Abstract
Until recently the “meso” level, located somehow between the “micro” and “macro” layers, has been neglected as a theoretical level in economic theory. There has been a long tradition of institutional economics though, which implicitly operates at this level, focusing on informal institutions that emerge as “aggregate” structures from direct interdependence and interaction of individual micro-level agents solving social coordination or dilemma problems. But it was not before the rise of more formal evolutionary modeling and simulation in the last 3 decades that the discussion of emergent structure at “meso”-levels has gained momentum. In the current paper, we discuss the emergence of cooperation as a social institution on a “meso”-sized platform. Departing from a commonly known situation of non-cooperative game theory, i.e., the repeated prisoners’ dilemma, cooperating agents learn to coordinate and cooperate while (and by) forming a “meso”-sized platform – the institution’s carrier group – giving rise to a process of co-evolution of (1) the institution of cooperation solving the dilemma, (2) a network of cooperating groups above minimum size but below maximum size, and (3) a better performance of the cooperating part of the whole population. An agent-based computer-simulation is used to analyze the factors contributing to this process (neighborhood structure, memory, monitoring, partner selection, incentive structure). The effects of these factors are confirmed and partially quantified. Starting with a review of the recent literature on the economics of “meso” (section “Size and ‘Meso’ Size in the Literature so far”), we proceed to analyze the co-evolution of institutional cooperation (section “Population Size in a Static ‘Single-Shot’ Perspective”) and the “meso”-sized carrier structures in a supergame of repeated games (section “The Population Perspective, More Complex Mechanisms, and Minimum and Maximum Critical Sizes”). In sections “The Population Perspective and the ‘Minimum Critical Mass’: A Graphical Display” and “‘Loosening’ Connectivity: ‘Contingent Trust’, Monitoring, Memorizing, Reputation, and Selection: With some Numerical Examples”, we add stochastic analysis, and section “Insights from Computer Simulation: An Agent-Based Model” considers an agent-based computer simulation, followed by section “A Real-World Example: Trust Polls, Country Size, and Macro-Performance” which reviews some empirical example of small and well-structured vs. large and ill-structured countries (“varieties of capitalism”). In the final section “Conclusions”, we summarize and conclude.
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Notes
- 1.
Group size is there but one critical factor among others and interferes with other factors to form different interaction conditions and trigger different resulting degrees of institutionalized cooperation, although these real societies explored are all “small-scale” (ranging in size between 75 and 1,219). This, however, does not imply that relative smallness of interaction arenas, or “meso” group size, as such would not tend to be a favorable condition of institutional emergence. In fact, size was found in that large cross-cultural field experiment to be a good predictor for payoffs to cooperation.
- 2.
A formal note on memory and its implications may be in order here. The cooperative (TFT) agent is supposed to have a memory length of one time unit (t = 1) which may considered to be equivalent to a required subjective “one-time-unit probability to meet again” perceived by agents. However, if cooperative agents were assumed to remember longer time spans, e.g., a memory of t = T, the maximum population size allowed for the institutionalization of cooperation c.p. will increase, since the probability of meeting a certain agent again in any of the future rounds within their memory period T would considerably increase, given the population size. Put differently, by contrast, population size may increase with increasing memory periods while keeping the “probability to meet again”, or “cumulated probability”, constant. From n = 1/p 2,t = 1+1 [see (3)], for instance, would follow the max. population size n = 1/[1–(1– p 2,t = T )1/T] + 1. Obviously, n increases with T. For example, for b = 4, a = 3, c = 2, p 2,t = 1 = 0.5, according to the single shot Inequality (1) the related maximum population size for t = 1 would be 3. An increase from t = 1 to t = 2 then increases n from 3 to about n = 4.4, for t = 3 to about n = 5.9, etc. It is obvious that memory length is a most critical factor for structural emergence. However, in this paper, we will deal with memory not in the frame of the single-shot logic but within the population perspective below when “connectivity” among agents will be loosened. However, memory will then work in the same direction.
- 3.
We are aware that the two different logics of intra- and inter-round (or inter-supergame) calculations should be explicitly modelled, not only under the restriction of “meeting the same again” but with its various potential outcomes. The pay-offs of a supergame of supergames would be the various potential capitalized pay-offs of individual supergames.
- 4.
The condition to meet the same again the perspective of the cooperator. The defector seems to be indifferent in his behavior to whom he will meet (he is assumed to always defect). However, he is not really indifferent since he would not wish to meet the same again but to meet a new cooperator every round whom he can exploit initially. Clearly the defector is interested in a small p 2 or large population size n while the cooperator is interested in the contrary.
- 5.
Note that p 1 is to be interpreted as the probability that a round in the structured supergame as explained above will go on for at least one more interaction, and p 1 x therefore 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 = log p10.5. For p 1 = 0.1, the expected value of future interactions is about 0.3. This is obviously a small number and a rather adverse condition for cooperation. Axelrod (1984/2006), for example, set some 200 future interactions, this implying a p 1 of about 0.9965.
- 6.
Note, however, that as soon as the minimum critical mass has been established this way, our system below will still behave deterministically when moving to its new equilibrium.
- 7.
As said, this still represents a static and deterministic ex-ante single-shot calculation.
- 8.
Note that the agent who decides to cooperate or defect based on these equations will not be part of the relevant k’s and n’s, which is relevant for small k’s and n’s.
- 9.
Possibly a case of pathological behavior similar to an ALL C player.
- 10.
We will consider a topology concrete geographical or social, i.e. neighbourhood, below in section “Insights From Computer Simulation: An Agent-Based Model”.
- 11.
A “half-distant” neighbor’s funnel, of course, will not completely be identical with A’s funnel but will overlap so that he might add, say 10 or 20 or more% information (depending on his distance) to A’s knowledge from his own funnel. Specific numbers would require a more elaborated model of overlaps of funnels in a topology. We will this and simply assume that only 50% of cooperators in A’s funnel can add information, these, however, may provide information from the complete set of their assumed 28 different other third cooperative agents.
- 12.
This might be a point for a complementary use of cooperative game theory. We owe the advice on cooperative game theory an anonymous referee and will denote the logical points of its complementary use in two more places in our argument.
- 13.
For example for an infinite two-dimensional rectangular lattice with the Moore neighborhood (horizontal, vertical and diagonal edges) the clustering coefficient as defined by Watts and Strogatz (1998) is 3/7 = 0.43. In our case on the other hand, for the graph used for this simulation, the clustering coefficient approaches 0 as the graph size tends to infinity.
- 14.
The agent could not just terminate one connection to another agent but would have to transfer to another location on the lattice changing her entire neighborhood. While it would still have been possible to implement the simulation like this, it would not have had any particular advantages to justify the greatly reduced flexibility of the mechanism.
- 15.
For technical reasons, the simulation program rounds small probabilities to 0 – otherwise the degrees of neighborhood to be considered (and thus the number of operations to be exercised by the simulation) would be infinite.
- 16.
Otherwise, depending on dn, this may lead to situations with the probability to interact with a specific agent decreases in D but the combined probabilities for all agents of this degree of neighborhood increases in effect leading to a greater impact of more distant parts of the population.
- 17.
Oscillating refers to what would happen if with a hypothetical constant threshold the payoffs of all agents would fall below that value and thus all the agents would always have to change their strategy.
- 18.
If the payoff distribution were symmetric, unbiased and non-trivial (not a single point), 25% of the population would fall below a value MEAN(Π) − SD(Π) which is equivalent to the above threshold with the parameter h = 1. However, the distribution will in our case generally be two-peaked and thus not symmetric. Still, the above threshold will seperate certainly less than half of the population (as long as the distribution is non-trivial SD(Π)! = 0) but more than zero of the least “lucky” agents.
- 19.
This is equivalent to an expected value of interactions per round of 1 + log 0.50.5 = 2. See footnote 5.
- 20.
- 21.
Simulations with larger numbers of agents and over longer time spans will be conducted in the future.
- 22.
For dn = 2 the graph would be a completely regular circle.
- 23.
“Network of cooperators” does in this case refer to the particular shape of the cooperating “meso”-group being part of the ad hoc network topology and forming a more stable area within this network since connections between cooperators are retained while everyone tries to cut connections to defectors.
- 24.
The share of cooperation rises, the mean payoff of cooperators rises, the share of cooperation in cooperators payoffs rises and the standard deviation of payoffs rises as well. All these trends are, as we outlined consequences of the same process. Therefore it is generally sufficient to illustrate the following investigations with just one or two of these graphics.
- 25.
We decreased the memory length, the probability for the round to continue (p1), and the TFT vs. TFT payoff a (of course keeping a larger as c, thus retaining the prisoners dilemma structure). All three changes proved to have negative effects slowing the emergence of cooperation considerably and also leading to a smaller final share of cooperators (though this share had already stabilized). An increase in this three values instead of decreasing them had, of course, the contrary effect, accelerating the emergence of cooperation. As these results are had been expected and discussed extensively in theoretical considerations, we do not include any extensive graphic documentation for these simulation runs.
- 26.
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Acknowledgements
Earlier versions of the paper on which the authors drew for this chapter have been presented at the 2006 Schloss Wartensee Workshop on “Evolutionary Economics”, St. Gallen, CH (the authors wish to express their thanks to K. Dopfer and the discussants there), the January 2008 AFEE session in New Orleans, the EAEPE conference in Rome, November 2008, the ASSA meetings in San Francisco, January 2009 (thanks to P. Arestis and J. Galbraith for the discussion there), and the EAEPE conference in Amsterdam 2009, as well as the annual conference of the Section of Evolutionary Economics of the Verein für Socialpolitik in Jena 2009, as well as several seminars and workshops at the PSU Portland (thanks to J.B. Hall and discussants), the MPI Jena (thanks to U. Witt and discussants), the New School NYC (thanks to D. Foley and participants), and the UM Kansas City (thanks to J. Sturgeon and discussants). The authors are especially grateful to H. Schwardt and M. Greiff for numerous discussions of all details of the current paper and anonymous referees who commented on earlier versions published in the Journal of Socio-Economics in 2009 and the Journal of Evolutionary Economics in 2010. However, the authors insist on the property rights of all remaining deficiencies.
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Elsner, W., Heinrich, T. (2011). Coordination on “Meso”-Levels: On the Co-evolution of Institutions, Networks and Platform Size. In: Mann, S. (eds) Sectors Matter!. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18126-9_6
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