The Autocrat's Credibility Problem and Foundations of the Constitutional State

Overview of the Autocrat's Credibility Problem

• The paper by Roger B. Myerson (2008) addresses a central moral-hazard problem in politics: a political leader's temptation to deny costly rewards promised to supporters once power is secured.

• Myerson uses a game-theoretic model to explore how elements of constitutional government, such as courts and councils, emerge to solve this trust problem.

• The primary thesis is that even an autocrat must be judged by his supporters to be credible. The standards of behavior active supporters expect of their leader constitute a "personal constitution," which serves as the foundation for all other state constitutions.

• Fundamental quote from Shakespeare's Richard II: "How art thou a king but by fair sequence and succession? … if you do wrongfully seize Hereford's rights … you pluck a thousand dangers on your head."

A Game-Theoretic Model of Contests for Power

• Income and Challenges: A ruler on an island receives a flow of taxes and rents denoted by $R$ per unit time. To maintain power, the ruler must defeat challengers who arrive according to a Poisson process with an expected rate $\lambda$.

• The Poisson Process Properties:

  • The waiting time $T$ until the next challenger arrives is an exponential random variable with mean $\frac{1}{\lambda}$.

  • The expected discount factor for rewards delayed by $T$ is $E(e^{-\delta T}) = \frac{\lambda}{\delta + \lambda}$, where $\delta$ is the discount rate.

  • A stream of income $y$ until the next challenger arrives is worth $\frac{y}{\delta + \lambda}$.

• The Contest Success Function: A leader's probability of winning a battle, $p(n|m)$, depends on the number of his captains ($n$) versus the rival's captains ($m$). The standard assumption for such contests is:

  • $p(n|m) = \frac{n^s}{n^s + m^s}$

  • Here, $s$ is a constant representing returns to scale, usually between $1$ and $2$.

• Costs and Rewards: Each captain incurs a cost $c$ to support the leader in battle. All agents are risk-neutral.

• Captain's Payoff Equations:

  • Let $U(n, y|m)$ be the expected discounted value of a captain's payoff during peace:

    • $U(n, y|m) = \frac{y - \lambda c}{\delta + λ - λ p(n|m)}$

  • The captain's expected payoff on the eve of battle is:

    • $-c + p(n|m)U(n, y|m) = \frac{p(n|m)y - c(\lambda + \delta)}{\lambda + \delta - \lambda p(n|m)}$

  • A captain only fights if this payoff is non-negative, which requires the wage $y$ to be at least:

    • $Y(n|m) = \frac{c(\delta + \lambda)}{p(n|m)}$

• Leader's Payoff Equations:

  • Let $V(n, y|m)$ be the leader's value during peace:

    • $V(n, y|m) = \frac{R - ny}{\delta + \lambda - \lambda p(n|m)}$

  • Let $W(n, y|m)$ be the leader's value on the eve of battle:

    • $W(n, y|m) = p(n|m)V(n, y|m) = \frac{p(n|m)(R - ny)}{\delta + \lambda - \lambda p(n|m)}$

Absolute Leaders and Third-Party Judgments

• Definition of Absolute Monarch: A leader released from the constraints of law. In game-theoretic terms, this means the leader is subject to no third-party judgments; relationships with supporters are purely bilateral.

• The Credibility Barrier: If a leader can violate norms without fear of collective punishment, he cannot credibly promise rewards. If he cheats one captain, it does not affect his relationship with others because they do not communicate.

• Feasibility Condition for Absolute Leaders:

  • A force of size $n$ is feasible against rivals $m$ if there exists a wage $y$ such that:

    1. $y \geq Y(n|m)$ (Participation constraint).

    2. $V(n, y|m) \geq V(k, y|m)$ for all $k \in [0, n]$ (Moral-hazard constraint).

  • This implies the leader will not benefit from paying fewer than $n$ captains and losing their future support.

• Proposition 1: An absolute leader would always be better off if he could commit to a larger force than what is feasible under pure absolutism. Specifically, if n > 0 is feasible, there exists some k > n such that v(k|m) > V(n, y|m) and w(k|m) > W(n, y|m). Absolute power is thus a competitive disadvantage.

Communication and the Leader’s Court

• The Princely Court: Throughout history, courts served as forums where supporters gathered. This allows for communication: the absence or complaint of one courtier signals a breach of trust to all others.

• Weak Court Feasibility:

  • A court is "weak" if it cannot depose the leader immediately but can guarantee the leader gets zero support against the next challenger if a breach occurs.

  • Condition: v(n|m) > \frac{R}{\delta + \lambda}.

• Strong Court Feasibility:

  • A court is "strong" if a loss of confidence results in the leader being immediately deposed (payoff goes to $0$).

  • Condition: v(n|m) > 0.

• Proposition 2 (Bounds of Suppression): If s > 0.5, a weak-court leader is limited in the size of rivals they can face. The rivals' force is bounded by $M_0 = \frac{R \lambda (2s - 1)^{2 - \frac{1}{s}}}{4s^2 c (\delta + \lambda)^2}$. If $\lambda$ (frequency of challenges) is low, weak courts are very ineffective.

• Proposition 3: For s > \frac{2}{3}, any force feasible for a weak court is such that the leader would prefer a larger force. Therefore, leaders have a strong incentive to organize a strong court capable of removing them to gain credibility for larger coalitions.

Negotiation-Proof and Oligarchic Equilibria

• Negotiation-Proof Equilibrium ($m_1$): An equilibrium where each leader chooses the force size $n$ that maximizes their pre-battle value $w(n|m)$, and in equilibrium, $n = m$.

  • Proposition 4: For s < 2, the equilibrium size is $m_1 = \frac{Rs}{c(4 \delta + 2 \lambda + s \lambda)}$.

  • The fraction of revenue paid to supporters is $\frac{m_1 Y(m_1|m_1)}{R} = \frac{2s(\delta + \lambda)}{4 \delta + 2 \lambda + s \lambda}$.

  • For s > 2, equilibria involve randomized strategies where expected payoffs for contestants are zero.

• Oligarchic Equilibrium ($m_2$): A system where rewards are shared equally among all active supporters (egalitarian norm). Oligarchs choose $n$ to maximize the per-capita payoff $Q(n|m) = \frac{w(n|m)}{n}$.

  • Proposition 5: For 1 < s < 2, the equilibrium is $m_2 = \frac{R[(s - 1) \lambda - (2 - s) \delta]}{c(\delta + \lambda)s \lambda}$.

  • Oligarchies tend to be smaller than monarchies (m_2 < m_1) because recruiting new members is costlier under egalitarian norms (the surplus must be shared equally, not given as a minimum wage).

  • If challenges are infrequent ($\lambda$ is low), an oligarchy might collapse ($m_2$ could be $0$).

Focal Coordination and Political Power

• The Foundation of Power: Myerson argues that political power is based on common recognition rather than prior consent (Hume, 1748). This is modeled via the Schelling Focal-Point Effect.

• The Rival-Claimants Game (Chicken):

  • If two peasants claim a field: conflict ($-k, -k$).

  • If one claims and one defers: ($r, 0$) or ($0, r$).

  • If both defer: ($0, 0$).

• Sovereign Jurisdiction: A recognized leader can pick an equilibrium by designating who should claim. Players obey because they expect the other to obey. This generating of order produces the revenue $R$ that leaders compete for.

• Multiple Equilibria: The status of a leader is a reputational equilibrium. Trust and distrust are two different equilibria of the same game. Legitimacy or "charisma" is what allows a leader to be the focal point for a large group of supporters.

Historical and Practical Implications

• The King in Parliament: Traditional English doctrine holds that sovereignty rests with the king in parliament, mirroring the requirement of a court for credibility.

• Tyranny as Exceptional: Rulers like Ivan the Terrible or Stalin, who destroy their own courts, represent a failure of rational expectations. In the long run, such regimes are competitively weak because they cannot recruit voluntary support for defense.

• Institutional Evolution:

  • English Common Law (1160): Established by Henry II to treat supporters of both sides (Stephen and Matilda) equally, ensuring elite trust.

  • Song Empire (980): Developed the Chinese civil service to integrate and reward former courtiers of the Ten Kingdoms.

  • Military Competition: Competition often forces states to extend rights to broader populations to earn their loyalty in battle.

• New vs. Old Democracies:

  • In established democracies, leaders have developed reputations within constitutional bounds.

  • In new democracies, leaders may have built support through illicit means (private violence, corruption). Forcing them into new rules might violate their "personal constitutions" with existing supporters.

  • Success in new democracies may depend on a federal division of powers, allowing new leaders to cultivate democratic reputations independently.

Numerical Example Summary

• Parameters: $R = 90$, $\delta = 0.05$, $\lambda = 0.2$, $c = 5$, $s = 1.5$.

• Results:

  • Absolute leader bound: Cannot raise force if m > 12.03.

  • Weak court bound ($M_0$): $16.13$.

  • Negotiation-proof equilibrium ($m_1$): $30$.

  • Oligarchic equilibrium ($m_2$): $18$.

  • In the negotiation-proof equilibrium ($n=30$), captain wage $y = 2.5$. The total wage bill is $0.833R$.

  • Coordination Trap: Against $m_1=30$, a leader needs at least $6.24$ supporters to be viable; otherwise, the required wage exceeds total revenue $R$.