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Every decision is a game.
Learn to play it.

Game theory × psychology, made entertaining and educational — the models that explain pricing wars, penalty kicks, peace treaties and playground politics, and the minds that play them. Stories first, equations second, games you can actually play.

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Start here

Game theory is the physics of strategic interaction

Whenever your best move depends on someone else's move — a rival's price, a negotiator's patience, a goalkeeper's dive — you're inside a game. Game theory gives you the map: players, strategies, payoffs, and the equilibria where everything settles.

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Predict

Where will a strategic situation settle? Nash equilibrium tells you the stable points.

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Cooperate

Why do partnerships break down — and how do repeated interactions rescue them?

⚔️

Compete

Pricing, auctions, market entry: who should move first, and when should you randomize?

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Divide

Coalitions and bargaining: how do rational players split a pie they built together?

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Understand

The psychology of play: why real people cooperate, retaliate, trust and bluff in ways pure rationality never predicts.

The core curriculum

The Top 10 models, each in 3 layers

A story you'll remember, a diagram you can see, an equation you can use. Click a layer tab inside each card.

Nash Equilibrium

stable balance · no one wants to move alone

Use for: general strategic prediction

Two coffee shops open across the street from each other. Each wants a price that pulls in customers — but undercut too hard and the other retaliates. After a few rounds, both settle at a price where neither can do better by changing alone. That resting point is the Nash equilibrium.

A strategy profile $s^*$ is a Nash equilibrium if no player gains by deviating unilaterally:

$$u_i(s_i^*, s_{-i}^*) \ge u_i(s_i, s_{-i}^*) \quad \forall i,\ \forall s_i$$

$s_{-i}^*$ = everyone else's strategies, held fixed.

Reach for it whenever you need to predict where a strategic situation will settle: price wars, arms races, traffic routes, standards adoption. It's the default solution concept of modern economics.

Where both best-response curves cross, nobody moves: equilibrium.

Prisoner's Dilemma

temptation to defect · private incentives hurt the group

Use for: cooperation problems & trust

Two farmers share a canal. If both conserve water, both harvests thrive. But each is tempted to take extra — even though that drains the other's field. Temptation wins, both overuse the canal, and both end up worse than if they'd cooperated.

Payoffs ordered $T > R > P > S$: defection dominates, yet $(C,C)$ beats $(D,D)$.

$$\begin{array}{c|cc} & C & D \\ \hline C & (R,R) & (S,T) \\ D & (T,S) & (P,P) \end{array}$$

Temptation $T$, Reward $R$, Punishment $P$, Sucker $S$.

Climate agreements, cartel cheating, doping in sport, overfishing, office free-riding. Any time individual incentives quietly sabotage the group outcome.

Rational play lands in the red cell — the whole tragedy in one matrix.

Repeated Games

the future disciplines the present

Use for: reputation & long-term deals

Two suppliers compete for the same retailer every month. One considers cutting quality to save money — but knows the retailer will remember. Because they'll do business for years, both behave better than in a one-shot deal. The shadow of the future changes today.

The stage game repeats at $t=0,1,2,\dots$; payoffs are discounted by $\delta$:

$$U_i = (1-\delta)\sum_{t=0}^{\infty} \delta^t\, g_i(a^t), \qquad 0 \le \delta < 1$$

Patient players (high $\delta$) can sustain cooperation that one-shot logic destroys.

Supplier relationships, alliances, cartels, tit-for-tat diplomacy, online seller ratings. Whenever the same players will meet again.

Discounting: tomorrow matters a bit less — but it still matters enough to behave.

Zero-Sum Games

one wins exactly what the other loses

Use for: pure competition

Two chess players sit down. Every advantage one gains makes the other exactly worse off. No shared profit, no win-win — only victory and defeat. The purest form of competition.

Payoffs always sum to zero:

$$u_1(s_1,s_2) + u_2(s_1,s_2) = 0 \;\;\Longleftrightarrow\;\; u_2 = -u_1$$

Solved by minimax: maximize your worst case, because their gain is your loss.

Sports, chess, poker heads-up, sealed-bid contests, adversarial security. If a deal could grow the pie, it's not zero-sum — a common real-world mistake.

The seesaw never creates value — it only moves it.

Sequential Games

move order is strategy

Use for: negotiations, entry, auctions

A challenger wants to enter a new market — but first watches whether the incumbent slashes prices to scare it off. The incumbent moves, the challenger reacts, and the outcome hangs on that order. Strategy isn't just what to do; it's when.

Modeled in extensive form as a game tree:

$$G = \big(N,\, H,\, P,\, \{A(h)\}_{h\in H},\, \{u_i\}_{i\in N}\big)$$

Histories $H$, player function $P$, actions $A(h)$. Solve by backward induction: start at the leaves.

Market entry, salary negotiations, legislative bargaining, chess openings, escalation games. Anywhere commitment and timing carry weight.

Backward induction: the leader reasons from the end of the tree to its first move.

Simultaneous-Move Games

decide before you can see

Use for: price setting, announcements

Two rival phone makers set launch prices without seeing each other's choice. Each guesses what the other will do and commits at the same time. No reacting in the moment — decisions under pure uncertainty about the other side.

Written in normal (matrix) form:

$$G = \big(N, \{S_i\}_{i\in N}, \{u_i\}_{i\in N}\big)$$

Solved with the same Nash condition — best responses to beliefs about others.

Simultaneous bids, product launches, campaign announcements, standardized test-day strategies. Whenever nobody sees anybody's move first.

A wall between the players: commit now, find out later.

Mixed Strategies

randomness as a weapon

Use for: staying unpredictable

Penalty shootout. If the kicker always shoots left, the goalie learns the pattern. So the kicker mixes left, right and center — with calibrated probabilities. Randomness stops being a weakness and becomes the strategy itself.

A mixed strategy is a probability distribution over pure strategies:

$$\sigma_i \in \Delta(S_i), \qquad \mathbb{E}[u_i(\sigma)] = \sum_{s\in S} \sigma(s)\, u_i(s)$$

In equilibrium you mix so the opponent is indifferent between their options.

Penalty kicks, poker bluffing, security patrols, tax audits, rock-paper-scissors. Real pros randomize at almost exactly the theoretical rates.

Your strategy is the whole distribution, not any single kick.

Cooperative Game Theory

join forces, then split fairly

Use for: coalitions & joint ventures

Three construction firms bid on a mega-project none can finish alone. As a coalition they combine cranes, crews and know-how — then face the harder question: how to split the gains so nobody walks. Winning is easy; sharing is the game.

A coalition game assigns value to every group:

$$(N, v), \quad v: 2^N \to \mathbb{R}$$

The core keeps every coalition on board:

$$\sum_{i\in N} x_i = v(N), \qquad \sum_{i\in S} x_i \ge v(S)\ \ \forall S \subseteq N$$

Joint ventures, cost-sharing (airports, pipelines), political coalitions, profit splits. Also the home of the Shapley value — the "fair share by contribution" formula.

The grand coalition creates the surplus; the core decides who keeps what.

Bargaining Models

patience and outside options set the price

Use for: negotiation & deal-making

A buyer and seller haggle over a house. Seller starts high, buyer counters low, both drift toward the middle — but the final number depends less on "value" than on who can wait longer and who has better alternatives. Patience is leverage.

The Nash bargaining solution maximizes the product of gains over each side's fallback $d$:

$$\max_{(u_1,u_2)\in F} (u_1 - d_1)(u_2 - d_2)$$

Better outside option $d_i$ ⇒ bigger share. Improve your BATNA, win the deal.

Salary talks, M&A, trade deals, divorce settlements, hostage negotiations. The formula behind "never negotiate without an alternative."

One surplus bar, one moving frontier: that's every negotiation.

Stackelberg Competition

the leader shapes the battlefield

Use for: leader–follower markets

A supermarket giant announces a milk price cut. Smaller stores watch, then set their own prices in response. Because the giant moved first — publicly and credibly — the followers react to its choice instead of choosing freely. The leader wrote the rules of the round.

The follower best-responds; the leader optimizes anticipating that response:

$$q_F^*(q_L) = \arg\max_{q_F} \pi_F(q_L, q_F)$$

$$q_L^* = \arg\max_{q_L} \pi_L\big(q_L,\, q_F^*(q_L)\big)$$

Platform pricing, supply chains, OPEC-style output leadership, first-mover product launches. First-mover advantage, formalized.

Commit first, and the follower's whole curve becomes your menu.

Don't just read it

Play the games

Three interactive labs. Each one teaches a model by letting you lose to it first.

🥷 Lab 1 · Iterated Prisoner's Dilemma

You vs. Tit-for-Tat: it cooperates first, then copies your last move. Can you beat the classic tournament champion?

You0

Tit-for-Tat0

Round0

Payoffs per round — both cooperate: 3/3 · both defect: 1/1 · lone defector: 5, sucker: 0.

⚽ Lab 2 · Penalty Kick (Mixed Strategies)

Pick a corner. The goalie studies your habits — the more predictable you are, the more saves it makes. Beat it by truly mixing.

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Goals0

Saves0

Your mix L/C/R–

Optimal play ≈ randomize close to your best equilibrium frequencies. Patterns get punished.

☕ Lab 3 · Coffee War (Nash Equilibrium)

Set your latte price. Your rival best-responds instantly. Slide until neither of you wants to move — you'll feel the equilibrium click.

Your price: $5.00

Rival's best response–

Your profit–

Rival profit–

Memorize the map

All 20 models as flashcards

Click any card to flip it. Front: the model. Back: the one-line intuition and its equation.

One screen to rule them all

The cheat sheet

Situation you're facing	Model to reach for	Memory hook
General strategic prediction	Nash equilibrium	stable balance
Cooperation keeps collapsing	Prisoner's Dilemma	temptation to defect
Same players, again and again	Repeated games	the future disciplines the present
Pure win/lose competition	Zero-sum	one wins, one loses
Moves happen in order	Sequential games	order matters
Everyone commits blind	Simultaneous games	decide without seeing
Predictability gets punished	Mixed strategies	randomness is strategic
Alliances & shared gains	Cooperative games	join forces, split fairly
Splitting a surplus	Bargaining models	patience is leverage
One firm sets the tone	Stackelberg	leader moves first

Train your mind

Learn to think steps ahead

A learning path, the movie scenes that secretly teach strategy, and a quiz to see how far ahead you already think.

📚 Your learning path

Nash equilibrium
Prisoner's Dilemma
Repeated games
Zero-sum games
Sequential games
Bargaining
Stackelberg
Cournot
Bertrand
Bayesian games

🍿 Strategy at the movies

A Beautiful Mind — the bar scene (imperfectly!) dramatizes Nash's idea.
The Dark Knight — the two-ferries scene is a Prisoner's Dilemma.
Golden Balls "Split or Steal" — a PD played on live TV.
The Princess Bride — the poisoned-cup duel is level-k reasoning.
Penalty shootouts — pro kickers mix at near-equilibrium rates.

📝 How far ahead do you think?

Watch & follow

The channel

Every model above becomes an episode: a 60-second TikTok hook and a deep-dive YouTube video. Season 1 roadmap:

EP 1

The $5 Trap

Why two coffee shops always end up at the same price — Nash equilibrium in the wild.

Nash

EP 2

Betray Your Best Friend?

We run the Prisoner's Dilemma on strangers in the street — with real money.

EP 3

The Revenge Algorithm

How Tit-for-Tat won the most famous tournament in game theory history.

Repeated

EP 4

Why Messi Kicks Left

Penalty data vs. mixed-strategy theory. The math says: stay random.

Mixed

EP 5

Never Split the Difference?

The Nash bargaining solution vs. real-estate haggling.

Bargaining

EP 6

Move First, Win More

Stackelberg leadership: when announcing your move is the move.

Stackelberg

▶ YouTube — deep dives ♪ TikTok — 60-second games

Channel links are placeholders — swap in your handles when the channels go live.

Every decision is a game.Learn to play it.