📈 economics

From Limited to Open Access Orders: An Evolutionary Game Theory Approach and a Case Study of South Korea

This paper employs an evolutionary game-theoretic model to formalize the transition from Limited to Open Access Orders, demonstrating that sustained institutional change requires the simultaneous satisfaction of North et al.'s three "doorstep conditions" as endogenous thresholds, a finding empirically validated through the calibration of South Korea's 1987 democratic transition.

Original authors: Mohammadreza Yavari, Shahram Fattahi, Salah Salimian, Farshad Keshavarz

Published 2026-10-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Mohammadreza Yavari, Shahram Fattahi, Salah Salimian, Farshad Keshavarz

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Societies are built on rules, the invisible frameworks that decide who gets to play, who gets to win, and who gets to be left out. For most of human history, these rules have favored a small group of powerful people. In these systems, often called limited access orders, the elite form a tight club where they share power and wealth to keep the peace. They control the violence, the money, and the ability to start businesses, using these privileges to ensure no one challenges their rule. It is a stable arrangement, but it is one that keeps the rest of the population in the dark, limiting economic growth and freedom.

However, some societies manage to break out of this club. They move toward what researchers call open access orders, where the rules apply to everyone, not just the insiders. In these systems, anyone can start a business, join a political party, or seek justice in court, and the government holds a monopoly on violence rather than letting warlords or private armies fight it out. This shift is one of the most important transformations in human history, yet it happens rarely and is incredibly difficult to understand. For a long time, scholars have described these changes as historical accidents or the result of specific leaders, but they have struggled to explain the exact mechanics of how a society tips from one state to the other.

A team of researchers from universities in Iran has taken a new approach to this puzzle. They built a mathematical model to simulate how a society moves from a closed, elite-controlled system to an open, inclusive one. Instead of just looking at history books, they treated the transition like a game where different groups of people constantly adjust their strategies based on what others are doing. They focused on the interactions between the powerful elite and the broader population, asking a simple but profound question: what specific conditions must be met for a society to successfully make the jump from a closed system to an open one?

To answer this, the researchers used a method called evolutionary game theory. Imagine a large room full of people, some of whom are willing to play by the new, open rules, and others who prefer to stick to the old, exclusive ways. The model tracks how the number of people willing to play by the new rules grows or shrinks over time. The researchers found that this process is not smooth or gradual. Instead, it is a struggle with two very different possible endings. A society can get stuck in the old, closed system forever, or it can flip into the new, open system. The key to making that flip is reaching a critical tipping point.

The study identifies three specific conditions that must be met for this transition to happen, which the researchers call "doorstep conditions." First, the powerful elite must agree to follow the law themselves, rather than acting above it. Second, organizations like companies or political parties must be able to exist on their own, surviving even if the specific people who founded them die or leave. Third, the state must have a firm, consolidated control over violence, ensuring that no single group can use force to settle disputes. The model shows that these three conditions act like a threshold. If a society has only one or two of them, it will likely fail to change or will slide back into the old ways. All three must be present and strong enough to push the society past the tipping point.

To test if their model worked in the real world, the team applied it to the history of South Korea. The country offers a clear example of this transition, moving from a military-led, closed system in the 1980s to a modern democracy with a robust economy. The researchers fed historical data about South Korea's political changes, legal systems, and economic growth into their simulation. They adjusted the numbers in their model until the simulated history matched the actual history of the country. The results were striking. The model successfully recreated the timeline of South Korea's transition, including the rapid changes that happened after 1987. However, the researchers noted that the model does not fully account for complex external shocks like the 1997 financial crisis, which required additional factors beyond the core evolutionary dynamics to explain the specific turbulence of that period.

The simulation revealed that while the speed at which the elite learned to adapt played a role, structural parameters—specifically organizational durability and critical mass thresholds—predominated over adaptive learning rates in driving the final transition outcomes. The researchers found that once the society crossed the critical threshold of elite support, the change became self-reinforcing. The benefits of the new system grew larger as more people joined in, making it harder for the old guard to resist.

However, the study also highlights the fragility of this process. The model shows that if the threshold is not crossed, or if the new institutions are too weak, the society can easily fall back into the old, closed system. This explains why some countries that start down the path of democracy or economic reform eventually stall or reverse. The researchers found that the transition is not just about having good laws on paper; it requires a deep structural change where the incentives for the powerful align with the rules of the open system. If the elite can still make more money by breaking the rules or hoarding power, the system will likely revert to the old ways.

The findings offer a clear warning for policymakers and development agencies. Trying to fix just one part of the system, like passing a new law without strengthening the organizations that enforce it, is unlikely to work. The model suggests that successful transitions require a coordinated effort to improve all three conditions at once. You cannot have open access without the rule of law, and you cannot have the rule of law without organizations that can stand the test of time. The study concludes that while the path to an open society is difficult and fraught with the risk of failure, it is not a mystery. It follows a logical pattern that can be understood, measured, and potentially guided, provided the right structural conditions are met to push the society over the edge.

Technical Summary: From Limited to Open Access Orders: An Evolutionary Game Theory Approach and a Case Study of South Korea

Problem Statement
While the framework of Limited Access Orders (LAOs) and Open Access Orders (OAOs) developed by North, Wallis, and Weingast (NWW) offers profound historical insights into social orders, the mechanisms governing the transition between them remain largely descriptive. Existing literature lacks dynamic, behaviorally grounded models that explain how elite strategies and informal norms co-evolve to shift institutional equilibria. This paper addresses the gap in formalizing the transition from LAOs to OAOs, specifically seeking to identify the conditions and mechanisms under which societies move from elite-dominated rent-seeking systems to impersonal, open-access institutions.

Methodology
The authors employ an evolutionary game-theoretic model utilizing replicator dynamics to simulate the strategic interactions among competing elite groups. The model treats the transition as an adaptive process under bounded rationality, where the share of elites supporting institutional reform (cooperators) evolves over time based on payoff differentials.

Mathematical Specification: The model defines the share of cooperators as $x \in [0,1]$ . Payoff functions for cooperators ( $f_C$ ) and defectors ( $f_D$ ) are nonlinear, incorporating:
- Strategic Complementarity ( $\alpha$ ): Increasing marginal returns to cooperation.
- Diminishing Returns to Defection ( $\beta$ ): Decreasing returns for rent-seeking as cooperation spreads.
- Threshold Parameter ( $\theta$ ): A critical mass of cooperators required to trigger full institutional benefits (formalizing NWW's "doorstep conditions").
- Organizational Durability ( $\omega$ ): A parameter capturing institutional inertia and the resistance of entrenched structures.
- Learning Rate ( $\lambda$ ): The speed of strategic adaptation.
- External Pressure ( $E$ ): Exogenous shocks (e.g., sanctions, mobilizations) that alter payoff structures.
Empirical Calibration: The model is calibrated using historical and institutional data from South Korea (1980–2020), a canonical case of LAO-to-OAO transition. The authors utilize data from V-Dem (Electoral Fairness, Associational Autonomy), Polity IV (Polity2), and the World Bank's Worldwide Governance Indicators (Rule of Law).
Optimization: Parameters ( $\lambda, \omega, \theta$ ) are endogenously calibrated via a two-stage optimization strategy (coarse grid search followed by L-BFGS-B local optimization) to minimize the Sum of Squared Residuals (SSR) between simulated trajectories and observed institutional indicators.

Key Contributions

Formalization of NWW Framework: The study provides the first formal mathematical model of the LAO-to-OAO transition, embedding NWW's three "doorstep conditions" (Rule of Law for Elites, Perpetually-Lived Organizations, Consolidated Control of Violence) as endogenous threshold parameters within a replicator dynamic system.
Bistable Dynamics and Thresholds: The model demonstrates that institutional transitions exhibit bistable dynamics, characterized by two stable equilibria (LAO at $x=0$ and OAO at $x=1$ ) separated by an unstable interior equilibrium (tipping point). It reveals that sustained transitions require the simultaneous satisfaction of threshold conditions; partial reforms leave societies vulnerable to elite rent-seeking traps or reversals.
Quantification of Structural vs. Adaptive Factors: Through calibration, the paper distinguishes the roles of structural parameters (organizational durability, critical mass thresholds) versus adaptive learning rates in driving transitions.

Results

Calibration for South Korea: The model achieves a high goodness-of-fit with South Korean data ( $R^2 = 0.931$ $R^{2} = 0.931$ for Rule of Law, $R^2 = 0.910$ $R^{2} = 0.910$ for Polity2).
- Critical Threshold ( $\theta^*$ ): Calibrated at 0.35, indicating that approximately 35% of elite support is required to trigger an irreversible transition.
- Learning Rate ( $\lambda^*$ ): Calibrated at 0.23, reflecting the rapid strategic realignment of Korean elites post-1987.
- Organizational Durability ( $\omega^*$ ): Calibrated at 0.75, highlighting significant institutional inertia and path dependency rooted in state-chaebol networks.
Dynamic Trajectory: The simulation reproduces the historical "S-shaped" trajectory of South Korea's transition: an initial incubation phase, a non-linear acceleration upon crossing the critical threshold (corresponding to the 1987 Democratic Uprising), and a gradual consolidation phase.
Sensitivity Analysis: The model is highly sensitive to organizational durability ( $\omega$ ), which dominates the timing and speed of transition. The learning rate ( $\lambda$ ) has a moderate influence. The results confirm that structural conditions (thresholds and durability) are more determinative of transition outcomes than the speed of elite learning alone.
Bifurcation: The model exhibits saddle-node bifurcation behavior, where stable and unstable equilibria converge and disappear as parameters shift, leading to discontinuous institutional changes.

Significance and Claims
The paper claims to advance institutional economics by shifting the study of institutional change from descriptive analysis to evidence-based policy design through formal modeling, while acknowledging the limits of such formalization.

Predictive Logic: It argues that transitions follow predictable evolutionary patterns rather than purely stochastic processes, allowing for the identification of specific parameter combinations that generate successful transitions within specific historical contexts. However, the authors caution that these parameter values reflect historical and cultural contexts that cannot be fully reduced to equations, and thus should not be viewed as universal constants.
Policy Implications: The findings suggest that development assistance should be coordinated rather than sector-specific. Simultaneous improvement across all "doorstep conditions" is necessary; isolated reforms are insufficient. The paper suggests that countries with structural parameters similar to the calibrated South Korean case (e.g., $\alpha > 1.2$ , $\beta > 0.8$ , $\gamma > 0.35$ ) may have a higher likelihood of successful transition, but emphasizes that these observed values are context-dependent rather than universal policy thresholds.
Reversibility: The model highlights that even consolidated OAOs remain vulnerable to reversal if rents and institutional power remain concentrated, explaining why some middle-income countries with formal democratic institutions remain trapped in limited access equilibria.

The authors maintain a modest tone regarding limitations, acknowledging that the model abstracts from the full complexity of social and cultural contexts, informal norms, and spatial network dimensions of elite coalitions. They posit that formal modeling and interpretive analysis are complementary approaches for understanding institutional development.

Technical Summary: From Limited to Open Access Orders: An Evolutionary Game Theory Approach and a Case Study of South Korea

More like this