Abstract
Previous game-theoretic studies of institutions have viewed institutional changes as either exogenous changes in game form or changes in the game equilibrium through exogenous shocks. Both views of institutions are static and cannot express endogenous changes in institutions. The latter approach states that multiple institutional systems can be kept stable through institutional complementarity and that the changes in institutional systems only arise from exogenous shocks that are sufficiently large to overturn such complementarity. However, they cannot account for the aspects of competition and co-existence where multiple institutions change their relative frequency through endogenous changes. In this article, we model the ecological systems of institutions, as an extensive synthesis of replicator dynamics and evolutionary games, to describe institutional systems that evolve phylogenetically associated with changes in population structure or a pool of rules as replicators, which corresponds to a gene pool. A mathematical model of rule ecosystem dynamics describes rule dynamics wherein multiple rules change their relative weights through evaluations by individuals. In this model, the concept “a meta-rule = an individual value consciousness” is introduced for the rule evaluation. Depending on the setting of the meta-rule, the dynamics of the game rules and individual strategic rules change. We can thus comprehend the endogenous formation, alteration, and extinction (i.e., the evolution of institutions) through the interactions among the game rules as well as those between the game rules and strategic rules. Many other studies focus on how rational individuals select strategies to maximize their payoffs without considering the bounds of rationality. Even when considering these, individual cognitive frameworks and values are typically given. By contrast, this study assumes that individuals have internal rules that express cognitive frameworks and values as meta-rules and analyzes the dynamic interactions between institutions, as social external rules at the meso level, and strategic rules and value consciousness, as individual internal rules at the micro level. In our model, institutional changes do not arise as game equilibria (i.e., players’ selection of strategies in a game), but rather as the rise and fall of game forms, as various rules, in multi-games based on a meta-rule. This view is based on an evolutionary approach where socio-economic evolution is considered to be a selection of rules and institutions rather than that of individuals or their strategies. We discuss the implications of the model of institutional ecosystems on the description of the socio-economy and its evolutionist institutional design.
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Notes
The definition and distinction of external/internal rules and outer/inner institutions by treating meso level institutions as game rules (outer institutions) and meta-rules as game rule evaluations (inner institutions) are different from previous ones (Nishibe 2006). While the game rules (outer institutions) set the range of behavior for each individual “from the outside”, or in a top-down manner, meta-rules (inner institutions) set the nature of the total game “from the inside” by using the relative frequency of each game rule, or in a bottom-up manner. While the “external/internal” in external/internal rules represents the static “boundaries of a set” or “areas”, “outer/inner” implies a dynamic “causal direction” or “determined relationship direction.” For this reason, we use the terms inner/outer institution. Note that outer and inner institutions are not distinguished by the explicit or implicit sharing of rules among individuals. If that were the case, then it would be more appropriate to use the terms “explicit/implicit institution” or “formal/informal institution.” In that case, the classifications would become closer to legal and regulatory/ethical and customary. Then, “implicit” or “informal” institutions would merely be unexpressed conventions or codes that arise within the domain of freedom set by “explicit” or “formal” institutions, and eventually fill the space left by “explicit” or “formal” institutions. The problem is that if “implicit” or “informal” institutions are only implicit parts of the game rules, they cannot be meta-rules for value consciousness on the fairness and appropriateness of the game rules at the meta level; thus, it would be impossible to show mutual determination between the outer and inner institutions found in this paper. Here, meta-rules that regulate the game rules are given for a provisional treatment. However, this does not mean that they exist transcendentally from the outset. They can change dynamically and endogenously. A meta-rule is synthesized as value consciousness from individuals’ evaluation in their minds. During the process, it is then transferred from the internal to the external.
Games that explicitly introduce bidirectional causality between the game rules and meta-rules are generally understood to be “triangular game processes” (Nishibe 2006). Meta-rules herein are of two types: “definition and modification meta-rules”, which predefine the rules and modify them on the basis of ex post facto evaluations, and “standard meta-rules”, which evaluate the rules on the basis of the game results. In RED introduced herein, meta-rules are first understood to be “standard meta-rules.” This is the game evaluation function \(\lambda^{g} = \lambda^{g} (\varvec{x,u}^{g} )\) given in Eq. (21). Each game rule is evaluated from high to low on the basis of this function. In general, game rule g is modified after having been evaluated low by these standard meta-rules (or perhaps by violating a meta-rule standard). For example, if a certain law or rule is determined to be unconstitutional, it will likely be altered. However, in RED, game rule g itself is not altered or edited after receiving a low evaluation, but rather its weight, w g, will decrease. In this manner, “definition and alteration meta-rules” include situations where only the weight, w g, of game rule g is modified; game rule g itself is not modified. Within triangular game processes, it is possible to include meta-meta-rules, even higher-level processes that can alter meta-rules. As outlined in this paper, within RED, meta-rules are assumed to be exogenous and do not include the processes wherein they are revised.
\(E(i, \,j)\) need not be given prior to interactions; it only needs to be the sum of the interaction results. Replicators are behavioral patterns and not thoughts to be used to select behaviors on the basis of the pre-calculation of the game results.
In general, explanations of replicator dynamics in the evolutionary game theory literature call these replicators “strategies” . Strategies are easily confused with moves in games, so some care must be taken. A strategy is a method for selecting a move. In individuals, replicators correspond to strategies and behaviors to moves. Different strategies (replicators) may make the same move (behave in the same way). The term “strategy rules” used in this paper refers to this type of strategy. For example, the tit-for-tat strategy in the iterated prisoner dilemma game is an if–then rule that states “if the other player cooperated in the last game, then I will cooperate with him/her this time; otherwise, if the other player betrayed me in the last game, then I will betray him/her this time”. This is a replicator of an individual. The specific moves are “cooperate” and “betray”. The All-C strategy can be written as “if *, then cooperate”, where “*” is a wild card representing any behavior. In other words, no matter what the past history between another player and an individual, this strategy is to always cooperate with the others. These two strategies execute the same “move”, cooperate, when the other player has cooperated in the last game.
Note that this is different from a strategy profile, which is a set of strategies selected by players for one game rule and represents a state of a society. Strategy rule \((i,\,j)\) herein expresses one’s way of deciding behavior, namely the internal rule, for two game rules.
When an individual choose strategy rule 1 for game rule 1 and strategy rule 2 for game rule 2, replacing row 1 with 2 and column 1 with 2 in the game rule 2 matrix makes the individual select strategy rule 1 for game rule 2.
The other settings for the simulation are the same as in Fig. 1.
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Acknowledgements
This research was partly supported by JSPS Kakenhi Nos. 17651088 and 21330063.
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This article is the revised English version of the Japanese original version (Hashimoto and Nishibe 2012).
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Hashimoto, T., Nishibe, M. Theoretical model of institutional ecosystems and its economic implications. Evolut Inst Econ Rev 14, 1–27 (2017). https://doi.org/10.1007/s40844-017-0071-8
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DOI: https://doi.org/10.1007/s40844-017-0071-8
Keywords
- Replicator as rule
- Institutional variety and endogenous change
- Institutional ecosystem
- Rule ecosystem dynamics
- Meta-rules
- Evolutionist institutional design
- Micro–meso–macro loops