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The process and a simple logic of ‘meso’. Emergence and the co-evolution of institutions and group size

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Abstract

‘Summing-up’ aggregation of micro decisions contrasts with structural emergence in complex systems and evolutionary processes. This paper deals with institutional emergence in the ‘evolution of cooperation’ framework and focuses on its size dimension. It is argued that some ‘meso’ (rather than ‘macro’) level is the proper level of cultural emergence and reproduction. Also Schumpeterian economists have discussed institutions as ‘meso’ phenomena recently, and Schelling, Axelrod, Arthur, Lindgren, and others have dealt with ‘critical masses’ of coordinated agents and emergent segregations. However, emergent group size has rarely been explicitly explored so far. In an evolutionary and game-theoretic frame, ‘meso’ is explained in terms of a sustainably cooperating group smaller than the whole population. Mechanisms such as some monitoring, memory, reputation, and active partner selection loosen the total connectivity of the static and deterministic ‘single-shot’ logic and thus allow for emergent ‘meso’ platforms, while expectations ‘to meet again’ remain sufficiently high. Applications of ‘meso-nomia’ include the deep structure of ‘general trust’ and macro-performance in ‘smaller’ and ‘well networked’ countries which helps to explain persistent ‘varieties of capitalism’.

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Notes

  1. I owe this idea to an early discussion with D. Foley. It has occurred in several complex models and simulations in the literature, though.

  2. I owe this idea to an anonymous referee.

  3. Regarding crucial terms, it should be mentioned at this point already that we refer to ‘coordination’ in a wide sense as an umbrella to ‘coordination’ in a narrow sense and to ‘cooperation’. Particularly, a ‘coordination problem’ (in a n.s.) is solved in a successful ‘coordination’ (n.s.) gained through some social ‘rule’. In contrast, a ‘dilemma problem’ is solved in a ‘cooperation’ (a coordination n.s. ‘plus habitual sacrifice’ of the short run extra pay-off), gained through an institution (i.e., a rule ‘plus endogenous sanction’). These game-theoretic terms have been established first by Schotter (1981). We will explain on some definition in more detail below.

  4. Terms again: We suppose a uniform periodization over time both within and between supergames. Within a supergame, the smallest interaction unit is called an interaction. A series of interactions after which new encounters may take place is called a round. In this paper, a round will typically be a whole supergame and new encounters will take place only after a supergame between the same agents is finished (if not indicated otherwise). Finally, if after a supergame some scoring takes place and some learning or replicator mechanism is applied to the relative scores then we may call this preceding period of interactions or rounds a generation.

  5. This in turn indicates the number of interactions played in a supergame. In order to avoid the supergame to switch back into a series of one-shots this number needs to be indefinite to the agents. Across several supergames this number may be attained as an average, while the individual supergame round may consist of a number of interactions that is determined by a random generator, as Axelrod had suggested in his tournaments.

  6. Note that this is not a strictly `combined' discount factor for both within and across supergames. This would have to insert the aggregate payoffs of the `inner' games into the calculation of a supergame of supergames. For the case of two cooperating agents in a series of supergames, this would be \(a \mathord{\left/ {\vphantom {a {\left( {1-\delta _1 } \right)+{ap_2 } \mathord{\left/ {\vphantom {{ap_2 } {\left( {1-\delta _1 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1-\delta _1 } \right)}+{ap_2^2 } \mathord{\left/ {\vphantom {{ap_2^2 } {\left( {1-\delta _1 } \right)+\ldots }}} \right. \kern-\nulldelimiterspace} {\left( {1-\delta _1 } \right)+\ldots }=a \mathord{\left/ {\vphantom {a {\left[ {\left( {1-\delta _1 } \right)\left( {1-p_2 } \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {\left( {1-\delta _1 } \right)\left( {1-p_2 } \right)} \right]}}}} \right. \kern-\nulldelimiterspace} {\left( {1-\delta _1 } \right)+{ap_2 } \mathord{\left/ {\vphantom {{ap_2 } {\left( {1-\delta _1 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1-\delta _1 } \right)}+{ap_2^2 } \mathord{\left/ {\vphantom {{ap_2^2 } {\left( {1-\delta _1 } \right)+\ldots }}} \right. \kern-\nulldelimiterspace} {\left( {1-\delta _1 } \right)+\ldots }=a \mathord{\left/ {\vphantom {a {\left[ {\left( {1-\delta _1 } \right)\left( {1-p_2 } \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {\left( {1-\delta _1 } \right)\left( {1-p_2 } \right)} \right]}}\). We would easily get mired in complicated algebraic exercises without adding much value to our basic argument. Our simple case implies, rather, that, when returning from Eq. (3) to Eq. (1a), p 2 = 1, and from Eq. (3) to Eq. (2), p 1 = 1 and r = 0. This could perhaps more easily modelled as a single supergame with transition probabilities of p2 for partners among interactions. See also Eq. (1b) in Section 3.4 below.

  7. ‘Strong total connectivity’, in contrast, would imply to meet every other agent in every round, i.e., probability of 1. Just to note that alternatively we might assume only one supergame being played, divided into an indefinite number of rounds, wherein every agent interacts each once with m < n other agents simultaneously. Here p 2 would apply to the transition between rounds within the one supergame and would be \(p_2 =m \mathord{\left/ {\vphantom {m {\left( {n-1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {n-1} \right)}\), thus entailing \(\delta _2 ={p_1 m} \mathord{\left/ {\vphantom {{p_1 m} {\left[ {\left( {1+r} \right)\left( {n-1} \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {\left( {1+r} \right)\left( {n-1} \right)} \right]}\). Weak total connectivity is multiplied by m here and so is the comprehensive discount factor δ 2. Obviously, this would increase the probability of emerging cooperation. However, we will develop a different line of argument in this paper.

  8. A famous case of the logical consequences of perfect enviousness, i.e., the ‘downward causation’ to the common minimum pay-off, is the story of the ‘traveller’s dilemma’, told by Basu (1994).

  9. 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 equilibria.

  10. Note that scale and related collective action (incl. innovation) capability is not confined here to spatial size. Otherwise we would follow an overly narrow ‘regional determinism’, as Lorentzen (2008) has argued.

  11. Note that ‘group (size)’ and ‘population (size)’ n are considered identical as long as the group is not explicitly determined yet as an entity below the size of the whole population (which will be attained later).

  12. Note that expectations might be co-determined independently from the group size, for instance by some exogenous authority.

  13. See Fn. 6 above.

  14. As said, we are fully aware that we should explicitly model the two logics of intra- and inter-supergame calculations. The pay-offs of the supergame of supergames would be the added discounted pay-offs of the individual supergames which include the stochastic term p 1, or δ 1, resp. The inter-supergame calculation includes p 2 while the intra-supergame calculations does not. The inter-supergame calculation, in turn, does not include δ 1. Nevertheless, in the following we calculate numerical examples using the single-shot logic as laid down in Section 3.1 as a first benchmark.

  15. This is equivalent to somewhat below 200 interactions for each pair of agents. Axelrod used a value of .99654, equivalent to an average of 200 interactions per supergame, where each pairing played five supergames the specific length of which was determined by a random procedure (around the median of 200 interactions).

  16. Note that the agent whose decision to cooperate or defect will be made based on these equations will not be part of the k’s and n’s. Obviously, this is particularly important in numerical calculations for small groups.

  17. Note that the system still is deterministic as soon as the minimum critical mass is (randomly) determined through some behavioral diversification as mentioned (‘search’). We will elaborate on the agency capacity required for this in more detail below.

  18. Note again that numerical calculations need to subtract the agent in question from both ks and ns, except we can assume that a cooperator is one of those of the minimum critical mass who have already decided to cooperate for other reasons (like the perhaps pathological last cooperator in Fn. 19).

  19. Admittedly, also a case of pathological behavior similar to an ALL C player. This last cooperator would not want to learn from being exploited all the time...

  20. If we had to deduct this agent from k and n, the minimum population size n would have to be three. But see Fn. 18.

  21. It might be a case for an additional employment of cooperative game theory, though.

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Acknowledgements

The author is grateful to K. Dopfer and the discussants of the 2006 Schloss Wartensee Workshop on ‘Evolutionary Economics’, St. Gallen, CH, to the participants of a 2008 AFEE session in New Orleans and G. Hodgson, the discussant in that session, further to R. Delorme, W. Dolfsma, D. Foley (and the students of his complex-modeling workshop at the New School, NYC), R. Franke, J.B. Hall (and the discussants at a PSU department seminar, Portland, OR), G. Hayden, F. Jennings, S. Katterle, A. Lascaux, W. Milberg, P. O’Hara, A. Pyka, P. Ramazzotti, J. Sturgeon (and the discussants at a UMKC seminar, Kansas City, MO), U. Witt (and discussants at a Seminar at MPI Jena), and J. Wood for comments on an earlier version. Also many thanks to my research and teaching assistants T. Heinrich, M. Greiff, and H. Schwardt. Finally, K. Dopfer has commented on the paper at the EAEPE conference in Rome, November 2008. However, the author insists on the property rights for all remaining deficiencies. A more conceptual earlier paper has appeared in the Forum for Social Economics 36.1 (2007), 1–16.

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  1. IINO—Institute of Institutional and Innovation Economics, Faculty of Economics and Business Studies, University of Bremen, Hochschulring 4, 28359, Bremen, Germany

    Wolfram Elsner

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Elsner, W. The process and a simple logic of ‘meso’. Emergence and the co-evolution of institutions and group size. J Evol Econ 20, 445–477 (2010). https://doi.org/10.1007/s00191-009-0158-4

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