1.


The intra- and inter-round calculations could be more explicitly modelled, not only under the general aspect of “meeting (the same) again”, but also with their various (four) potential outcomes of all (both) kinds of interaction partners. The pay-offs would be the capitalized pay-offs across all SGs.


2.

As usual, the smaller the interest rate r, the larger the discount factor δ, and the larger the future looms, which is consistent with general capital-value calculations of future incomes and with the single-shot calculation above.


3.

Note the condition to “meet (the same) again” is the perspective of a cooperator. The ALLD-defector is indifferent to whom he will meet (being assumed to always defect). Logically, thus, one could assign him a δ = 0. In another perspective, however, he is not indifferent since he would exactly not wish to meet the same again but to meet a new cooperator every interaction, whom he then can exploit once. The defector, rather, is interested in a large anonymous population, where he can move around and change partners for every interaction, while the cooperator is interested in a smaller one, with more stability and less disembedding mobility, thus a larger probability to meet the same again or any other cooperator, actively selected or not (see below on agent capacities), according to inequalities (1) and (4).


4.

After sufficient clustering, they might want to care for more stability and reduced uprooting or disembedding mobility, as possible, to keep expectations high. We have dealt with the role of uprooting (over-)mobility and perceived (over-)turbulence elsewhere (e.g., Elsner, 2024). But too much stability for too long may have other adverse long-run implications, namely for the petrifaction of institutions. However, we are dealing here with the conditions of institutional emergence, diffusion, and establishment, not further development, decline, and collapse (see, e.g., Elsner, 2021).


5.

TFT has a memory length of one time unit (t = 1) as a standard, TF2T would have t = 2. If cooperators were assumed to remember longer time spans, e.g., t = T, the maximum relevant population size still allowing for institutionalization of cooperation c.p. may increase, since the probability of meeting a certain agent again through active partner selection would increase. From a maximum size n = 1/p2,t=1 + 1 (Eq. (3)) we may model, for T, a maximum size n = 1/[1–(1–p2,t=T)1/T] + 1. Then, obviously, n increases with T. Just to give a numerical size order: For b = 4, a = 3, c = 2, p2,t=1 = 0.5, according to inequality (1), the related maximum population size for t = 1 would be 3. An increase to t = 2 increases n to n ~ 4.4, for t = 3 to n ~ 5.9. However, an infinite memory is no option, and there have been evolutionarily advantageous combinations of both memory and forgetfulness (e.g., Neligh, 2024).


6.

Again, this may come with the danger of too great a cliquishness and later petrifaction of institutions and institutional lock-in on an inferior path. But again, we are not dealing here with institutional decline and collapse.


7.

Note that p1 is to be interpreted as the probability that a round in the structured SG will go on for at least one more interaction. p1x, therefore, is the probability that it will continue for at least x more interactions. The expected value of the number of interactions per round therefore is x = logp10.5. For p1 = 0.1, the expected value of future interactions is about 0.3. Obviously a small number, and a rather adverse condition for cooperation. Axelrod (2006 [1984]) set an average expectation of some 200 future interactions, implying a high p1 of about 0.9965, obviously favorable for cooperators.


8.

Note that the agent who just decides to cooperate or defect based on these equations will logically not be part of the relevant k’s and n’s, which may be relevant for very small k and n.


9.

Again, high mobility among interactions is implied, equivalent with the assumption that people remain anonymous to each other and always play as if they were strangers. Under strict anonymity, they do not build longer-run relations.


10.

A neighbor’s funnel may overlap with A’s funnel so that he might add, say 10, 20, or 50% information (depending on distance) to his knowledge. Specific numbers would require an elaborated model of overlaps of funnels in a specific topology.


11.

In real life, we cannot freely reject any interaction partner who may come up. With some, we have to interact, whether we enjoy it or not, interact successfully or not, e.g., in environments of family, hierarchies, or the state.