Game theory

October 16th, 2025

GameAn activity with rules, goals, and outcomes, often involving competition or strategy. From Old English gamen (joy, fun, amusement). Originally meant any form of entertainment or sport. In game theory, "game" doesn't mean fun or leisure. It's a technical term for any situation where multiple decision-makers interact, and the outcome depends on everyone's choices. Chess is a game. Poker is a game. But so is a salary negotiation, a nuclear arms standoff, or deciding whether to cooperate with your flatmate. Game theory formalises these interactions mathematically. The "game" is the structure of incentives, choices, and payoffs. Understanding the game you're in is the first step to playing it well. theoryA system of ideas explaining something, based on principles and evidence. From Greek theoria (contemplation, speculation), from theorein (to look at, observe). A theory isn't a guess. It's a framework for understanding patterns. Newton's theory of gravity. Darwin's theory of evolution. Game theory. These are rigorous systems that explain and predict behaviour. Game theory uses mathematics to model strategic interactions. It provides tools to analyse decisions when outcomes depend on multiple actors. The theory helps you see patterns: why cooperation emerges, why conflicts escalate, why some strategies dominate others. It's not about what people should do morally. It's about what they will do rationally, given the incentives. Theory turns vague intuition into precise prediction. is the study of strategic decision-makingChoosing actions based on how others will respond to your choices. "Strategic" comes from Greek strategos (general, military commander), from stratos (army) + agein (to lead). Strategy originally meant military planning. Now it means any situation where your best choice depends on what others do. Playing chess strategically means thinking several moves ahead, anticipating your opponent's responses. Negotiating strategically means considering how your offer affects their counteroffer. Strategic thinking is interdependent thinking. It's not just "what's best for me?" but "what's best for me, given what's best for them, given what's best for me?" Game theory formalises this recursive logic. Non-strategic decisions are independent: choosing what to eat for breakfast. Strategic decisions are interdependent: choosing whether to cooperate when your outcome depends on whether they cooperate.. It's about understanding how people make choices when the outcome depends not just on what you do, but on what others do too. Your decision affects their decision, which affects yours, which affects theirs. It's the mathematics of interaction.

The name is misleading. This isn't about games in the fun sense. It's about situations where your choices and someone else's choices are interdependentWhen two things depend on each other, where each affects the other. From Latin inter- (between, among) + dependere (to hang from). Interdependence means mutual reliance. Your choice affects their outcome, and their choice affects yours. This is different from independence (your choice doesn't affect them) or dependence (your outcome depends on them, but not vice versa). Most strategic situations are interdependent. If you lower your prices, your competitor lowers theirs. If you cooperate, your partner might cooperate or betray. If you escalate a conflict, they might back down or escalate further. Game theory exists because of interdependence. When choices are independent, there's no strategic interaction. When they're interdependent, you need to think about what they'll do, knowing they're thinking about what you'll do. That's the core of game theory.. Negotiations, relationships, business deals, social dynamics, conflicts, cooperation. Any time you're thinking "what will they do if I do this?" you're already doing game theory, you just might not know it.

The Prisoner's Dilemma:

Two criminals are arrested. The police separate them and offer each the same deal: betray your partner and testify against them, and you go free whilst they get 10 years. If you both stay silent, you both get 1 year on a lesser charge. If you both betray each other, you both get 5 years.

Partner stays silent Partner betrays
You stay silent Both get 1 year You get 10 years, they go free
You betray You go free, they get 10 years Both get 5 years

The rationalBased on reason and logic rather than emotion or impulse. From Latin rationalis, from ratio (reason, calculation), from reri (to reckon, think). Rationality in game theory means choosing the option that maximises your expected payoff, given what you know. A rational player doesn't act randomly or emotionally. They calculate. If betraying gives you a better outcome regardless of what your opponent does, betraying is rational. This doesn't mean it's moral, fair, or socially optimal. It just means it's the best choice for you individually. Game theory assumes players are rational because it makes predictions tractable. In reality, people aren't perfectly rational—they're influenced by emotions, fairness concerns, and bounded information. But rationality is the baseline. Understanding what rational play looks like helps you see when and why people deviate from it. choice is to betray. If your partner stays silent, betraying gets you freedom instead of 1 year. If your partner betrays, betraying gets you 5 years instead of 10. No matter what they do, you're better off betraying. So both prisoners betray each other and both get 5 years, even though they'd both be better off staying silent and getting 1 year each.

This is the dilemma: individually rational decisions lead to collectively worse outcomes. You see this everywhere. Two companies in a price war both lower prices until neither makes profit. Two countries in an arms raceA competitive buildup of weapons between nations or groups. "Arms" comes from Latin arma (weapons, tools of war). An arms race occurs when one side increases military capability, prompting the other to do the same, creating an escalating cycle. The Cold War arms race between the US and USSR is the classic example: both built thousands of nuclear weapons, spending trillions, not because either wanted war, but because neither could afford to fall behind. It's a Prisoner's Dilemma. Both would be better off not spending on weapons (cooperate). But if one side arms and the other doesn't, the armed side has an advantage. So both arm (defect), ending up worse off than if neither had armed. Arms races aren't limited to militaries: companies in advertising wars, students in credential races, social media platforms in feature battles. Any competitive escalation where both sides would prefer restraint, but neither dares to stop first. both spend billions on weapons neither wants to use. Two people in an argument both escalate until the relationship is damaged beyond what either wanted.

One-shot games vs repeated games:

The Prisoner's Dilemma changes completely if you're playing it more than once. If you know you'll interact with the same person repeatedly, cooperation becomes rational. You can punish betrayal and reward cooperation. "I'll cooperate if you do, but if you betray me, I'll betray you next time."

This is why long-term relationships work differently from one-time transactions. You don't screw over someone you'll see again tomorrow. The shadow of the future changes behaviour. ReputationThe beliefs or opinions others hold about someone's character or behaviour. From Latin reputatio, from reputare (to think over, consider), from re- (again) + putare (to reckon, judge). Your reputation is your track record made visible. In repeated games, reputation becomes an asset. If you're known as trustworthy, people cooperate with you. If you're known as a cheat, they don't. Reputation solves the Prisoner's Dilemma because it makes betrayal costly. Betray once and you lose future cooperation. This is why merchants in medieval markets valued reputation: cheat one customer and word spreads, destroying your business. Modern platforms use ratings and reviews to create reputation systems: Uber drivers, eBay sellers, Airbnb hosts. Reputation turns one-shot games into repeated games by creating information flow. Even if you'll never meet the same person twice, if others know your history, reputation matters. It's the social mechanism that enforces cooperation without central authority. matters when games repeat.

Lending money to friends works this way. If you lend $20 to a stranger, you'll probably never see it again. Betraying you (not paying back) is rational for them because there's no future interaction. But if you lend $20 to a friend you'll see regularly, they're more likely to pay you back. Not because they're morally superior, but because the game repeats. If they don't pay you back, you won't lend to them again, and the relationship suffers. The future matters.

Group projects follow the same logic. If it's a one-time project with strangers, free-ridingBenefiting from a resource or effort without contributing. "Free ride" emerged in American English in the late 1800s, originally meaning a ride on a train or vehicle without paying. In game theory and economics, free-riding means consuming a public good without paying the cost. If everyone contributes to a group project and you don't, but still get credit, you're free-riding. The problem: if everyone free-rides, nothing gets done. Free-riding is rational for individuals (why work if you get the benefit anyway?) but destructive for groups. It's why public goods (parks, clean air, national defence) are underprovided without enforcement. You benefit from clean streets whether you litter or not, so why bother? Free-riding is a coordination failure. The solution: make contribution enforceable (laws, social pressure, reputation). In small repeated groups, free-riders get punished (excluded, ostracised). In large anonymous groups, free-riding is harder to prevent, which is why public goods require collective action or government. is tempting. Let others do the work, take credit anyway. But if you're in a course where you'll work with the same people repeatedly, free-riding destroys your reputation. No one will want to work with you next time. The repeated game enforces cooperation.

Tit-for-tat:

In the 1980s, political scientistA scholar who studies politics, government, and political behaviour. "Political" from Greek politikos (of citizens, civic), from polis (city). "Scientist" from Latin scientia (knowledge), from scire (to know). Political science applies systematic, empirical methods to understand power, institutions, and collective decision-making. It's not just opinion or philosophy. It uses data, experiments, and formal models to test theories about voting, war, cooperation, and governance. Political scientists study why democracies emerge, why wars happen, how institutions shape behaviour, and why people vote the way they do. Game theory is a major tool in political science because politics is fundamentally strategic: leaders anticipate each other's moves, voters respond to campaign promises, countries negotiate knowing others will do the same. Political science brings rigour to questions that affect millions of lives. Robert AxelrodAmerican political scientist (born 1943) famous for his work on cooperation and game theory. In 1980, Axelrod ran a computer tournament where strategies competed in repeated Prisoner's Dilemmas. He invited game theorists, computer scientists, and mathematicians to submit programmes. The simplest strategy, tit-for-tat (cooperate first, then copy opponent's last move), won decisively. Axelrod's book "The Evolution of Cooperation" (1984) showed that cooperation can emerge between selfish actors without central authority, just through repeated interaction and reciprocity. His work influenced economics, biology (explaining animal cooperation), international relations (how countries cooperate without world government), and social science broadly. Axelrod demonstrated that "nice" strategies (never defecting first) outperform aggressive ones in iterated games, a counterintuitive finding that reshaped thinking about conflict and cooperation. His research explains why humans, despite self-interest, cooperate so extensively. ran a tournament where computer programmesSets of instructions that tell a computer what to do. From Greek programma (public notice, written order), from pro- (before) + graphein (to write). In British English, "programme" is the standard spelling for a planned series of events or broadcast shows, whilst "program" is used for computer code. In American English, "program" covers both. A computer programme is an algorithm encoded in a language machines can execute. Axelrod's tournament used programmes (strategies coded into software) to play repeated Prisoner's Dilemmas. Each programme made decisions automatically: cooperate or defect, based on past moves. The programmes competed over thousands of rounds to see which strategy accumulated the most points. This method removes human emotion and bias, testing pure strategic logic. The surprising result: the simplest, most cooperative programme (tit-for-tat) won. Complexity didn't help. Being nice, retaliatory, and forgiving did. played repeated Prisoner's Dilemmas against each other. Programmes could cooperate or defect, and they played hundreds of rounds. Which strategy won?

Tit-for-tat. The simplest strategy: cooperate on the first move, then do whatever your opponent did last time. If they cooperated, you cooperate. If they betrayed, you betray once, then go back to cooperating if they do. It's forgiving but not a pushoverSomeone easily taken advantage of, who doesn't stand up for themselves. From "push" (to exert force) + "over" (to fall or yield). A pushover is someone you can push, and they fall over without resistance. In game theory and social dynamics, being a pushover means always cooperating even when others defect. If you lend money and never get repaid, but keep lending, you're a pushover. If someone disrespects you repeatedly and you tolerate it, you're a pushover. The problem: pushovers get exploited. Tit-for-tat avoids this by retaliating once after betrayal. It's not vindictive (it doesn't hold grudges), but it's not a pushover (it punishes defection immediately). This balance is crucial. Always cooperating invites exploitation. Always defecting prevents cooperation. Tit-for-tat threads the needle: cooperative by default, but willing to punish when necessary. That's why it works.. It signals "I'll work with you, but don't take advantage."

Tit-for-tat won because it's nice (never defects first), retaliatory (punishes betrayal immediately), forgiving (doesn't hold grudgesPersistent feelings of resentment or ill will towards someone. From Old French grouchier (to grumble, complain). A grudge is when you can't let go of a past wrong. You remember it, resent it, and often seek revenge or avoid the person. Grudges are emotionally costly: they keep you angry, damage relationships, and prevent reconciliation. In game theory, holding grudges is irrational in many contexts. If someone defected once but now wants to cooperate, refusing to forgive locks you both into mutual defection. Tit-for-tat is forgiving: it punishes betrayal once, then returns to cooperation if the other player does. This prevents grudges from trapping you in bad equilibria. Forgiveness isn't weakness. It's strategic. It allows relationships to recover from mistakes. The key: don't be a pushover (punish betrayal), but don't hold grudges (allow redemption). That's the tit-for-tat balance.), and clear (easy to understand). People quickly learn that cooperation pays and betrayal doesn't.

Good friendships often follow tit-for-tat. You invite someone to your party, they invite you to theirs. You help them move house, they help you when you need it. If someone stops reciprocatingResponding to an action with a corresponding action, giving back in return. From Latin reciprocare (to move backwards and forwards), from re- (back) + pro- (forward). Reciprocity is mutual exchange: you do something for me, I do something for you. It's the foundation of cooperation. Reciprocity can be positive (I help you, you help me) or negative (you hurt me, I hurt you). Tit-for-tat is a reciprocity strategy: match cooperation with cooperation, defection with defection. Humans have a deep instinct for reciprocity. We feel obligated to return favours and punish those who don't reciprocate. This is why gift-giving creates social bonds, why "I owe you one" feels binding, and why failing to reciprocate damages relationships. Reciprocity sustains cooperation without contracts or enforcement. It's why societies function. The norm of reciprocity is universal across cultures. Violate it, and you're ostracised. Honour it, and you build trust. Game theory formalises what humans intuitively know: reciprocity works., you stop investing in the friendship. You're not vindictiveHaving or showing a desire for revenge, holding a grudge and seeking to harm. From Latin vindicta (vengeance, revenge), from vindicare (to lay claim, avenge). A vindictive person doesn't just retaliate, they punish excessively and hold onto anger. In game theory, vindictiveness is irrational. If someone defects and you retaliate forever, you both lose. Tit-for-tat isn't vindictive: it punishes betrayal once, then forgives if the other cooperates. This allows cooperation to resume. Vindictiveness traps you in cycles of retaliation. You defect, I defect, you defect, I defect, endlessly. Both suffer. The rational move is to signal "I'll punish betrayal, but I'm willing to cooperate again if you are." That's not vindictive. It's strategic. Vindictiveness might feel satisfying emotionally, but it's costly. It destroys relationships, perpetuates conflicts, and prevents mutually beneficial outcomes. The key: punish when necessary, forgive when possible. Retaliation without vindictiveness., but you're not a doormatA person who lets others treat them badly without standing up for themselves. From "door" + "mat" (a floor covering for wiping feet). Literally, a mat people walk on. Metaphorically, someone who allows others to "walk all over them." In game theory and relationships, being a doormat means always cooperating even when exploited. If you lend money and never get repaid, but keep lending, you're a doormat. If you do all the work in a group project whilst others free-ride, and you accept it, you're a doormat. The problem: doormats enable bad behaviour. If you never punish defection, why would anyone cooperate? They get the benefits without the costs. Tit-for-tat avoids being a doormat by retaliating once after betrayal. It's not vindictive (it doesn't hold grudges), but it's not a doormat (it doesn't tolerate exploitation). The balance is key. Being too forgiving invites abuse. Being too retaliatory prevents cooperation. Tit-for-tat threads the needle: cooperative but not exploitable. That's why it works in friendships, business, and life. either. The friendship is sustained by mutual reciprocityThe practice of exchanging things with others for mutual benefit. From Latin reciprocus (returning, alternating), from re- (back) + pro- (forward). Reciprocity is the give-and-take that sustains relationships. You help me, I help you. You invite me, I invite you. You respect me, I respect you. It's not transactional in a calculated way, but there's an intuitive ledger. If the balance tips too far (I always give, you always take), the relationship breaks. Reciprocity works because it's self-enforcing. I cooperate knowing you'll reciprocate. If you don't, I stop. No external enforcement needed. This is why gift economies function, why honour codes work, and why trust emerges. Reciprocity is a human universal. Anthropologists find it in every culture. It's encoded in language: "thank you" acknowledges a debt. Reciprocity turns zero-sum thinking (your gain is my loss) into positive-sum (we both gain through exchange). It's the foundation of trade, friendship, alliance, and civilisation. Game theory shows mathematically why reciprocity is stable: it's individually rational and collectively beneficial..

Workplace relationships work the same way. If a colleague helps you with a project, you help them next time. If they refuse to help, you remember that. You don't sabotage them, but you also don't go out of your way for them. Tit-for-tat creates stable cooperation in professional environments where people interact repeatedly.

Zero-sumA situation where one person's gain equals another's loss, so the total is always zero. From mathematics: if you gain +5 and I lose -5, the sum is zero. "Zero-sum" was coined by game theorists in the 1940s. Poker is zero-sum: your winnings are others' losses. Dividing a cake is zero-sum: if I get more, you get less. Most competitive sports are zero-sum: one team wins, the other loses. Zero-sum games create pure conflict: there's no mutual benefit, only redistribution. What one side gains, the other loses. This shapes strategy: in zero-sum games, helping your opponent hurts you. There's no cooperation, only competition. The problem: people often misperceive non-zero-sum situations as zero-sum. They think relationships, negotiations, or business are "win or lose" when they're actually "win-win" or "lose-lose." This mindset destroys value. Viewing salary negotiations as zero-sum (every pound I get, you lose) ignores creative solutions that benefit both. Zero-sum thinking is appropriate in pure conflicts (war, chess, court cases). In most life situations, it's a mistake. vs non-zero-sumA situation where both parties can gain or both can lose, the total isn't fixed. From "non-" (not) + "zero-sum." Coined in game theory to contrast with zero-sum games. Trade is non-zero-sum: you value my apples more than I do, I value your oranges more than you do. We trade and both gain. Cooperation is non-zero-sum: we work together and achieve more than alone. Non-zero-sum games create opportunities for mutual benefit. Your gain doesn't require my loss. We can both win. Or both lose if we fight instead of cooperate. This is why negotiation, relationships, and teamwork work. The pie can grow. Most real-world interactions are non-zero-sum, but people often treat them as zero-sum (if you win, I lose), which is catastrophic. It turns potential cooperation into destructive competition. Recognising non-zero-sum situations is crucial: it opens possibilities for joint gain. The key insight: life isn't a fixed pie. Value can be created or destroyed depending on how people interact. Game theory helps identify when situations are zero-sum (pure conflict) vs non-zero-sum (potential cooperation).:

Zero-sum games are where one person's gain is another's loss. Poker, tennis, dividing a cake. If I get more, you get less. The total is fixed.

Non-zero-sum games are where both players can win or both can lose. Trade, negotiation, relationships. If we cooperate, we can both be better off. If we fight, we can both be worse off.

Most real-life situations are non-zero-sum, but people often treat them as zero-sum. This is a catastrophic mistake. Viewing relationships as zero-sum (if you win, I lose) destroys them. Viewing negotiations as zero-sum leaves value on the table. Viewing life as zero-sum makes you competitive when you should be cooperative.

Many people think negotiation is zero-sum: every pound they gain, the employer loses. But it's not. You can ask for flexible working, professional development budget, better title, more interesting projects. The employer can offer equityOwnership stake in a company, represented by shares. From Latin aequitas (equality, fairness), from aequus (equal, level). Equity literally means "equality" or "fairness." In finance, equity is ownership. If you own 10% of a company's equity, you own 10% of the company. Equity holders (shareholders) have claims on profits and assets after debts are paid. Equity is riskier than salary but potentially more valuable: if the company succeeds, your shares appreciate. If it fails, they're worthless. In negotiations, offering equity instead of cash can be win-win (non-zero-sum): you pay less now, they gain more if the company grows. Equity aligns incentives: if you own part of the company, you care about its success. This is why startups use equity to attract talent they can't afford to pay in cash. It's a bet on future value, not present value. Equity transforms employees into partners, changing the game from "extract maximum salary" to "build maximum value.", bonuses tied to performance, or other benefits that cost them less than cash but are valuable to you. If you frame it as "how do we both get what we want?" rather than "how do I take as much as possible?" you'll reach better outcomes.

Couples who view disagreements as zero-sum ("if I compromise, I lose") end up in destructive cycles. Couples who view them as non-zero-sum ("how do we both get what we need?") find solutions that work for both. It's not about winning arguments. It's about solving problems together.

The coordination game:

Sometimes the problem isn't competition or cooperation. It's coordination. You both want the same outcome, but you need to agree on which one.

Two people want to meet up. One prefers coffee shops, the other prefers parks. But both prefer meeting somewhere over not meeting at all. The game is about coordinating on a shared choice, not about winning or losing.

Friend goes to coffee shop Friend goes to park
You go to coffee shop Both happy Both miss each other
You go to park Both miss each other Both happy

The solution is communication. Just agree on a place. But when communication isn't possible, you need coordination mechanismsSystems or processes that achieve a particular result. From Greek mēkhanē (machine, device), from mēkhos (means, expedient). A mechanism is how something works. A clock's mechanism is gears and springs. A market mechanism is supply and demand setting prices. In game theory, coordination mechanisms solve coordination problems. When people need to align behaviour but can't communicate, mechanisms help: defaults (do what's normal), conventions (follow established patterns), focal points (choose the obvious option). These mechanisms work because they're predictable. If everyone knows everyone else will follow the convention, it becomes self-enforcing. Mechanisms turn coordination problems into solved problems. You don't need central control or communication. The mechanism itself guides behaviour. This is why social norms, traditions, and standards are powerful: they're coordination mechanisms that work without anyone in charge.. Defaults, conventionsEstablished practices or norms that people follow. From Latin conventio (agreement, assembly), from convenire (to come together). Conventions are shared rules that emerge through repeated interaction. They're not laws (no one enforces them) and not instincts (they're learned). They're social agreements. Driving on the left in the UK is a convention. Shaking hands when you meet is a convention. Speaking English in England is a convention. Conventions solve coordination problems: everyone benefits if everyone does the same thing. The specific choice (left vs right) doesn't matter. What matters is everyone choosing the same. Conventions are self-enforcing: if everyone follows them, it's rational for you to follow too. Deviate and you're worse off. This is why conventions persist even when arbitrary. They're equilibria. Once established, they're stable. Changing conventions is hard because it requires everyone to change together. Conventions are how societies coordinate without central planning., focalA point or option that stands out as the obvious choice, making coordination easier. From Latin focus (hearth, fireplace), the central point where people gather. Economist Thomas Schelling introduced "focal points" in game theory. When people can't communicate but need to coordinate, they often converge on the same choice because it's salient, obvious, or natural. If you and a friend get separated in a city, where do you meet? The most famous landmark. That's a focal point. It's not necessarily the best choice, just the most obvious one. Focal points solve coordination problems through shared expectations. You choose it because you think they'll choose it, and they choose it for the same reason. Examples: meeting at noon rather than 11:47am (round numbers are focal), choosing the capital city as a meeting point, defaulting to the status quo in negotiations. Focal points work because humans share similar salience structures. Certain options just feel natural. Game theory recognises this: sometimes the solution isn't calculated, it's intuitive. points. "Let's meet where we met last time." "Let's go to the most obvious place." "Let's follow the usual pattern."

It doesn't matter which side of the road people drive on. What matters is that everyone picks the same side. The UK drives on the left, most countries drive on the right. Both work. The disaster is when people don't coordinate. Conventions solve coordination games.

Why do people queue instead of pushing? Because everyone's better off if everyone queues. If one person pushes, they gain a small advantage but create chaos. If everyone pushes, no one gains and everyone wastes energy fighting. The norm (queue) is a coordination mechanism. Everyone benefits if everyone follows it.

Nash equilibriumA stable state where no one can improve their outcome by changing strategy alone. Named after mathematician John Nash (1928-2015), who formalised the concept in 1950. Nash won the Nobel Prize in Economics in 1994 for this work. An equilibrium is a balance point. In game theory, it's when everyone's strategy is a best response to everyone else's strategy. No one benefits from unilaterally changing. Example: in the Prisoner's Dilemma (one-shot), both defecting is a Nash equilibrium. If you're defecting and I'm defecting, neither of us improves by switching to cooperation alone. Nash equilibria aren't necessarily optimal or fair. They're just stable. Both prisoners would be better off cooperating, but that's not an equilibrium (each has incentive to defect). Nash equilibrium explains why bad situations persist: changing alone doesn't help. You need coordinated change. It's why traffic jams continue, why arms races escalate, why overfishing happens. Understanding Nash equilibria helps identify when you're stuck and what's needed to escape.:

A Nash equilibrium is a situation where no one can improve their outcome by changing their strategy, assuming everyone else keeps theirs the same. It's a stable state. Not necessarily optimal, just stable.

In the Prisoner's Dilemma (one-shot), both players betraying is a Nash equilibrium. If you're betraying and I'm betraying, neither of us benefits from switching to cooperation (we'd just get 10 years instead of 5). It's stable, even though we'd both be better off cooperating.

Nash equilibria explain why bad situations persist. Not because people are stupid, but because unilaterallyDone by one side alone, without agreement from others. From Latin uni- (one) + lateralis (of the side), from latus (side). Unilateral means "one-sided." In international relations, a unilateral action is taken by one country without consulting allies (unilateral military strike, unilateral trade policy). In game theory, changing unilaterally means you change your strategy whilst others keep theirs. This matters for Nash equilibrium: an equilibrium is stable if no one can improve by changing unilaterally. If you're stuck in traffic and you alone take a different route, you're still stuck (because thousands of others are still there). The change needs to be multilateral (many-sided) or coordinated. Unilateral change often fails because your outcome depends on others' choices. This is why collective action problems are hard: individual action doesn't help, but coordinating everyone is difficult. Recognising when unilateral change is futile saves wasted effort. Focus on coordination instead. changing your behaviour makes you worse off. You're trapped until everyone changes together.

Everyone's stuck in traffic. If you alone take public transport, you're still stuck (because you're one car among thousands). Only if many people switch does traffic improve. So everyone stays in their car, and the jam persists. It's a Nash equilibrium. Changing alone doesn't help.

Everyone's on their phone at dinner. If you put yours away but everyone else stays on theirs, you're just bored and excluded. If everyone puts their phones away, everyone has a better time. But unilaterally changing doesn't help. The equilibrium is everyone on their phones, even though everyone would prefer the alternative if they could coordinate.

Signalling and credibility:

Game theory cares a lot about signals. What you say is cheap. What you do is expensive. Actions reveal information.

If someone says "I'll help you," that's a claim. If they show up at 6 amAnte meridiem, Latin for "before midday." From ante (before) + meridiem (midday, noon), from medius (middle) + dies (day). "AM" designates times from midnight (12:00 am) to just before noon (11:59 am). "PM" is post meridiem (after midday), from noon to just before midnight. The system comes from ancient Rome, which divided the day at noon. The sun's position at noon (highest point, meridian) was the reference. Modern timekeeping inherited this. Midnight is 12 am (first minute after noon of the previous day). Technically confusing: 12 am is the start of a new day, not the end. Why does this matter for game theory? Showing up at 6 am is costly. Waking early, sacrificing sleep, starting your day inconveniently. That cost makes the signal credible. Saying "I'll help anytime" is cheap. Actually showing up at 6 am proves commitment. The earlier the time, the costlier the signal. This is why "I'll be there at 6 am" is more credible than "I'll be there at 2 pm." The cost is the point. It's hard to fake, so it's trustworthy. to help you move house, that's a signal. The cost (waking up early, spending their day) makes the signal credible. You believe them because they paid a price to prove it.

CredibleBelievable, trustworthy, able to be believed. From Latin credibilis, from credere (to believe, trust). Credibility means others believe you'll do what you say. In game theory, credible signals and threats are those you'll actually follow through on, not empty words. A signal is credible if it's costly to fake. Saying "I'm committed" is cheap. Investing time, money, or reputation is costly and therefore credible. A threat is credible if carrying it out is rational for you. "I'll burn my own money if you don't cooperate" isn't credible (why would you?). "I'll cut you off if you keep exploiting me" is credible (you're better off without a toxic relationship). Credibility matters because people respond to credible commitments, not empty promises. If your threats aren't credible, they're ignored. If your promises aren't credible, they're not trusted. Building credibility requires costly investment. You prove trustworthiness by following through repeatedly, even when it's inconvenient. Credibility is an asset in repeated games. Lose it once and it's hard to recover. signals are costly, hard to fake, and reliably correlated with the thing they're signalling. Peacocks have massive tails. That's costly (hard to escape predators, requires energy). But it signals genetic fitness. Only healthy peacocks can afford the cost. PeahensFemale peafowl, the counterpart to male peacocks. From "pea" (peafowl, from Latin pavo) + "hen" (female bird). Peacocks are male, peahens are female. Peacocks have elaborate, colourful tail feathers (trains) used to attract peahens. Peahens are drab, brownish birds. Why? Sexual selection. Peahens choose mates based on tail quality. Peacocks with bigger, brighter tails get more mates. This creates evolutionary pressure: males with impressive tails reproduce more, passing on genes for impressive tails. But why do peahens prefer big tails? The handicap principle: only healthy, genetically fit males can afford the cost of growing and maintaining a massive tail. It's a costly signal. Predators easily spot them, the tail is heavy and cumbersome, and it requires energy to produce. Weak males can't fake it. Peahens trust the signal because it's expensive. This applies beyond biology: in human contexts, costly signals (expensive education, conspicuous consumption, public commitments) work the same way. They're credible because they're hard to fake. Peahens and peacocks are a biological example of game-theoretic signalling. trust the signal because it's expensive to fake.

Saying "I love you" is cheap. Anyone can say it. Moving cities for someone, introducing them to your family, making long-term plans together, those are costly signals. They're credible because they're hard to fake. You believe someone's commitment when they've invested in ways that would hurt if they left.

Everyone says they're hardworking. That's cheap talk. But if you've built side projects, contributed to open source, or taught yourself a skill in your spare time, that's a costly signal. You invested time and effort, which is harder to fake than words. Employers trust costly signals over self-reported claims.

The threat that you never use:

The best threats are the ones you never have to carry out. If your threat is credible, people believe you'll do it, so they don't call your bluff. If it's not credible, it doesn't work.

For a threat to be credible, it has to be rational for you to follow through. If carrying out the threat hurts you more than it hurts them, it's not credible. They'll ignore it.

This is why parents struggle with threats. "If you don't behave, we're going home." But going home ruins the parent's day too. The kid knows this. The threat isn't credible. Compare that to "If you don't behave, no screen time tonight." That's easy to enforce and doesn't cost the parent much. It's credible.

"If you don't meet my salary request, I'll walk away." That's only credible if you actually have other options. If you're desperate and they know it, the threat is empty. They'll call your bluff. This is why you never negotiate without a backup plan. Your alternatives make your threats credible.

"If you keep doing this, I'll leave." That's only credible if you're actually willing to leave. If you've said it five times and never followed through, it's not a threat. It's noise. Empty threats destroy credibility faster than no threats at all.

How to actually use this:

Game theory isn't about manipulating people. It's about understanding the structure of interactions so you can make better decisions.

Is this a one-shot game or a repeated game? If you'll interact with this person again, cooperation matters. If it's one-time, trust is harder to build. Adjust your strategy accordingly.

Is this zero-sum or non-zero-sum? If it's non-zero-sum (most situations are), stop thinking in terms of winning and losing. Start thinking in terms of "how do we both get what we want?"

What's the Nash equilibrium? If you're stuck in a bad situation that no one can unilaterally escape, you need coordination. Get people to agree to change together, or change the incentives so individual action makes sense.

What are the incentives? People respond to incentives, not intentions. If someone's behaving in a way you don't like, don't assume they're malicious. Assume the game they're playing rewards that behaviour. Change the game, change the behaviour.

What signals am I sending? Your actions speak louder than your words. If you want people to trust you, send costly signals. If you want to be taken seriously, make credible commitments. If you keep saying one thing and doing another, no one will believe you.

Am I cooperating with cooperators and retaliating against defectorsThose who betray, break agreements, or fail to cooperate. From Latin defectus (failure, revolt), from deficere (to desert, fail), from de- (away) + facere (to do). To defect means to abandon your side or betray a commitment. In game theory, defecting means choosing not to cooperate. In the Prisoner's Dilemma, defecting is betraying your partner. In group projects, defecting is free-riding. Defectors gain short-term benefits (exploit others' cooperation) but damage long-term relationships. In repeated games, defectors get punished: others stop cooperating with them. This is why reputation matters. Be known as a defector and no one trusts you. Tit-for-tat handles defectors by retaliating once, then forgiving if they cooperate again. This prevents exploitation without holding grudges. The key: distinguish defectors from cooperators. Cooperate with cooperators, punish defectors. This maintains cooperation whilst preventing exploitation. Most successful strategies in game theory tournaments balance these: cooperate by default, retaliate against defection, forgive if cooperation resumes. That's how you handle defectors without becoming one yourself.? Tit-for-tat works. Be nice, be forgiving, but don't be a pushover. If someone repeatedly takes advantage, stop cooperating. If they change, give them another chance.

Final thoughts:

Game theory doesn't tell you what to value. It doesn't tell you whether you should care about fairness, loyalty, or self-interest. But once you know what you want, it tells you how to get it. It's the logic of strategic interaction. And whether you study it or not, you're playing the games every day. You might as well understand the rules.

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