PA30: Commitment Problems, Expected Value, and the Political Economy of Conflict

Exam Logistics and Course Overview

Students are informed that they will have $75\,\text{minutes}$ for the upcoming exam. Logistics will be discussed further in section, but attendees are advised to arrive early as the preceding class often runs behind. Upon arrival, students should log into their browsers and complete the two-factor authentication process to ensure they are ready to begin precisely at $2:00\,\text{PM}$. Once the exam is initiated, the $75\,\text{minutes}$ countdown begins, excluding those with approved accommodations who have had their additional time pre-programmed into the system. Regarding the content, today's lecture is relevant to the exam as it reviews and builds upon concepts introduced in previous sessions, specifically how institutional mechanisms can solve commitment problems and provide individuals with certainty by punishing appropriation.

Olson’s Stationary Bandit and the Formation of the State

A critical insight from the work of Olson is the transition from roving to stationary banditry. Roving banditry is described as inherently self-defeating. In this scenario, individuals like Arthur Rosenwald might enter a town to steal all available resources. This creates a disincentive for citizens to invest in labor, plant crops, build businesses, or invest in education for themselves or their children. If bandits are expected to seize all production, no one makes forward-looking investments, leading to a state of poverty where there is eventually nothing left for the bandits to steal. To maximize their take, bandits eventually establish a domain, exerting control andProviding protection within that territory. This stationary bandit becomes a centralized authority that collects taxes rather than engaging in random plunder. Their primary interest is boosting tax revenue rather than maximizing general welfare, as seen in the example of the Islamic State, which focused on tax revenue rather than just oil. This authority provides protection to ensure folks engage in productive activities that can be taxed. However, this creates a secondary commitment problem where citizens fear being overtaxed. This often leads to checks on executive power; for example, the British monarchs ceded power to Parliament to provide the rising elite with the certainty they needed to invest, in exchange for the funding required to fight wars.

Probability, Expected Value, and Risk Assessment

The lecture introduces expected value as a mechanism for evaluating risky bets or gambles. If a person takes a bet multiple times, they can calculate what they expect to earn on average. For a bet where one has a $50\,\%$ chance of losing $\$5$ and a $50\,\%$ chance of winning $\$10$, the expected value ($EV$) is calculated as follows:

$EV = 0.50 \times (10) + 0.50 \times (-5) = 2.50$

While a single iteration only results in a gain of $\$10$ or a loss of $\$5$, the $EV$ of $\$2.50$ represents the long-term average. Another example involves a bet where flipping heads results in paying $\$100$ and tails results in receiving $\$100$, yielding an $EV$ of $\$0$. This logic is applied to tax evasion scenarios. If a citizen is caught cheating, the penalty is $\$100$. If there is a $1\,\%$ chance of being caught and a $99\,\%$ chance of not being caught (paying $\$0$), the expected value of cheating is:

$EV_{\text{cheat}} = 0.01 \times (-100) + 0.99 \times (0) = -1$

If the legal tax is $\$5$, the citizen is tempted to cheat because paying $\$1$ on average is cheaper than the $\$5$ certain payment. This underscores that individuals consider the likelihood of detection, not just the severity of the fine—a principle applied to daily decisions like speeding in a car.

War as a Costly Gamble and the Bargaining Range

War can be conceptualized as a gamble over territory where two sides, A and B, fight over something they both value ($\$1$ or a common value). Side A has a probability $p$ of winning, and Side B has a probability $1 - p$. Fighting is costly, with each side incurring a positive cost $c$. The expected payoff for Side A and Side B can be expressed as:

$E[A] = p \times (1) + (1 - p) \times (0) - c = p - c$

$E[B] = (1 - p) \times (1) + p \times (0) - c = 1 - p - c$

Using a numerical example where $p = 0.4$ and $c = 0.2$:

$E[A] = 0.4 - 0.2 = 0.2$

$E[B] = (1 - 0.4) - 0.2 = 0.6 - 0.2 = 0.4$

In this scenario, Side A expects to gain $0.2$ and Side B expects to gain $0.4$. However, if they split the territory $50/50$ (giving each $0.5$) without fighting, both are better off since $0.5$ is greater than both $0.2$ and $0.4$. There exists a spectrum of splits (e.g., $30/70$) where both sides receive more than their anticipated payoff from war. This range is known as the Bargaining Range. Because war is risky and costly, there should always be a set of negotiated settlements that both parties prefer over fighting. The rationalist puzzle of war asks why, if this bargaining range exists, states still choose to fight.

Understanding the Scale of War Costs

To illustrate the immense costs of war, the lecture provides a temporal analogy for large numbers. One million seconds was approximately $11.7\,\text{days}$ ago. One billion seconds was $31.7\,\text{years}$ ago (roughly $1993$). One trillion seconds was roughly $31,700\,\text{years}$ ago, during the last ice age. The total cost of recent wars is estimated at $\$5,000,000,000,000$. To put this into perspective, the total annual college tuition paid in the United States is roughly $\$350,000,000,000$. The $\$5\,\text{trillion}$ spent on these wars could have funded all U.S. college tuition for $15\,\text{years}$. This highlights that rational states have immense incentives to locate negotiated settlements within the bargaining range to avoid such staggering expenditures.

Commitment Problems and Preventive War

Commitment problems arise when parties cannot credibly promise to uphold a deal, leading to conflict despite the existence of a bargaining range. A classic example involves a state (B) asking a rebel group (A) to disarm in exchange for power. Rebel group A may refuse because once they are defenseless, the state has an incentive to renege and demand more. The rebels would rather fight now from a position of relative strength than risk a future where they are subject to exploitation. This also applies when power shifts naturally over time. A side that sees its power diminishing may launch a preemptive or preventive war to lock in a more advantageous bargain today rather than negotiate from a position of weakness tomorrow.

In the case of the Iraq War, the George W. Bush administration feared that Iraq's potential acquisition of weapons of mass destruction (WMD) would shift power decisively in Saddam Hussein's favor. Even if the U.S. remained stronger in absolute terms, the shift would force the U.S. into less advantageous bargains. Similarly, the conflict in Ukraine is influenced by Vladimir Putin's fear that Ukraine's future membership in NATO would diminish his future bargaining power. In current tensions with Iran, the U.S. worries that a nuclear-equipped Iranian regime could not credibly commit to not using that leverage, while Iran worries that giving up its program—its only source of leverage—would leave it vulnerable to U.S. exploitation.

Challenges in Ending Civil Conflict

Barbara Walter's research indicates that civil wars are particularly difficult to end, not because of indivisible stakes or ancient ethnic hatreds, but because of commitment problems. Even when mutually acceptable solutions are found, neither side can credibly commit to honoring a peace agreement. Parties may fear being the only one to demobilize (the "sucker"), leaving them vulnerable to torture or exploitation. Consequently, groups may hide weapons as a safeguard, which further undermines trust. Solving these problems often requires third-party institutions, such as outside powers or international organizations, to act as guarantors of the ceasefire and use their strength to ensure the terms of the agreement are upheld.

Political Survival and the Destruction of Infrastructure

Commitment problems also explain why political leaders sometimes pursue policies that intentionally shrink their economies. Jerome Osimolu and James Robinson, in their book Why Nations Fail?, cite the example of Shakas Stevens, who became the president of Sierra Leone in $1967$. Stevens dismantled a critical railway connecting the agricultural and mining hubs to ports. He did this because the rail line and the economic growth it generated were concentrated in the stronghold of his political opposition. Fearing that economic growth would translate into political power for his rivals, and because the opposition could not credibly commit to keeping him in power if they became strong enough to oust him, Stevens chose to sacrifice national growth to maintain his own power. Similar logic applies to contemporary situations; for instance, the Houthi rebels in Yemen have refused UN assistance to secure a decaying oil tanker off the coast. They view the potential environmental and economic catastrophe as strategic leverage to stay in power, fearing that once the risk is neutralized, their opponents would renege on political promises.

Autocratic Tenure and the Fear of Prosecution

Finally, the lecture addresses why autocrats, such as Paul Biya of Cameroon, who is $93\,\text{years old}$, remain in office despite their age and the stresses of leadership. These individuals often maintain power through oppression and human rights violations. They fear that stepping down will lead to prosecution for their crimes. The international community's desire for justice and human rights can paradoxically create a trap; because autocrats fear imprisonment or trial if they leave office, they are incentivized to remain in power indefinitely, further entrenching the cycle of repression.

Questions & Discussion

Question: Why do warring parties choose to keep fighting rather than settle even when mutually acceptable solutions exist? Answer: They might value the win more than the cost, or more likely, they face a commitment problem where neither side can guarantee the other won't strike again after a settlement. The fear of being the only one to demobilize leads to a situation where they prefer the risky gamble of war over a peace agreement they believe will be broken. This is why outside powers are often necessary to solve these commitment issues and enforce a ceasefire.