Abstract
This paper investigates how pre-existing institutions foster economic development through trade. A non-cooperative game-theoretic model is proposed that combines three strands of social science: economics, political science, and sociology. Idealized market participants follow rational decision theory within a reward structure that embodies two types of institutions. Regulative institutions operate on threat of punishment, and normative institutions on perceptions of what is good and right. This composite model allows a more quantitative analysis of the question, raised by Douglas North, of how societies diverge from the efficient state predicted by classical micro-economics. The main finding is that value can be created by different types of institution even when they are imperfect, and the range of minimum–maximum effectiveness varies with the types of economic transactions that are technologically possible. It is hoped that further refinements of the model will yield greater understanding of how the success of societies and organizations can be predicted by a few simple rules.
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Notes
An exception to this is when the equilibrium state itself is path-dependent. When a different equilibrium is reached depending on what was assumed early on, then we have a self-fulfilling cognitive effect. We revisit this in Sect. 3.
In the context of an employee in a bureaucracy, this corresponds with keeping one’s head down, nose to the grindstone, and not contributing ideas, critiques or initiative to the organization, out of fear that someone will steal the idea or use it against the originator.
This does not consider the effects of marauding armies or roving slavers who invade homes. But if we consider the military advantage of defense over offense then it becomes clear that in order to raise the military force to be a marauder or slaver, one must first have an institution that delivers military fealty of soldiers to captains. This is what we are trying to build in this model, so we first focus on a historical period where this has not happened yet.
As mentioned in Sect. 2.5.2, this is over and above the risk of the trading partner retaliating or “cheating back”, because legal pursuit is only triggered after the predatory behavior has taken place. Provided the aggrieved party did not also run afoul of the law, the culprit will be apprehended (with probability \(\pi\)) even long after the transaction is over. In addition, unlike individual retaliation, the cost to the law enforcer is not a factor in the decision to pursue.
Existing economic theory, such as supply–demand curves under monopoly or competition, already yields well known conclusions regarding the causes and effects of asymmetry in transactions.
An organization entrusted with maintaining an institution of either variety may end up extracting more value than it adds. This imbalance is suggested by other researchers (Olson 1971) (notably). We plan to analyze this issue in depth using the theta–pi model in a future paper.
Mathematically more complex equilibria are found by calculus or numeric methods, but the games the occur in this paper are all solved by inspection.
Except for cases where an equilibrium fails to exist, such as when the payoff matrix is such that the winning strategy is a mixed strategy. For example a game like rock-paper-scissors only has an equilibrium in mixed strategies, namely to pick one of the three move at random exactly one third of the time. The prisoners’ dilemma game does not have a mixed strategy equilibrium, but some of the derivative games used in this decision model might.
It could also be said that the organization supporting the institution is collecting its dues in the form of impunity for a small class of individuals rather than in the form of direct taxation. The role of the king’s retinue or “elite” in governance is much studied, (Olson 1971; Sekeris 2011, e.g.), but the theta–pi model adds in the effect of empathy on the process. The addition of empathy only slightly changes the value of nepotism as a motivation for governing “elites” to develop (Olson 1971).
Technically, for very large \(\theta\) values, K might become smaller than 0.5 and the lower bound on it \((K_{min})\) would then be found using the make–take–sit values of the elite instead.
That is, when the “nobility” is also “noble” in behavior.
We can call this Phase 1d for “degenerate”, since transactions where being cheated is written off as a charity are unlikely to be the most prevalent in a society.
When empathy rather than retributive action is the main institution, the “Make” line is parallel to the “Take” line, and “Make” is a better choice for a wider range of E.
This is explained by more a rapid increase in \(E_{i}\) due to both “Make” and “Take” curves moving closer together in contrast to only the “Take” curve inclining.
The increase in universal empathy decreases \(E_{i}\) for the non-elite, while the elite’s payoff curves remains functionally the same.
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Acknowledgments
The authors acknowledge the personal role of Ryan Orr and Richard Scott at Stanford University in catalyzing the initial concept of this paper, and of Ali Yassine at the American University of Beirut for material and moral support.
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Nasrallah, W.F., Cheaib, K.A. An equilibrium model of how regulative and normative institutions influence micro-economic and organizational behavior. Comput Math Organ Theory 22, 383–411 (2016). https://doi.org/10.1007/s10588-015-9205-x
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DOI: https://doi.org/10.1007/s10588-015-9205-x