They take a critical look at the Nowak & Sigmund (1998) model. They conclude that, while indirect reciprocity could evolve in principle, there are serious problems with image scoring strategies. The main weakness lies in their failure to represent the true strategic interests of an individual.
Specifically: there seems to be no possibility that an individual could personally benefit by basing a decision wholly or partly on the image score of a potential recipient for help. The only influence of this choice is on the image score of the donor.
Thus, a rational individual in this setting should use a strategy that takes his or her own score into account, but ignores the score of a potential recipient. Additionally, it would be in the individual's interest to know how other group members react to recipients with different scores, in order to assess the consequence of a change in one's score.
They performed similar computer simulations and found that the previous success of image-scoring strategies was the result of restrictive conditions that are unlikely to be representative in historical human societies. Typically, image scoring would not evolve in a more realistic version of the scenario.
Sudgen's (1986) "Standing strategy": Individuals are initially in good standing and lose this by failing to help a recipient in good standing. Good standing can be regained by helping when in the position to do so. The strategy is therefore to help when not in good standing or when the potential recipient is in good standing, otherwise don't help.
The standing strategy is evolutionarily stable, and is a viable candidate mechanism for human cooperation based on indirect reciprocity.
Image Scoring Model:
In order to study the case of moderately sized social groups while limiting effects of genetic drift, use an idealization island model. A certain proportion of the gametes forming a new generation are locally derived, and the rest are randomly drawn from the global gene pool.
A total population consisting of g groups each with n members, with total population size N = gn.
Interactions consist of m rounds per generation. Two individuals are randomly chose from the group in each round, as recipient and potential donor. Cost c and benefit b.
New generation: sum the payoffs for each genotype for each group, and normalize to produce within-group expected relative reproductive success. Similarly summing over the entire population and normalizing gives you global expected relative reproductive success. A new individual is locally derived with probability p and globally derived with probability 1 – p. Random mutation with probability \mu.
Scoring: Each individual has a score s, which is initially zero. A potential donor's score increases by one unit in an interaction if help is given and otherwise decreases by one unit (bounded between +/– 5). An individual's score is known to all group members.
-Given this structure, a strategy could base decisions on the total set of past and present scores of the group members.
Classes of image-scoring strategies:
1. Offer help when own score is less than h
2. Offer help when recipient's score is at least k
3. Offer help when own score is less the h and recipient's score is at least k.
Errors: a probability e of performing the opposite action as intended.
Results:
-The strategy of k = 0 can be invaded by a small group of mutants using h = 1.
-When there is error, the strategy of k = 0, h = 1 can be invaded by h = 1, which then allows a strategy of pure defect to invade.
-In mixed evolutionary simulations, focused on h-and-k strategies. When just big population, k = 0, h = 1 strategies dominate, with and average of 39% aid given (Fig 2a). For an island model with limited gene flow (p = 0.9), no strategies dominated, and help is only given 9% of the time (Fig. 2b). With stronger gene flow (p = 0.5), there were very few cooperative strategies, and help was only offered 2% of the time.
Standing Strategy Model:
The standing strategy can invade both cooperators (k = –1) and discriminators (k = 0) and robust to both errors of action and of perception. It is an ESS against all these strategies.
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