Game Theory
5.1 Why Do Arms Races Happen?
Both the US and the Soviet Union would have preferred a world with fewer nuclear weapons. Building and maintaining arsenals cost trillions. The risk of accidental annihilation was constant. Both sides knew this. Both sides kept building. Why?
The answer is structure. Each side's best response to the other side's arsenal was to build more — regardless of what they preferred in the abstract. This is game theory: situations where your best choice depends on what others choose, and theirs depends on yours.
5.2 The Prisoner's Dilemma
Two suspects are arrested and interrogated separately. Each can stay silent (cooperate) or betray the other (defect). The payoffs, in years of prison (lower is better):
| B stays silent | B betrays | |
|---|---|---|
| A stays silent | (1, 1) | (10, 0) |
| A betrays | (0, 10) | (6, 6) |
Work through A's reasoning. If B stays silent, A gets 0 by betraying vs. 1 by staying silent — betray is better. If B betrays, A gets 6 by betraying vs. 10 by staying silent — betray is still better. Betrayal is the best move no matter what B does. This is a dominant strategy. B reasons identically. Both betray. Both get 6 years. Had they both stayed silent, both would have gotten 1.
This is the central result: individual rationality produces collective disaster. Each person does the smart thing given the other's incentives, and the result is worse for everyone than the outcome they could have reached through mutual cooperation.
The deep structure reappears everywhere:
Arms races. Each nation arms because the other is arming. Mutual disarmament would be better for both, but neither can trust the other to disarm — and being the one who disarms while the other doesn't is the worst outcome (the 10-year sentence). So both arm. Both are less safe.
Climate change. Every country benefits from a stable climate. Cutting emissions is expensive. The benefits are global; the costs are local. Each country's dominant strategy is to let others cut emissions while continuing to burn cheap fuel. If every country reasons this way, no one cuts.
Tax competition between countries. Ireland lowers its corporate tax rate; multinationals relocate there; other countries lower theirs to compete; everyone ends up with lower tax revenue and multinational corporations pay less than they would have if no one had started cutting. Each country's move was individually rational. The collective outcome is a race to the bottom.
5.3 Nash Equilibrium
The Prisoner's Dilemma illustrates a broader concept. A Nash Equilibrium is a set of strategies, one for each player, where no one can improve their outcome by changing their own strategy alone. Not the best outcome, but the stable one: the point from which no individual has an incentive to deviate.
Mutual betrayal in the Prisoner's Dilemma is a Nash Equilibrium: if you switch to cooperation while the other player betrays, you go from 6 years to 10. A traffic jam is a Nash Equilibrium: every driver has chosen the route that is best given everyone else's choices, and the result is gridlock that is worse for everyone than a coordinated alternative — but no individual driver can fix it by changing their route alone.
This explains persistence. When a terrible outcome endures despite everyone wanting something better — an inefficient bureaucracy, a dysfunctional healthcare market — ask: is this a Nash Equilibrium? If so, moral exhortation ("just cooperate!") won't work. You need to change the game — the rules, the payoffs, or the information structure.
5.4 Coordination Games
Not all strategic problems are conflicts. Some are about coordination.
Two people are lost in New York City and must find each other without communicating. Where do they go? In Thomas Schelling's experiments, most converge on Grand Central Station at noon — a focal point, a solution that stands out through cultural convention and shared expectation.
Focal points explain coordination without central direction. Driving on the right or left, languages, currencies, technical standards — all are coordination equilibria sustained by mutual expectation.
Path dependence is the dark side. Once established, switching costs make a coordination equilibrium persist even when better alternatives exist. QWERTY was designed in the 1870s to prevent mechanical typewriter jams — a constraint irrelevant for over a century, yet it persists because every typist learns it (because every keyboard uses it) and every keyboard uses it (because every typist knows it).
This matters for power. Whoever establishes the coordination standard captures the rents from lock-in. In 2022, Western nations cut Russian banks off from the SWIFT payment network — a devastating sanction, possible only because SWIFT is a coordination equilibrium that everyone depends on. But the sanction also demonstrated the geopolitical leverage embedded in controlling the standard. China's CIPS, Russia's SPFS, and the broader BRICS push for payment alternatives are attempts to break the equilibrium and establish competing focal points. Whether they succeed depends on whether they can overcome the switching costs that protect the incumbent.
5.5 Zero-Sum vs. Positive-Sum
A zero-sum game has fixed total payoffs: what one gains, another loses. Dividing a pie, a war over fixed territory.
A positive-sum game allows cooperation to expand the total. Trade is positive-sum (specialization increases output). Innovation is positive-sum (it creates value that didn't exist before).
The most common error in political reasoning is treating a positive-sum situation as zero-sum. "They're stealing our jobs" frames trade as a fixed pie. It isn't. Trade creates new specialization patterns and new products — though it also creates losers, and the distribution of gains and losses is a separate and legitimate political question.
The reverse error also exists: treating a zero-sum situation as positive-sum makes you a naive target. Geopolitical competition for territory or military dominance has genuinely zero-sum dimensions. Pretending otherwise invites exploitation.
Most real situations are mixed: the pie can be expanded, but the distribution is contested. Identify which dimension you're in before choosing a strategy.
5.6 Mixed Strategies
Some games have no stable pure-strategy outcome. Penalty kicks: the kicker aims left or right, the goalkeeper dives left or right. If the kicker always kicks left, the goalkeeper always dives left. The solution: randomize in a ratio that makes the goalkeeper unable to exploit any pattern.
The logic extends directly to:
Tax auditing. The IRS cannot audit everyone. If it always audited the same taxpayers, the rest would know they were safe. Random auditing at low rates creates uncertainty that deters evasion across the entire population — not because every cheater is caught, but because every cheater faces a nonzero chance.
Bluffing in negotiation. A negotiator who never bluffs is transparent (opponents know a strong stance always means a strong position). A negotiator who always bluffs is equally transparent. The optimal approach mixes truthful signals and bluffs in a way that keeps the opponent uncertain — the same logic as penalty kicks, applied to diplomacy.
5.7 How to Analyze a Strategic Situation
When you encounter a situation involving multiple actors whose outcomes depend on each other's choices:
- Who are the players? What can each actually do?
- What are the payoffs? What does each player care about?
- Is it zero-sum or positive-sum? Is there value to be created through cooperation, or is it purely about distribution?
- Is there a dominant strategy? Can any player do better regardless of what others do?
- What is the Nash Equilibrium? What is the stable outcome? Is it good or terrible?
- Is there a coordination problem? If so, who controls the focal point, and who benefits from lock-in?
- Is it one-shot or repeated? Repeated interaction changes everything — the shadow of the future enables cooperation that one-shot games cannot sustain.