

“The interactions both with the co-players and with the experimenters are kept as anonymous as possible, usually under double-blind conditions.”

In the paper

“Players faced with a full history of all previous rounds take in general a longer time to reach their decision, suggesting that they attempt to take into account, not only their recipient's last move, but also that of their recipient's recipient.”

What the sources say

• ?Not checked — no full text of the sourcecites [64] Engelmann, D. & Fischbacher, U. Indirect reciprocity and strategic reputation building in an experimental helping game. Univ. Zürich working paper no. 132 http://www.iew.unizh.ch/wp/iewwp132.pdf (2002). source

In the paper

“There is evidence for 'upstream' indirect reciprocity in cyclical networks: as expected, short loops and a high benefit-to-cost ratio favour cooperation 65 .”

What the sources say

• ?Not checked — no full text of the sourcecites [65] Milinski, M., Semmann, D., Bakker, T. C. M. & Krambeck, H. J. Cooperation through indirect reciprocity: Image scoring or standing strategy? Proc. R. Soc. Lond. B 268, 2495–2501 (2001) source

In the paper

“It could be that co-operators fare less well than defectors within each group, but that groups of co-operators fare better than groups of defectors 57 .”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [57] Takahashi, N. & Mashima, R. The emergence of indirect reciprocity: Is the standing strategy the answer? Hokkaido Univ. working paper no. 29 http://lynx.let.hokudai.ac.jp/COE21/pdf/029.zip (2003).

In the paper

“On one hand, it is a game between two players only, the donor and the recipient, but on the other hand it has to be played within a larger group.”

In the paper

“Both strategies are not evolutionary stable, but their ability to catalyze cooperation in adverse scenarios and their simplicity constitute their strength.”

In the paper

“There are 16 second order rules.”

In the paper

“In the Trust Game, donors who trust their responder will expect to gain from transferring money.”

In the paper

“We expect, however, that SCORING plays a similar role in indirect reciprocity as Tit-for-tat in direct reciprocity.”

In the paper

“In each case, there are many other discriminating strategies, which are likely to take over eventually.”

In the paper

“Hence, there are 2 3 =8 different assessment rules.”

In the paper

“It is very likely that games of indirect reciprocity provided the selective scenario that led to cerebral expansion in human evolution.”

In the paper

“A responder with an income-maximising strategy should send nothing back.”

In the paper

“Any donor expecting this should therefore transfer nothing.”

In the paper

“Trust, 'a lubricant of social life' 77 , plays an essential part in many types of economic transactions.”

What the sources say

• ?Not checked — no full text of the sourcecites [77] Boyd, R. & Richerson, P. J. The evolution of indirect reciprocity. Soc. Networks 11, 213–236 (1989) source

In the paper

“If all do, they multiply their endowment by the factor r.”

In the paper

“Indirect reciprocity based on reputation serves as a link between diverse forms of cooperative interaction.”

In the paper

“In contrast, donors in the Indirect Reciprocity game know that they can expect no direct return, even if their recipient is trustworthy.”

In the paper

“The reputation of players may not only be determined by their own actions, but also by their associations with others.”

In the paper

“There are 16 action rules.”

In the paper

“In a world of binary moral judgements, there are four ways of assessing donors in terms of 'first order assessment': always consider them as good, always consider them as bad, consider them as good if they refuse to give, or consider them as good if they give.”

In the paper

“If we view a strategy as the combination of an action rule and an assessment rule, we obtain 4096 strategies.”

In the paper

“In extended versions of indirect reciprocity, where donors can sometimes deceive others about the reputation of the recipient, SCORING is the 'fool-proof' concept of 'I believe what I see'.”

In the paper

“In human evolution, there was a tendency from the simple cooperation promoted by kin or group selection to the strategic subtleties of direct and indirect reciprocity.”

In the paper

“There are 256 third order assessment rules.”

In the paper

“SCORING judges the action and ignores the stories.”

In the paper

“Indirect reciprocity, in addition, has to monitor interactions among other people, possibly judge the intentions that occur in such interactions, and keep up with the ever changing social network of the group.”

In the paper

“The donations in the indirect reciprocity game, which are channelled towards those who contributed much to the public goods, can be viewed as rewards.”

In the paper

“It is known that many players show an initial willingness to contribute to the public goods a substantial amount of their endowment, but this willingness often vanishes within a few rounds.”

In the paper

“Since each player receives, in return for the own contribution, only the fraction r/N , the incomemaximising strategy is to contribute nothing.”

In the paper

“But settling on this strategy, for instance, on the specific number T, seems to require an institution able to guarantee honest labelling.”

In the paper

“The moralistic assessment of the other members in the population, even if they are only observed at a distance, provides a powerful tool for channelling support toward those who collaborate, and thus an incentive to join group efforts.”

In the paper

“This very crude form of assessment seems to suffice for the purpose of reputation-building, and seems to be reasonably proof against manipulation.”

In the paper

“All they can gain from the transfer is an increased reputation for altruism and trustworthiness.”

In the paper

“Direct reciprocity requires precise recognition of individual people, a memory of the various interactions one had with them in the past, and enough brain to conduct multiple repeated games simultaneously.”

In the paper

“Helping another individual is costly but buys the reputation of being helpful.”

In the paper

“Altruism toward genetic relatives can evolve by kin selection provided Hamilton's rule 14 holds: the coefficient of relatedness, r , between the donor and the recipient has to exceed the cost to benefit ratio of the altruistic act,”

What the sources say

• ?Not checked — no full text of the sourcecites [14] Hamilton, W. D. Narrow Roads of Gene Land Vol. 1 (Freeman, New York, 1996) source

In the paper

“While language might help to compare and synchronize these lists 41 , ultimately reputation is in the eyes of the beholder.”

What the sources say

• ?Not checked — no full text of the sourcecites [41] Nowak, M. A. & Sigmund, K. The dynamics of indirect reciprocity. J. Theor. Biol. 194, 561–574 (1998) source

In the paper

“Kin selection works in 'viscous' populations where chances are high that neighbours are genetic relatives.”

In the paper

“The observers, the donor and the recipient can inform others about what has happened.”

In the paper

“Indirect reciprocity, in contrast, is built on reputation.”

In the paper

“The Public Goods game for N =2 players has the structure of a Prisoner's Dilemma.”

In the paper

“Two players who cooperate earn more than two players who defect; but a defector cheating on a cooperator earns the highest payoff, and the exploited cooperator earns the lowest.”

In the paper

“Direct reciprocity is captured in the framework of the repeated Prisoner's Dilemma.”

In the paper

“An individual who has been at the receiving end of a donation may feel motivated to donate in turn.”

In the paper

“An entirely different approach to indirect reciprocity is based, not on the reputation of the recipient, but on the experience of the donor.”

In the paper

“If two players, in a trust game, are simultaneously in the role of the donor, and then simultaneously in the role of the responder, they play two rounds of a Prisoner's Dilemma.”

In the paper

“In a natural extension of the basic model of indirect reciprocity, an action between a donor, A, and a recipient, B, is observed by a subset of the population 35 .”

What the sources say

• ?Not checked — no full text of the sourcecites [35] Nowak, M. A. & Sigmund, K. A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner's dilemma game. Nature 364, 56–58 (1993) source

In the paper

“Therefore, the reputation of a person is not simply a label that is visible to all others, but instead each person has a private list of the reputation of others.”

In the paper

“There are many possibilities of error: the action or the intention of the donor can interpreted differently by different people, some individuals may receive conflicting information from different sources, some individuals may not receive any information at all.”

In the paper

“The probability that brothers share a 'selfish gene' is ½; the same probability for cousins is 1/8.”

In the paper

“In both cases, the decision to give help can be interpreted as a misdirected act of gratitude.”