Notes on Collective Goods, Game Theory, and Policy Implications (Lecture Transcript)
Course Logistics and Quiz Access
Zoom sound check and archive: lecture will be archived; students can replay beginning if they missed part of the live stream.
Course site navigation: home page -> week with dates (September 5 today; September 2–4 last week). Quizzes listed at the bottom under "Quizzes".
Chapter 1 quiz details (Chapter 1 quiz on Canvas):
Due today by 11:59 PM (tonight).
15 questions; 75 points.
Attempt: 1 attempt or unlimited attempts (the quiz is set to unlimited attempts).
The quiz replaces an existing Quiz 2 in the Gradebook; the system keeps a placeholder Quiz 2, but the Chapter 1 quiz is the one that counts.
The instructor will automatically add +5 points to everyone who completes this quiz, so it totals 80 points for the quiz component.
If not taken by midnight today, makeup is required under the syllabus rules (illness or other approved reasons; makeup must be completed within one week after missing the assignment).
Rationale: the Chapter 1 quiz helps you prepare for the upcoming midterm; many questions will appear on the midterm.
Access paths to the Chapter 1 quiz:
On the Canvas home page under the current week (as shown in the lecture).
Through the syllabus link (integrated into the LMS; it will appear in the calendar as a due item once due date is live).
When in student view, red calendar markers indicate due dates.
Grading and points: 75 points for the quiz base, +5 points for attempting the quiz, totaling 80 points toward the quiz component; quizzes collectively contribute to class participation and preparation for the midterm.
Makeup policy: requires illness or documented excuse and completion of makeup work within one week.
Schedule and class structure:
Monday/Wednesday class has an online third lecture each week to add 50 minutes of content (two 50-minute in-person lectures plus an online third).
Tuesday/Thursday class meets twice for 75 minutes each (total 150 minutes).
The online third lecture helps synchronize content across sections when the in-person time is tight.
Lecture revisions: the today’s slide deck is a revised version of Lecture 3 (updated after class); the instructor notes changes to cover material that wasn’t fully addressed in earlier sessions due to schedule constraints or interruptions (e.g., club invitations, technical issues, time management). The revised slides are labeled with “revised” in the title.
Rant summary: the instructor explains time constraints caused by back-to-back classes and logistical challenges (e.g., hallway logistics, climbing stairs, breaks) and emphasizes fairness in delivering the same content to all sections.
Contact and office hours: in-person and Friday Zoom office hours; options to ask questions via microphone or typed chat; the session is archived for later review; private questions could be handled in a separate, unarchived breakout or Zoom room if needed.
Scantrons for in-person quizzes: the in-person quiz on Monday uses Scantrons (preferred form 882); the instructor will hand-grade the first set; midterm scanning requires the 882 form or compatible forms; cheaper knockoffs are acceptable for quizzes (not for midterm, due to scantron identification).
Open notes policy: quizzes are open-notes/open-book; devices allowed; midterms/finals restrict materials to paper notes only.
Real-world connections: the instructor ties course content to real-world examples (e.g., national parks, traffic and environmental rules, the debate on public goods) to illustrate the practical importance of collective action problems and policy solutions.
Core Concept: Politics and Collective Goods
Core claim (Cornelia/Jacobsen): Basically all politics is about defining and allocating collective goods.
Political science as a methodology for studying how societies decide how to define and allocate these goods.
“Collective goods” includes both public and private goods because private goods rely on system-level support (money supply, weights and measures, transportation networks, protection of private property, etc.).
Even when discussing security or defense, the provision of collective goods matters: protecting borders and resources is a form of ensuring collective goods availability.
Expanded definition of politics (Cranell & Jacobson):
Politics is the process through which individuals and groups seek agreement on a course of common or collective action even as they disagree on the intended goals of that action.
Practical implication: people may sign onto the same policy for different reasons (e.g., a bill might benefit one district in job creation while benefiting another district by providing needed infrastructure).
Types of Goods: A Framework for Understanding public/private and rival/nonrival access
Four kinds of goods, defined by two dimensions: rivalry (rival vs nonrival) and excludability (excludable vs nonexcludable).
Key definitions:
Excludable: there exists a mechanism to prevent non-payers from using the good (e.g., charging for access).
Rival: consumption by one person reduces availability to others.
The four categories:
Private goods: Rival and Excludable
Example: a sandwich (limited number; you can exclude others by selling the sandwich).
Public goods (pure public goods): Nonrival and Nonexcludable
Example: clean air; national parks in unrestricted form (though access can be limited for safety); air is typically considered a public good because everyone benefits without reducing others’ access.
Common-pool resources: Rival and Nonexcludable
Example: swordfish in the North Atlantic; finite stock shared by all fishers; no practical exclusion across the sea.
Toll goods (club goods): Nonrival and Excludable
Example: cable TV (bandwidth is generally nonrival for typical usage; access is controlled by a subscription; some capacity constraints can create rivalry, but exclusion keeps it manageable).
The 2x2 framework (for reference)
Nonrival, Nonexcludable: Pure public goods
Rival, Nonexcludable: Common-pool resources
Nonrival, Excludable: Toll/Club goods
Rival, Excludable: Private goods
Formal representation (LaTeX-friendly):
Public goods:
Private goods:
Common-pool resources:
Toll/Club goods:
Why government intervention matters:
Pure public goods are hard to provide due to free-rider problems: nonexcludable and nonrival makes it costly to compel payment, so a government-backed mandate (taxes) or regulation is often necessary to ensure provision.
Even private goods depend on a societal framework (money supply, institutions, law enforcement, and infrastructure) that makes private goods viable.
Free rider problem: benefiting from a good without paying the cost of providing it, especially when the good is nonexcludable.
Pure Public Goods and the Free Rider Problem
Pure public goods defined as nonrival and nonexcludable; difficult to provide because anyone can benefit without paying.
Examples and implications:
Clean air is a public good; everyone benefits, so there’s a temptation to free ride by not paying the costs (e.g., not paying taxes that fund pollution-control measures).
National defense and public education are typically funded by the government to ensure broad access.
The role of government: compel payment (via taxes or penalties) to ensure the good is provided.
Without a regulator, free riders undermine provision; the public good may be under-produced or not produced at all.
The role of public policy in securing the common good: coordinate resources, standardize measurement, and maintain a system that supports public goods.
Common Pool Resources and the Tragedy of the Commons
Common-pool resources are rival but nonexcludable.
Example: swordfish in the North Atlantic; many fishers share limited stock.
Tragedy of the Commons: overuse occurs when individuals act in their own self-interest, depleting a shared resource.
Quotas as a policy tool: a government-imposed limit on total harvest to prevent overfishing; once the quota is reached, fishing is illegal until the next season.
Alternative solutions to the tragedy of the commons: spatial allocation of property (in land-based cases) to align incentives; in oceanic resources, property division is impractical, hence quotas become the next-best option.
Real-world example from Perfect Storm: quotas were used to manage swordfish stocks to avoid depletion; the consequences for fishers can be severe given fixed annual income and the cost of missed trips.
In the ocean context, common-pool resource management often requires regulatory mechanisms because the resource cannot be easily divided into parcels of ownership.
The tension between economic incentives and resource sustainability explains why quotas are often controversial but sometimes essential for long-term viability of the resource.
Toll Goods (Club Goods) and Exclusion
Toll/Club goods have exclusion (you must pay or meet criteria to access) but are typically nonrival; capacity is often sufficient for standard use.
Example: cable TV access is largely nonrival for typical usage; access is restricted to paying subscribers.
In some cases, capacity constraints create rivalry (e.g., peak-time bandwidth); but the exclusion mechanism helps manage demand.
Toll goods illustrate how exclusion can address scarcity, though it may still encounter capacity limits or equity concerns.
Real-World Illustrations of Public Goods, Common Pool, and Stag/Tragedy Dynamics
National Parks (e.g., Yosemite): a pure public good in concept; funded by taxpayers; can become crowded, effectively imposing a rival condition on peak days (turnstiles in some contexts).
Yosemite example details:
Crowding leads to queue effects (e.g., Clouds Rest, Half Dome) and safety concerns; in extreme cases, park resources become temporarily exclusive to ensure safety and order.
Public goods and nonexcludability can become rival during peak demand, illustrating the practical limits of public goods in the real world.
Half Dome anecdote: natural public resource that is technically nonrival and nonexcludable, but crowding and safety demands create a de facto rival environment on busy days.
The Perfect Storm and swordfish quotas example: quotas as a management tool to prevent overharvesting; reveals the tension between livelihoods and resource sustainability.
The Everest example (toll/club-like dynamics): hiking permits act as a gate to limit participation and manage risk; crowded conditions can still lead to dangerous outcomes, illustrating how even regulated access cannot fully prevent tragedy when demand is high.
Stag hunt and lighthouse analogy: collective action problems in communities seeking public improvements (e.g., building a lighthouse) require cooperative funding; free-riding risks delay or derail the project unless simultaneous commitment is enforced (the “Lighthouse Day” concept).
Stag hunt vs Prisoner's Dilemma: important distinctions for when cooperation is optimal vs when defection is rational; stag hunt aligns incentives for mutual cooperation when the payoff of cooperation is high; Prisoner’s Dilemma demonstrates that defection can be individually rational but collectively worse off.
Game Theory Core Concepts: Stag Hunt, Prisoner’s Dilemma, Nash Equilibrium, and Pareto Optimality
Stag Hunt (cooperation game):
Both players cooperating yields the best collective outcome (e.g., capturing the stag or building the lighthouse).
The risk is if one player defects (goes after a rabbit instead), the other player may not achieve the optimal outcome unless the other continues cooperating.
Pareto optimal outcome in a stag hunt is often cooperative: both players cooperate for the best joint outcome.
Prisoner’s Dilemma: noncooperative outcome dominated by defection at the individual level, leading to a worse overall payoff if both defect.
Classic setup: two players choose to confess (defect) or remain silent (cooperate). unilateral defection yields the highest personal payoff, but mutual defection yields a worse collective outcome.
Key payoff structure (example 1: Prisoner’s Dilemma payoffs in years of prison)
If both confess: (5, 5) years imprisoned.
If one confesses and the other remains silent: (0, 20) or (20, 0) years respectively.
If both remain silent: (1, 1) years.
These payoffs illustrate that unilateral defection is best for the individual, yet mutual defection leads to a higher total prison time.
Nash Equilibrium (in Prisoner’s Dilemma):
Definition: a strategy profile where no player can gain by unilaterally changing their strategy.
In the Prisoner’s Dilemma, the Nash equilibrium is (Confess, Confess) (defect, defect) because each player does better by defecting regardless of the other player's action.
Formal expression (informal): for all i, ui(si^, s{-i}^)
geq ui(si', s{-i}^*).
Pareto Optimality: the option where no one can be made better off without making someone else worse off.
In Prisoner's Dilemma, the Pareto optimal outcome is (Remain Silent, Remain Silent) with total payoff lower for both individuals but better for the group compared to mutual confession? In the standard PD, the Pareto optimal outcome is typically the mutual cooperation outcome if that yields a better payoff for both than mutual defection; however, in the year-payoff example, (1,1) is Pareto efficient relative to (0,20) or (20,0) because no one can be made better off without making the other worse off given the numeric payoff structure. The key point: Pareto optimality concerns improvements without hurting someone else, not necessarily the lowest collective cost.
The Golden Balls game: a real-world demonstration of Nash equilibrium and Pareto outcomes in a two-player split/steal scenario with a large jackpot.
Payoff diagram (illustrative):
If both split: each receives £50,075
If one splits and the other steals: stealer receives £100,150; splitter receives £0
If both steal: £0 each
Why it mirrors Prisoner’s Dilemma: each player’s dominant strategy is to steal, but mutual stealing yields zero for both, while mutual splitting yields a large but split payoff.
The “Nash equilibrium” outcome in Golden Balls is the defecting (steal, steal) outcome, unless players can coordinate to both split; the Pareto optimal outcome is (Split, Split) in this setup if both players cooperate.
Important distinction recap:
Nash Equilibrium: the self-interested best response; may not be Pareto optimal.
Pareto Optimal: no one can be made better off without making someone else worse off; not guaranteed to be achieved in noncooperative settings.
Practical and Philosophical Implications
Free rider problem justifies regulatory frameworks (e.g., taxes, environmental regulations, DMV enforcements) to ensure provision of public goods and maintenance of shared resources.
Tragedy of the commons demonstrates why open-access resources can be depleted without governance, and why workable policies (quotas, permits, property rights) are necessary.
Stag hunt demonstrates why cooperation yields superior outcomes and under what conditions cooperation is stable; Lighthouse Day-style mechanisms show how coordination can be achieved when individual incentives threaten collective outcomes.
The Golden Balls example illustrates how Nash equilibrium can lead to suboptimal group outcomes and why communication and trust are critical for Pareto improvements in non-cooperative settings.
Key Terminology to Master for the Exam
Politics: the process by which groups seek common action amid disagreements over goals.
Collective goods: goods that are defined by the community’s access and provisioning (including those produced via state actions).
Excludable vs Nonexcludable
Rival vs Nonrival
Public goods (pure public goods): Nonrival + Nonexcludable
Private goods: Rival + Excludable
Common-pool resources: Rival + Nonexcludable
Toll/Club goods: Nonrival + Excludable
Free rider problem
Tragedy of the commons
Quotas and other regulatory solutions
Stag Hunt (cooperation game)
Prisoner’s Dilemma
Nash Equilibrium
Pareto Optimality
Golden Balls (split/steal) as a pedagogical device
Real-world examples and metaphors: Everest tolls, Lighthouse, Yosemite, Perfect Storm
Quick Reference: Payoff Structures (Illustrative)
Prisoner’s Dilemma payoff matrix (years in prison):
A Confess, B Confess: (5, 5)
A Confess, B Silent: (0, 20)
A Silent, B Confess: (20, 0)
A Silent, B Silent: (1, 1)
Golden Balls payoff matrix (pounds):
Split/Split: (£50,075, £50,075)
Split/Steal: (£0, £100,150)
Steal/Split: (£100,150, £0)
Steal/Steal: (£0, £0)
Connections to Foundational Principles and Real-World Relevance
The study of collective goods links to foundational political science questions about how societies organize resources and coordinate action.
Game theory concepts (Nash equilibrium, Pareto optimality) provide a formal language to analyze the incentives and outcomes of cooperation vs defection in public policy, environmental stewardship, and international relations.
Real-world examples show the policy relevance of these theories: taxes and enforcement to support public goods; quotas and permits to prevent resource collapse; cooperative arrangements (like lighthouse projects) to realize shared benefits.
Additional Notes and Context from Today’s Session
The lecture emphasized that content delivery may be revised after initial sessions to cover material that didn’t fit into earlier classes due to time constraints and interruptions (e.g., club interruptions, technical issues).
The instructor underscored the importance of reviewing revised slides and attending the live session or the archive to ensure no material is missed across sections with different meeting times.
The quiz policy is designed to reward participation and preparedness for the midterm while maintaining fairness across sections and new enrollees.
Office hours offer flexibility for private questions, and there is consideration for unarchived private Zoom rooms for sensitive questions.
Summary Takeaway for Exam Prep
Be able to identify and explain the four kinds of goods with their rivalry and excludability properties:
Public goods: Nonrival + Nonexcludable
Private goods: Rival + Excludable
Common-pool resources: Rival + Nonexcludable
Toll/Club goods: Nonrival + Excludable
Understand the free rider problem and why governments enforce taxation and regulation to provide public goods.
Recognize and differentiate Stag Hunt vs Prisoner’s Dilemma: stable cooperation vs dominant-defection dynamics; know the Nash equilibrium and what constitutes Pareto optimal outcomes.
Be able to apply these concepts to real-world examples (lighthouse projects, fisheries quotas, Everest permits, etc.).
Memorize key numerical values associated with the PD and Golden Balls payoff structures and be able to explain how they illustrate Nash vs Pareto outcomes.