Game Theory — Glossary

Foundations Lessons 01–02

Game

A situation where your best choice depends on what other decision-makers choose — and they're reasoning about you too. The defining feature is interdependence, not competition. Choosing a restaurant alone = a decision. Pricing against a competitor who reacts = a game.

Player

A decision-maker in the game — a person, clinic, company, country, or AI agent.

Strategy

A complete plan of action: one of the options available to a player.

Payoff

A number for how much a player values an outcome — higher is better. Bundles everything they care about (money, time, reputation, risk), not just cash.

Utility

The formal name for that "all-things-considered value" a payoff represents. Winning a price war this month but training a rival to retaliate forever is low utility, even if the cash looks good.

Ordinal payoffs

Payoffs that capture only the order of outcomes (best, 2nd, 3rd…), not magnitudes. Enough to find dominant and dominated strategies — so an honest ranking often solves a game with no real numbers.

Cardinal payoffs

Payoffs whose sizes and differences carry meaning. Needed when weighing uncertain outcomes or mixing strategies. Quick method: anchor worst = 0, best = 100.

Robustness / sensitivity test

Before pinning a payoff down, ask whether your conclusion changes if it were a bit different. If no, leave it rough; if yes, that payoff is near a decision-flipping threshold — measure it carefully.

Payoff matrix

A grid laying out a two-player game: your strategies as rows, theirs as columns, each cell holding (your payoff, their payoff).

Strategic interdependence

The condition that makes something a game: your outcome depends on others' choices, so you can't pick well without modelling them.

Rationality

A player pursues their own payoff consistently. Not selfish — payoffs can include caring about others. Usually assumed to be common knowledge.

Solving games: dominance & equilibrium Lessons 01, 03, 04

Dominant strategy

A strategy that gives a strictly higher payoff than all your others, no matter what the others do. If you have one, play it — no prediction needed.

Strictly dominated strategy

Always worse than some other strategy of yours, whatever the opponent does. The first law: never play one — and assume a rational opponent won't either.

Weakly dominated strategy

Never better, sometimes worse (ties in some cases). Riskier to eliminate — the order you remove them can change the answer.

Iterated elimination of dominated strategies (IEDS)

Repeatedly delete either player's strictly dominated strategies, re-examine the smaller game, and repeat until nothing more can go. What survives is your prediction — even when you have no dominant strategy yourself.

Common knowledge of rationality

Everyone is rational, everyone knows that, everyone knows everyone knows it, and so on. The assumption that makes iterated elimination valid.

Level-k / depth of reasoning

How many steps ahead a player reasons about others' reasoning. Most real people stop at level 1–2; being one level deeper than your opponent is itself an edge (the "2/3 of the average" game).

Best response

Your payoff-maximising strategy given a specific choice by the others. Dominance is the special case of being a best response to everything.

Nash equilibrium

A strategy profile where every player is best-responding to the others, so no one can do better by changing alone. The central solution concept; it need not be the best outcome for the players.

Mutual best response

The defining test of a Nash equilibrium: each player's choice is a best reply to the others'.

Pure strategy

A single, fixed (non-random) choice.

Mixed strategy

Randomising over your options with chosen probabilities. Needed in games with no pure equilibrium (e.g. matching pennies).

Prisoner's dilemma

Each player has a dominant strategy to defect, so both defect — yet both would be better off cooperating. Individually rational → collectively bad. Price wars, ad-spend arms races, over-prescribing races.

Coordination Lesson 05

Coordination game / stag hunt

A game where matching beats not matching; typically has multiple Nash equilibria, one better for all (payoff-dominant) and one safer (risk-dominant).

Multiple equilibria

More than one Nash equilibrium exists; rationality alone doesn't say which one players land on.

Focal point (Schelling point)

An equilibrium selected by sheer salience — the option each player expects the other to expect — even with no communication.

Battle of the sexes

A coordination game where both want to match but each prefers a different equilibrium — coordination plus a distributional tug-of-war.

Cheap talk

Costless, non-binding communication before a game. Coordinates when interests align; just noise when they conflict.

Convention

An equilibrium held in place by history and shared expectation (a standard, a default). Displacing it needs a coordination mechanism, not merely a better option.

Sequential play & commitment Lessons 06–07

Sequential game

Players move in a defined order; later movers see earlier moves before choosing.

Game tree (extensive form)

A diagram of decision nodes and branches showing the order of play and the payoffs at each ending.

Backward induction

Solve a sequential game from the end: at each final decision pick the chooser's best move, then fold that choice back toward the start.

Subgame perfect equilibrium

The path that survives backward induction — every player acts optimally at every point they could reach (no reliance on empty threats).

Credible threat (or promise)

One the actor would actually carry out, because doing so is in their interest when the moment arrives.

Non-credible threat

One the actor has no incentive to execute when the time comes. Backward induction prunes it automatically.

First-mover advantage

The benefit of committing early when your move reshapes the follower's best response in your favour.

Commitment

An observable, hard-to-reverse action that changes your own future best move — and therefore what the other side rationally expects. Giving up options can make you stronger.

Commitment device

The concrete mechanism that locks you in: burning a bridge, a binding contract, a public pledge, a delegated rule, a sunk investment, or reputation.

Credibility

The property that makes a threat or promise believable: it's observable and costly/hard to reverse, so the other side knows you'll follow through.

Brinkmanship

Deterring by a dangerous, credible threat. Powerful but inflexible — it can trap both sides if both over-commit.

Repetition Lesson 08

Repeated game

The same players play a stage game across many rounds, observing history as they go.

Shadow of the future / discount factor

How much future payoffs weigh against today's. When the future matters enough, cooperation that a one-shot game destroys becomes sustainable.

Tit-for-tat

Cooperate first, then copy the other player's last move. Nice, retaliatory, forgiving, clear — and a tournament winner (Axelrod).

Grim trigger

Cooperate until the first defection, then defect forever. Harsher and less forgiving than tit-for-tat.

Folk theorem

In indefinitely repeated games, patient-enough players can sustain a wide range of cooperative outcomes as equilibria.

Backward-induction unraveling (finite horizon)

A known final round makes defection dominant there, and that logic cascades backward through every earlier round — cooperation can collapse. Keep horizons open.

Reputation

A track record across repeated dealings that functions as a commitment device — others expect you to behave as you have.

Information Lesson 09

Asymmetric information

One side knows something relevant the other doesn't (quality, type, intent). Breaks naive trust.

Signaling

The informed party takes a costly, hard-to-fake action that credibly reveals its type (certification, a long guarantee, published outcomes).

Screening

The uninformed party designs a menu of choices so the other side self-selects and reveals its type (tiered pricing, deductibles).

Single-crossing condition (costly signal)

A signal separates types only if it costs more for the low/bad type than the high/good type — otherwise everyone fakes it.

Separating vs pooling

Separating: different types take different actions and are identified. Pooling: all types look the same and stay indistinguishable.

Adverse selection

When hidden quality drives good types out and leaves mostly bad ones (the "lemons" problem).

Self-selection

The mechanism a screen relies on: each type voluntarily picks the option that fits it, revealing private information.

Bargaining Lesson 10

Bargaining

Dividing a surplus that exists only if the parties agree.

BATNA

Best Alternative To a Negotiated Agreement — what you get if talks fail. Your true source of leverage.

Reservation value

Your walk-away point: the worst deal you'd still accept rather than take your BATNA.

ZOPA (zone of possible agreement)

The range of deals that beat both sides' reservation values. A deal exists only if it's non-empty.

Surplus

The size of the ZOPA — the value the negotiation is fighting to divide.

Anchoring

A credible, well-justified first offer that pulls the final settlement toward it.

Cost of delay / patience

What each side loses per round without a deal. The more patient side captures more of the surplus.

Designing games: mechanism design Lesson 11

Mechanism design

"Game theory in reverse": choosing the rules so rational, self-interested players produce the outcome the designer wants.

Incentive compatibility

A mechanism where the desired/honest behaviour is each player's own best move — so you needn't police them.

Second-price (Vickrey) auction

Sealed bids; the highest bidder wins but pays the second-highest bid. Bidding your true value is a dominant strategy.

Dominant-strategy truthfulness

Telling the truth is best regardless of what others do — the strongest, most robust form of incentive compatibility.

Stable matching (Gale-Shapley)

A matching with no pair who'd both rather abandon their assignment for each other. Basis of residency matches and kidney-exchange chains (Roth).

Revelation principle

Anything achievable by any mechanism is achievable by a direct, incentive-compatible one — so you only need to search for truth-telling rules.