IR Chapter 3 Part 1 Notes
Prisoner’s Dilemma: quick review and equilibrium
We started from the classic prisoner's dilemma (PD) to illustrate how states interact and why cooperation can fail.
The class asked: what is the equilibrium outcome in this game? Answer: both players defect (D) and end up with a suboptimal payoff.
Definition: an equilibrium is a situation where no player has an incentive to unilaterally change their strategy given the other player's choice.
In the discussion, you hear that it is a dominant strategy for both players to defect: regardless of what the other does, defecting is the best reply.
If the other player cooperates, defection yields a higher payoff (e.g., 4 vs 3 for the defector).
If the other player defects, defection still yields a higher payoff (e.g., 2 vs 1).
Classroom translation: the equilibrium outcome is that both defect and serve 5 years each (the professor uses a prison sentence interpretation to illustrate the payoff).
PD payoff structure (illustrative matrix for one player; payoffs are years in prison here): \begin{array}{c|cc} & \text{P2: C} & \text{P2: D} \\hline \text{P1: C} & (3,3) & (1,4) \\n \text{P1: D} & (4,1) & (2,2) \ \end{array} fs: (C,C) = (3,3); (C,D) = (1,4); (D,C) = (4,1); (D,D) = (2,2).
The equilibrium is (D,D) with both getting 2 (interpreted as 5 years each in the lecture example).
Why this matters for international relations (IR): it shows how rational, self-interested actors can end up in a poor, non-cooperative equilibrium when they don’t trust the other side to cooperate.
Repeated interaction and trust can move outcomes toward cooperation: if states interact over time, they may develop expectations, reputations, and credible commitments that promote cooperative behavior.
Cold War example referenced: lack of trust between two nations can lead to prioritizing security and deterrence over collaboration.
Takeaway: even when cooperation could yield a larger pie (e.g., in a stag hunt), strategic dynamics can trap both sides in a suboptimal outcome unless there’s trust, long-term relationships, or mechanisms to sustain cooperation.
Cooperation vs bargaining: definitions and differences
Cooperation vs bargaining definitions used in the session:
Cooperation: moving from a suboptimal status quo toward the Pareto frontier by expanding the pie (producing a bigger total gain).
Bargaining: negotiating along the Pareto frontier to split a fixed pie; one side loses what the other gains.
The lecture ties these ideas to why wars happen: if states could cooperate, they wouldn’t fight; wars occur because bargaining often fails and the pie cannot be grown or shared smoothly.
Outline for the day: first consider what states fight over; then examine why bargaining fails; focus today on incomplete information as a cause of war; Thursday will cover credible commitment and indivisibility.
What do states fight over? Types of conflicts and examples
A common empirical finding in IR: about 57% of wars since the mid-1800s have been over territory; the line between territory and policy/regime-type is blurry.
Other major war causes include attempts to change policies or regimes in rival states (e.g., attempting to replace a regime or alter a policy alignment).
Desert Storm (1990-1991) is discussed as a Gulf War example with both territorial and policy dimensions (oil fields, debt forgiveness, and post-war governance goals).
Resources and geography matter a lot: oil and natural gas, water, farming and strategic resources.
The price of entry for war is very high, but leaders still wage war to secure is a crucial question; we’ll come back to why that happens despite high costs.
Examples discussed:
Kashmir (Jammu and Kashmir): India vs. Pakistan over territory; border regions with multiple claimants (India controls parts, Pakistan controls others; China also claims parts). The dispute is driven by ethnic, religious, and strategic considerations.
Golan Heights: Israel vs. Syria; strategic mountain region allowing surveillance and military advantage; captured in 1967 and still controlled by Israel.
Holy Land (Jerusalem): religious significance makes dividing the territory difficult; divisibility issues can block bargaining.
Water resources: Jordan River, Nile, Dam disputes (e.g., Sudan–Egypt tensions over dam projects); rivers cross borders and create cross-border resource stakes.
Other resources: oil fields in the Persian Gulf, natural gas, diamonds, agriculture, and broader resource bases.
Ethnic, cultural, and religious identities often intertwine with claims to territory, making some areas “indivisible” in practice.
A final note from the discussion: sometimes the conflict is fueled by long-standing animosity and trust deficits, not only rational calculations about land value.
Why war is costly and why states still fight
War is extremely costly in lives and money; this creates a core bargaining puzzle: why not just bargain to avoid costs?
Some numbers and points raised:
U.S. federal budget share for defense is debated in class; estimates ranged from around 25-30% to much lower figures like 13% depending on framing and year; the instructor notes uncertainty in the moment.
Even if a war is won, costs include lives, infrastructure destruction, and long-term economic and political costs for the leaders.
The bargaining framework: imagine war as an option to enforce a bargain that neither side would accept today; the expected border after war, net of costs, must beat the status quo for the war to be attractive.
Analogy with court cases and labor disputes: most disputes are settled by bargaining before trial/strike because the costs of litigation/strikes are high; war behaves similarly as a costly, high-stakes bargaining process.
The core question is: why do wars occur if there is a potential bargain that benefits both sides?
The answer lies in the three bargaining impediments to be explored: incomplete information, credible commitment problems, and indivisibility.
The bargaining model: territory as a fixed pie and the bargaining range
The bargaining model treats territory (or other agreed outcomes) as a fixed quantity that must be split if no war occurs.
A simple illustration: two states A and B negotiate over a fixed land area.
Each side has an ideal share (A wants all the land; B wants all the land).
There is a continuum of possible borders between the two extremes, creating a set of feasible settlements where both sides gain more than the status quo but less than their ideal.
If they fight, the border could move to some hypothetical post-war position, but this comes with costs (lives, money).
The bargaining range is the set of borders both sides would prefer to the war outcome, given the costs of war.
The status quo border is some baseline; moving the border closer to the opponent may be appealing if the war costs are high and the post-war result would still yield a favorable outcome.
The key idea: even if both sides would prefer a better border, if war costs make the post-war gain not worth the costs, they should settle within the bargaining range instead of fighting.
An important caveat: sometimes the status quo lies outside the bargaining range; in such cases, one side would still threaten or fight to force a better deal, depending on the relative costs and benefits.
The example with India and Pakistan (Kashmir) is used to illustrate this: both sides would prefer some shift in the border but not at the cost of a full-scale war; nuclear deterrence factors into the dynamics and reduces the likelihood of a hot war, keeping things in a locked bargaining range with periodic skirmishes.
Incomplete information: resolve, commitment, and divisibility
Incomplete information about resolve: actors may not know how willing the other side is to fight or whether they will follow through with a threatened war; this uncertainty can lead to miscalculation and bluffing.
The Desert Storm discussion is a vivid example: Saddam’s threat to Kuwait hinged on uncertain American willingness to intervene; Kuwait’s leadership questioned whether the U.S. would actually commit to a costly intervention.
Credible commitment problem: even if both sides know the likely war costs and benefits, they may doubt whether a current bargain will be honored in the future.
The Neville Chamberlain example: appeasing Hitler by conceding Czechoslovakia arguably incentivized further demands; the commitment problem arises because concessions today may pave the way for larger demands tomorrow.
Indivisibility: some goods cannot be divided without severe costs or loss of core value, making bargaining difficult or impossible.
The Holy Land (e.g., Jerusalem) is often cited as indivisible due to religious and cultural significance; this makes negotiated division unlikely.
The three concepts explain why two rational actors might still fail to reach a bargain and end up in war, despite the costs.
Desert Storm (Gulf War) as an incomplete information case study
Setting: Iraq had fought a long, costly war with Iran, leaving Saddam Hussein deep in debt to Kuwait.
Saddam’s position: Saddam demanded debt forgiveness and controlled or claimed ownership of oil fields near the Iraqi-Kuwaiti border; he argued Kuwait was over-pumping oil from the border fields, stealing Iraqi revenue.
Kuwait’s position: Kuwait offered a greatly reduced debt-forgiveness package (about $0.5 billion) while Saddam demanded roughly $10 billion in value. Kuwait believed Saddam might be bluffing and hoped to avoid a costly confrontation.
The role of resolve and credibility:
Saddam did invade Kuwait in 1990 after Kuwait refused to forgive the debt, convincing some observers that Saddam was not bluffing.
The United States and coalition partners faced uncertainty about whether others would join the fight and about the political costs of going to war at home.
Outcome and lessons:
Saddam believed the coalition would not mobilize effectively or would be too costly to sustain; in retrospect, the coalition did mobilize, but not all potential supporters joined the effort, which influenced Saddam’s calculations.
The episode illustrates incomplete information about resolve and the strategic incentives to bluff, mislead, or test the other side’s willingness to fight.
The session notes that the 2003 invasion of Iraq (the second Gulf War) had even less international backing than the 1991 war, highlighting how changes in coalition composition affect perceived credibility and the likelihood of intervention.
Takeaway: war is not a random outburst; it arises in part because each side’s beliefs about the other’s resolve, capability, and commitment shape strategic choices under incomplete information.
Credible commitment, incomplete information, and indivisibility in depth
Credible commitment problems arise when one side cannot credibly commit to restraining future demands or actions; past actions or domestic political constraints may undermine future commitments.
Incompleteness of information about resolve leads to bargaining failures: even if the players’ current situation seems optimal, uncertainty about future actions can derail agreements.
Indivisibility prevents straightforward division of a good; when a critical value cannot be split without losing its core significance, bargaining becomes challenging or impossible.
The combination of these factors helps explain why wars can occur even when both sides would prefer a negotiated outcome that avoids the costs of war.
Summary: connecting the dots between theory and real-world conflicts
The PD demonstrates how rational actors can end up in a non-cooperative equilibrium due to dominant strategies to defect, unless there is a mechanism to sustain cooperation (repetition, reputation, long-term relationships).
Cooperation vs bargaining: cooperation aims to expand the pie; bargaining aims to divide a fixed pie; both are means of diplomacy, but failures in bargaining or lack of trust can push actors toward conflict.
The post-World War II era shows a leveling off of interstate wars, possibly due to a combination of factors (nuclear deterrence, more states, economic interdependence, and institutional constraints), while civil wars increased in some periods and then stabilized.
Clausewitz’s maxim frames war as the continuation of political aims by other means: wars are fought to achieve policy outcomes, not for sport; the strategic choice is to assess whether war or bargaining better serves political objectives.
The bargaining framework with territory as an example shows how both sides’ valuations, costs of war, and expected outcomes shape whether a peaceful settlement is possible. The bargaining range captures the set of settlements both sides would prefer to war, given costs.
Incomplete information, credibility, and indivisibility are central in explaining why wars happen despite high costs and despite potential bargains that would make both sides better off.
Practical implications for policy and diplomacy:
Build credible commitments (e.g., verifiable agreements, independent enforcement) to mitigate commitment problems.
Reduce information asymmetries through transparency, signaling, and verification.
Recognize when indivisibility is a structural barrier and explore alternative arrangements or sequential bargaining.
Next session focus: a deeper dive into credible commitment and indivisibility, and how these ideas illuminate contemporary conflicts (e.g., Russia-Ukraine, Israel-Palestine, other territorial and security contests).
Key terms to remember
Prisoner’s Dilemma (PD): dominant strategy to defect leads to non-cooperative equilibrium; cooperation can be achieved via repetition, reputation, or enforcement mechanisms.
Cooperation vs Bargaining: expanding the pie vs splitting a fixed pie; Pareto frontier concepts.
Pareto frontier: outcomes where no one can be made better off without making someone worse off.
Bargaining range: set of outcomes both sides prefer to war, given war costs and expected gains.
Incomplete information: uncertainty about the other side’s resolve, capabilities, and preferences that can lead to miscalculation.
Credible commitment problem: doubt about whether a signatory will honor the agreement in the future.
Indivisibility: goods that cannot be divided without destroying key values; makes bargaining difficult or impossible.
Deterrent threat vs compelled threat: deterrence preserves the status quo; compellence seeks to move the status quo.
Mutually Assured Destruction (MAD): nuclear deterrence reducing the likelihood of major interstate war due to fear of nuclear retaliation.
Desert Storm (Gulf War 1990–1991): a case study in incomplete information about resolve and coalition-building under uncertainty.
Kashmir, Golan Heights, Holy Land, water resources: examples illustrating how territory, resources, and symbolic value influence bargaining and conflict.
Connections to broader themes and future topics
The discussion sets the foundation for Thursday’s topics: credible commitment and indivisibility, and how they explain ongoing conflict in the modern world.
The material connects basic game theory (PD, bargaining) to real-world state behavior, alliance dynamics, and strategic signaling.
The ethical and practical implications include the high costs of war and the importance of designing institutions and processes that reduce misperceptions, provide verifiable commitments, and address indivisible concerns when possible.