Glossary

Adverse selection

Also: the lemons problem, lemons problem, the market for lemons

When the better informed side decides whether to take part, the ones who accept an offer are the ones it suits the offerer least.

Affiliated values

Also: affiliation, affiliated signals, correlated values

An information structure in which bidders' signals are positively dependent, so one bidder holding a high signal makes it more likely that the others hold high signals too.

All-pay auction Game

Also: all pay auction, all-pay contest, lobbying contest

When losers pay their bids as well as the winner, no bid is safe to settle on, so contestants must randomise and the whole prize is consumed by the bidding however many of them there are.

Altruistic punishment

Also: costly punishment, peer punishment, third-party punishment

Paying a personal cost to punish a defector who has not harmed you, which raises and sustains contribution in public goods games even though the punishing is itself a second-order public good.

Assurance game Game

Also: assurance problem, trust dilemma, coordination under risk

How much confidence cooperation needs is a number you can compute, and when it falls below one half a small reassurance is enough to select the good equilibrium.

Asymmetric information

Also: information asymmetry, informational asymmetry, private information

One side of a dealing knows something that matters to both of them and the other side does not.

Backward induction

Also: rollback, rollback analysis, backwards induction

Work out the last move first, then the move before it, and keep stepping back until you reach the start.

Bank run game Game

Also: bank run, Diamond-Dybvig game, depositor run game

A bank that is perfectly sound can be destroyed by depositors who each believe only that the others are about to arrive, and the belief is the safer one to hold, which is why the ruinous outcome is the one a cautious depositor reaches.

Bargaining power

Also: bargaining strength, disagreement point, threat point

The ability to claim a larger share of a surplus, which comes from having a better fallback, more patience or a more credible refusal rather than from need.

Battle of the sexes Game

Also: Bach or Stravinsky, battle of the sexes game, coordination with conflicting preferences

Agreeing matters more than what you agree on, but the two of you disagree about which to agree on.

Bayesian game

Also: game of incomplete information, incomplete information game, Bayesian normal form

A game in which each player privately holds one of several possible characteristics, drawn from a distribution everyone knows.

Bayesian incentive compatibility

Also: BIC, Bayesian incentive compatible, Bayes-Nash incentive compatibility

Honesty is optimal in expectation, given that everyone else is reporting honestly and given shared beliefs about the distribution of private information.

Bayesian Nash equilibrium

Also: BNE, Bayesian equilibrium, Bayes-Nash equilibrium

Each type of each player picks the action that is best given what they know, assuming every other type is doing the same.

Beauty contest game Game

Also: guess two-thirds of the average, p-beauty contest, guessing game

The right guess depends on how many steps of reasoning everyone else will take, so playing well means being right about other people's depth rather than going as deep as possible yourself.

Beer-quiche game Game

Also: beer and quiche, beer or quiche, Cho-Kreps signalling game

When a signal is cheap enough that the wrong type can also afford it, equilibrium alone cannot say who sends it, and the only way to choose between the answers is to ask which type could ever have hoped to gain by departing from them.

Belief system

Also: assessment, beliefs, beliefs at an information set

A statement, for every point in the game where a player cannot tell which situation they are in, of how likely they think each one is.

Bertrand competition with differentiated products Game

Also: differentiated Bertrand, Bertrand with product differentiation, price competition with differentiated products

Once varieties are imperfect substitutes an undercut captures only part of the rival's demand, so margins survive and each firm now wants to raise its price when its rival raises theirs.

Bertrand duopoly Game

Also: Bertrand competition, Bertrand model, Bertrand paradox

Two firms are enough to drive price to marginal cost when the products are identical, because the prize for undercutting is the whole market rather than a share of it.

Best response

Also: best reply, best response function, best response correspondence

The strategy that pays most against a specific belief about what the others will do.

Bid shading

Also: shading, shade the bid, bidding below value

Bidding below your own valuation, by the margin that trades a lower chance of winning against a larger surplus when you do win.

Braess's paradox Game

Also: Braess paradox, the Braess paradox, road paradox

Giving people one more option can leave every single one of them worse off, because each takes it for a reason that is individually sound and collectively self-defeating, so a network can be improved by removing capacity.

Brinkmanship

Also: brinksmanship, going to the brink, the threat that leaves something to chance

Deliberately raising a shared risk of disaster that neither side fully controls, so that a threat too costly to carry out on purpose becomes frightening anyway.

Burning the boats Game

Also: burning your bridges, burning the bridges, burning the ships

Destroying your own line of retreat can leave you better off, because what the other side is choosing against is the options you still have rather than the intentions you declare.

Centipede game Game

Also: centipede, the centipede, Rosenthal's centipede

Backward induction can unravel a long and mutually profitable sequence at its very first move, and the longer the sequence the more obviously wrong the prediction looks.

Characteristic function

Also: coalition function, worth function, v

The rule that assigns to every coalition the total payoff its members can guarantee themselves without help from anyone outside it.

Cheap talk

Also: costless communication, non-binding communication, pre-play communication

Messages that cost nothing to send, which can still carry real information when the speaker's interests run with the listener's rather than against them.

Cheap talk Game

Also: Crawford-Sobel, strategic information transmission, the expert and the decision maker

Talk that costs nothing can still carry information, but only in lumps coarse enough that the sender does not want to lie about which lump it is in, and past a certain conflict of interest no lump is coarse enough.

Chicken Game

Also: game of chicken, the chicken game, chicken game

Both equilibria need someone to give way, so the fight is over who is believed to be unable to.

Coalition

Also: coalitions, grand coalition, S

A subset of the players considered as a group that can act together and is credited with whatever it can achieve on its own.

Colonel Blotto Game

Also: Blotto game, Colonel Blotto game, force allocation game

When one budget has to cover several contests at once, any plan the enemy can guess can be beaten by abandoning where you are strong and overwhelming where you are not, so strength must be hidden rather than merely sufficient.

Combinatorial auction

Also: package auction, package bidding, bundle auction

An auction in which bidders bid on bundles rather than on single items, so complementarities between items can be expressed directly, at the cost of a winner determination problem that is computationally hard.

Commitment

Also: commitment device, credible commitment, binding commitment

Deliberately giving up some of your own options so that others can rely on what you are going to do.

Committee voting game Game

Also: committee voting, voting game, collective choice game

When no single vote can change the result on its own, an outcome both voters rank last is still a Nash equilibrium, which is why equilibrium alone is too weak a test of how a committee will behave.

Common knowledge

Also: common knowledge of rationality, higher-order knowledge, higher-order beliefs

Something everyone knows, that everyone knows everyone knows, and so on without end.

Common prior assumption

Also: common prior, CPA, Harsanyi doctrine

Everyone starts from the same beliefs about how types are drawn, and differs only in what they privately went on to learn.

Common-pool resource game Game

Also: commons game, extraction game, appropriation game

Every user of a shared resource counts the harm their own extra effort does to their own catch and ignores the identical harm it does to everyone else's, so the overuse is built into the access rules and widens with each additional user admitted.

Common-value auction Game

Winning tells you your own estimate was the highest, which is bad news, so the bid has to be shaded before you learn whether you won.

Conditional cooperation

Also: conditional cooperator, conditional cooperators, reciprocal contribution

A disposition to contribute roughly in step with what the rest of the group contributes, which makes an experimental population a mixture of distinct types rather than one representative agent.

Condorcet winner

Also: Condorcet candidate, majority winner, pairwise majority winner

The alternative that beats every other alternative in a pairwise majority vote, which exists whenever preferences are single-peaked on one dimension and need not exist otherwise.

Congestion game

Also: congestion games, Rosenthal congestion game, routing game

A game in which each player chooses a set of shared resources and the cost of a resource depends only on how many players chose it, a structure that guarantees a pure Nash equilibrium exists.

Consistency of beliefs

Also: Kreps-Wilson consistency, consistent assessment, consistency requirement

Beliefs away from the expected path count as reasonable only if they are the limit of beliefs worked out from strategies in which every move still has some small chance of being played.

Cooperative game

Also: coalitional game, cooperative game theory, coalitional form game

A game described by what each group of players can achieve together rather than by the individual moves available to them, with binding agreements assumed possible.

Coordination

Also: coordination problem, coordination game, pure coordination

Players want the same thing and the only difficulty is settling on which of several workable arrangements to use.

Coordination failure

Also: failure to coordinate, coordination failures, bad equilibrium

A group settles on an equilibrium that every member would rather leave, purely because each expects the others to stay, so nothing is wrong with the situation except the beliefs holding it in place.

The core

Also: core of a cooperative game, coalitional stability

The set of divisions that no group of players could beat by walking away and keeping what they could make on their own.

Correlated equilibrium

Also: correlated equilibria, Aumann correlated equilibrium, correlating device

Players take private advice from a shared random signal and nobody wants to ignore the advice they get, which widens rather than narrows the set of Nash outcomes.

Cournot duopoly Game

Also: Cournot competition, Cournot model, quantity competition

Competing in quantities leaves each firm producing output that its rival would rather it did not, so the market settles strictly between monopoly and perfect competition instead of at either extreme.

Credibility

Also: credible threat, non-credible threat, incredible threat

A threat or a promise counts only if carrying it out would still suit the person making it once the moment arrives.

Cyclic population game Game

Also: generalised rock paper scissors, replicator dynamics example, RSP population game

The same mixed equilibrium can be an attractor, the centre of endless cycles, or something a population flies away from, so locating the rest point tells you nothing about whether anyone ever reaches it.

Deadlock Game

Also: deadlock game, the deadlock game

Having a dominant strategy is not in itself the problem: here both players defect, both get what they most prefer of the available outcomes, and there is nothing to repair.

Deferred acceptance

Also: deferred acceptance algorithm, Gale-Shapley algorithm, proposal algorithm

The Gale and Shapley procedure in which one side proposes down its preference list while the other merely holds its best offer so far rather than accepting it, which produces a stable matching that is optimal for the proposing side and strategy-proof for that side.

Dictator game Game

Also: the dictator game, dictator allocation, unilateral division game

Stripping out the other side's power to refuse turns anything handed over into evidence about what the giver wants rather than about what they were forced to pay.

Direct mechanism

Also: direct revelation mechanism, direct-revelation mechanism, DRM

A set of rules in which each participant simply reports their private information and the rules then fix the outcome and any payments.

Discounting

Also: discount factor, discount rate, time preference

A payoff received later is worth less than the same payoff now, and how fast it shrinks decides how much the future weighs in today's choice.

Dollar auction Game

Also: the dollar auction, Shubik's dollar auction, escalation auction

A sequence of decisions each of which is clearly worth taking on its own can carry both parties far past the point where either would have begun, because what is already spent is gone and only the next increment is ever up for decision.

A dominance-solvable 3x3 game Game

Also: dominance solvable game, iterated dominance example, 3x3 dominance solvable game

A single prediction can survive even when nobody starts with a dominant strategy, because each round of ruling out what the other side would never do is what creates the next round.

Dominant-strategy incentive compatibility

Also: DSIC, dominant strategy incentive compatibility, strategy-proofness

Honesty is optimal for each participant no matter what anyone else reports, so no beliefs about the others are needed.

Driving convention Game

Also: which side of the road, driving game, left or right

When the players want only to match and are indifferent about which way, nothing inside the game can pick an equilibrium, so the answer has to come from history outside it.

Duel Game

Also: duel game, timing game, when to fire

When to act is the whole of the strategy, and the right moment is fixed not by how good your own shot has become but by how good the other person's is about to be.

Dutch auction Game

Also: descending auction, descending price auction, clock auction

A clock that falls through prices nobody has taken teaches a bidder nothing, so the plan of what to do at every price has to be fixed in advance and the auction is a sealed bid wearing a sequence's clothes.

El Farol bar problem Game

Also: El Farol problem, the bar problem, minority game

If everybody forecasts the crowd the same way the forecast destroys itself, so the only expectations that can survive being held in common are ones nobody holds in common.

English auction Game

Also: ascending auction, open outcry auction, ascending price auction

An ascending price does the bidder's thinking for them: there is never a reason to be in the room above your own value or out of it below, so the winner pays whatever it took to see off the last rival and nobody needs a view about anyone else.

Entry deterrence Game

Also: entry game, market entry game, incumbent and entrant

A threat that would hurt the person making it is not believed by the person it is aimed at, so announcing it deters nobody.

Evolutionarily stable strategy

Also: ESS, evolutionary stability, evolutionarily stable strategies

A way of behaving that, once almost everyone in a population follows it, cannot be displaced by a small group behaving differently.

Extensive form

Also: game tree, extensive form game, extensive-form representation

A game written down as a tree showing who moves when, what they may do, and what they know at the time they do it.

Externality

Also: spillover, spillover effect, external cost

An action imposes a cost or hands a benefit to someone who had no say in it and is neither paying nor being paid for it.

Finite game of perfect information Game

Also: finite perfect information game, Zermelo game, chess as a finite game

Every finite game of perfect information already has an answer waiting in it, so chess is interesting only because nobody has finished the calculation.

Finitely repeated prisoner's dilemma Game

Also: finitely repeated prisoner's dilemma, known end date, finite repetition

A known last round takes away the only reason to cooperate in it, and that absence then travels backwards until no round is left in which cooperating pays.

First mover advantage

Also: first mover advantage, moving first, leader advantage

Moving first pays when the move cannot be taken back, so the other side has no choice but to respond to it.

First-price sealed-bid auction Game

Also: first price auction, first-price auction, sealed bid auction

When you pay what you bid you must shade below your value, and the right bid is simply what you expect the strongest rival to be worth in exactly those cases where your bid wins.

Focal point

Also: Schelling point, Schelling points, focal points

When several equilibria are available and nothing in the payoffs chooses between them, players settle on whichever one stands out to both of them for reasons outside the game.

Folk theorem Result

Also: the folk theorem, folk theorems, perfect folk theorem

In a relationship that lasts long enough between players who are patient enough, almost any outcome that beats what each can guarantee alone can be held in place by the threat of punishment.

Forward induction

Also: forward induction reasoning, inference from deviation, reading intent from a move already made

Working out what a player must have been aiming at from a move they have already made, rather than only reasoning backwards from the end.

Free rider problem

Also: free riding, free rider, free-riding

When a benefit cannot be withheld from those who did not pay for it, each person's best move is to let others provide it, so too little of it gets provided.

Gift exchange game Game

Also: gift exchange, labour gift exchange, wage-effort game

A wage paid before the work is done buys nothing anyone can be held to, so self-interest prices the job at the floor and the reliable experimental finding that generous wages do buy effort is a fact about the contract being incomplete rather than about the workers being irrational.

Grim trigger

Also: trigger strategy, permanent punishment, grim strategy

Cooperate for as long as the other side does, and if they ever fail to, refuse to cooperate for the rest of the relationship.

Harmony Game

Also: harmony game, no conflict game, no dilemma game

Some situations have no strategic problem in them at all, and naming that case is what stops you treating every interaction as a dilemma waiting to be found.

Harsanyi transformation

Also: Harsanyi doctrine, move by Nature, Nature move

Turning a game where players do not know who they face into an ordinary game by letting chance pick the types first and telling each player only their own.

Hawk-dove Game

Also: hawk dove, hawk-dove game, snowdrift game

Aggression pays only while it is rare, so a population settles at a mix rather than on a type.

Hold-up

Also: hold-up problem, holdup problem, hold up problem

Once one side has sunk money or effort it cannot recover, the other side can demand a bigger share of the gains.

Hold-up problem Game

Also: holdup problem, hold up game, the hold-up game

Investment that cannot be protected by contract simply never happens, so the loss from hold-up falls before the bargaining rather than during it.

Hotelling linear city Game

Also: Hotelling model, linear city model, spatial competition

The margin a firm can hold is precisely what it costs its marginal buyer to switch, so differentiation is not a by-product of competition but the thing that makes any profit possible at all.

Imperfect information

Also: imperfect information game, unobserved move, hidden move

At least one player has to choose without knowing everything that has already happened.

Imperfect public monitoring

Also: imperfect monitoring, noisy monitoring, public monitoring

Repetition in which players observe only a noisy public signal of what was played rather than the actions themselves, so punishment must be triggered on evidence that is sometimes wrong and the efficient outcomes of the perfect-monitoring folk theorem are no longer attainable.

Imputation

Also: imputations, efficient individually rational payoff vector

A way of dividing the worth of the grand coalition that leaves nothing on the table and gives every player at least what they could get alone.

Incentive compatibility

Also: IC, incentive compatible, truthfulness

The property that every participant does best for themselves by reporting their private information honestly.

Individual rationality

Also: IR, participation constraint, voluntary participation

The requirement that taking part in the mechanism leaves every participant at least as well off as staying out of it.

Infinitely repeated prisoner's dilemma Game

Also: supergame prisoner's dilemma, discounted repeated prisoner's dilemma, grim trigger game

Taking away the last round replaces one prediction with an infinity of them, so the theory stops saying what patient players will do and starts saying only what a patient relationship is capable of holding together.

Information set

Also: information sets, indistinguishable nodes, the dotted line in a game tree

The group of situations a player cannot tell apart from one another when it is their turn to move.

Information unravelling

Also: unravelling, unraveling, information unraveling

Once the best types prove how good they are, staying quiet marks you as worse, so the next best must prove it too, and disclosure spreads all the way down.

Insurance screening Game

Also: Rothschild-Stiglitz insurance, competitive insurance screening, self-selection in insurance

When the uninformed side moves first it cannot buy information, only design a menu, so separation is paid for by handing the good type a deliberately worse deal, and if good types are common enough no menu survives at all.

Intuitive criterion

Also: Cho-Kreps intuitive criterion, the intuitive criterion, Cho-Kreps criterion

An equilibrium is thrown out if a type could credibly explain an unexpected move by pointing out that only a type who stood to gain from it would ever have made it.

Investor coordination game Game

Also: investment coordination game, joint investment game, investor game

A project that is worth doing can fail to happen for no reason beyond each investor expecting the other to stay out, so the bad outcome is a belief rather than a preference.

Iterated deletion of dominated strategies

Also: IDSDS, iterated elimination of strictly dominated strategies, iterated strict dominance

Delete dominated strategies, then delete those dominated in what remains, and repeat.

Keynesian beauty contest Game

Also: Keynes beauty contest, newspaper beauty contest, the beauty contest of Keynes

When the prize goes to whoever matches the average opinion rather than to whoever judges best, the task stops being to work out the answer and becomes to work out what everybody else will think is obvious.

Late bidding

Also: sniping, bid sniping, last-minute bidding

Withholding a bid until the closing seconds of an auction with a hard ending time, so that rivals have no chance to respond and the bidder's own information is never revealed to them.

Level-k reasoning

Also: level-k thinking, k-level reasoning, steps of reasoning

How many rounds of 'they think that I think' a player actually performs, which in practice is one or two.

The linkage principle Result

Also: linkage principle, Milgrom and Weber ranking, revenue ranking under affiliation

When bidders' signals are affiliated rather than independent, the open ascending auction raises more expected revenue than the second-price sealed-bid auction, which in turn raises more than the first-price auction, because a format that links the winner's payment more closely to the information held by rivals leaves the winner less information rent.

Locally envy-free equilibrium

Also: locally envy-free, envy-free equilibrium, symmetric equilibrium

An equilibrium of a position auction in which no advertiser would rather swap into the slot immediately above it and pay that slot's price, which is the prediction the generalised second-price literature uses because truthful bidding is not dominant there.

The market for lemons Game

Also: lemons market, Akerlof lemons, used car market

Hidden quality makes the price itself select who turns up, and because the sellers who accept are always the worse half the market can shut completely despite every trade in it being worthwhile.

Matching pennies Game

Also: matching pennies game, odds and evens, heads or tails game

With pure opposed interests there is nothing to settle on, so the only stable play is to be unpredictable.

Matchmaker game Game

Also: matchmaker game, the matchmaker

Subgame perfection does not always deliver one answer, because when the subgame has several equilibria the first mover's best move depends on which of them he expects to be played.

Maximin

Also: maximin strategy, max-min, security strategy

Pick the strategy whose worst possible outcome for you is the best of all the worst cases, which fixes the payoff you can guarantee yourself whatever anyone else does.

Mechanism design

Also: reverse game theory, implementation theory, mechanism

Designing the rules of a game so that self-interested players, acting on private information, produce the outcome the designer wants.

Median voter game Game

Also: Downsian competition, two-candidate position choice, convergence to the centre

When the two sides choose positions rather than prices, each is dragged to the one voter in the middle, and that single voter settles the result however the rest of the electorate is spread.

Median voter theorem Result

Also: Downsian convergence, the median voter, median voter model

When the options lie on a single line and each voter prefers whatever is nearest to them, two competing candidates are both pulled to the middle voter's position.

Minimax

Also: minimax strategy, min-max, minimax theorem

Pick the strategy that holds the other side's best achievable payoff as low as possible, which in a two-player zero-sum game yields the same number and the same play as maximin.

Mixed strategy

Also: mixed strategy Nash equilibrium, randomised strategy, randomized strategy

Randomising over strategies, which is the only equilibrium available in games of pure conflict.

Moral hazard

Also: hidden action, shirking, hidden effort

Someone takes less care, or more risk, because the cost of it falls on another party who cannot see what they are doing.

Myerson's lemma Result

Also: Myerson lemma, payment identity, envelope characterisation

In a single-dimensional setting a mechanism is truthful exactly when its allocation rule never penalises a higher report, and the payments are then pinned down up to a constant.

Nash bargaining solution

Also: NBS, Nash solution, Nash product

The split of a bargaining surplus picked out by maximising the product of the two parties' gains over what they would get if talks broke down.

Nash demand game Game

Also: demand game, simultaneous demand game, Nash bargaining game

Every division of the surplus is an equilibrium of the game people actually play, so a theory of bargaining must choose among equilibria rather than solve for one.

Nash equilibrium

Also: Nash equilibria, equilibrium point, mutual best response

A profile where every player is already playing a best response to the others.

Nash existence theorem Result

Also: existence of Nash equilibrium, Nash's theorem, Nash existence

Every game with finitely many players and finitely many actions has at least one equilibrium once players are allowed to randomise.

Nim Game

Also: game of Nim, Nim game, take-away game

Some games are decided before anyone moves, because whether a position wins or loses is a fact about the position rather than about how well it is played.

Normal form

Also: strategic form, matrix form, payoff matrix

A game written down as a list of players, the strategies open to each of them, and the payoff for every combination of strategies.

Optimal auction

Also: revenue-maximising auction, Myerson auction, optimal auction design

The selling rule that maximises the seller's expected revenue rather than social value, typically by holding back the object unless bidding passes a reserve.

Pareto efficiency

Also: Pareto optimality, Pareto improvement, Pareto optimal

No alternative makes someone better off without making someone else worse off.

Partnership effort Game

Also: team production, partnership game, joint effort game

When output is shared but effort is not, each partner sets their whole cost of working against only their share of what it produces, so even willing partners under-supply effort and no equal division of a fixed output can repair it.

Payoff

Also: payoff function, payoffs, preferences over outcomes

A number standing for how much a player values an outcome, not the outcome itself.

Payoff dominance

Also: payoff dominant equilibrium, payoff-dominant, Pareto dominant equilibrium

Of several equilibria, the payoff dominant one is the equilibrium every player strictly prefers to the others.

Penalty kick Game

Also: penalty kick game, penalty shootout, goalkeeper and kicker

When your two options differ in strength, equilibrium mixing is not fifty-fifty but is tuned so that the opponent gains nothing by leaning either way.

Perfect Bayesian equilibrium

Also: PBE, perfect Bayesian equilibria, weak perfect Bayesian equilibrium

Strategies and beliefs that fit together, so that beliefs follow from the strategies wherever they can and every player acts optimally from every point they might find themselves at.

Perfect information

Also: games of perfect information, full observability, observable history

Every player sees the whole history of play before choosing, so nobody is ever unsure which situation they are in.

Pirate game Game

Also: pirates and gold, the pirate puzzle, pirate division game

What you must pay someone is set by what they would get if you were gone, not by what they are contributing or by any notion of a share, and working that out from the end tells you the price of each vote exactly.

Pooling equilibrium

Also: pooling, pooling outcome, uninformative equilibrium

Every type ends up behaving the same way, so watching what someone does tells you nothing about which type they are.

Population game

Also: population games, large population game, random matching game

A game played by a large population of randomly matched members, in which a strategy's payoff depends on the current population shares rather than on any named opponent's choice.

Price of anarchy Result

Also: price of anarchy, PoA, cost of anarchy

The ratio of the social cost of the worst Nash equilibrium to the social cost of the optimum is bounded above by a constant that depends on the class of cost functions and not on the size of the game, and for selfish routing with affine latencies that constant is 4/3 however complicated the network.

Principle of minimum differentiation Result

Also: Hotelling's law, Hotellings law, minimum differentiation

Two sellers choosing where to sit on a line of customers each move towards the other until both sit at the centre, so competitors end up more alike than the customers would prefer.

Prisoner's dilemma Game

Also: prisoner's dilemma, prisoners' dilemma, the prisoner's dilemma

Individually rational choices can make everyone worse off, and talking about it does not help.

Proper equilibrium

Also: Myerson proper equilibrium, properness, proper equilibria

A refinement in which players still make mistakes, but a mistake that costs more is made very much less often than one that costs less.

Public goods game Game

Also: voluntary contribution mechanism, VCM, public good game

Keeping your own money beats giving it away by exactly the same margin by which giving it away beats keeping it for the group, so the shortfall is not a failure of understanding and explaining the arithmetic to people does not close it.

Purification Result

Also: Harsanyi purification, purification theorem, purifying mixed strategies

A mixed strategy can be read as the limit of pure choices made by slightly different privately known types, so that nobody actually has to randomise.

Quality disclosure Game

Also: the persuasion game, verifiable disclosure, unravelling game

Saying nothing is itself a statement, and once buyers read silence as the worst possible news everybody with better news than that is forced to speak, so full disclosure arrives with no law requiring it and nothing burnt to achieve it.

Quantal response equilibrium

Also: QRE, noisy best response, logit equilibrium

A fixed point in which every player responds to the others' actual choice frequencies with a logistic rather than an exact best response, so better actions are more likely but not certain and Nash equilibrium is the zero-noise limit.

Race to the bottom

Also: race for the bottom, the Delaware effect, competitive deregulation

When buyers, firms or capital can move to whichever jurisdiction asks least of them, each jurisdiction's best move is to ask less than its rivals, so standards fall below what any of them wanted.

Rationalisability

Also: rationalizability, rationalisable strategies, rationalizable strategies

The strategies left once you keep only those that are a best response to some belief about others who are themselves doing the same.

Reciprocal altruism

Also: reciprocity, direct reciprocity, reciprocal cooperation

Bearing a cost to help another in the expectation of being helped in return, which selection can favour when the same pair meets repeatedly and help can be withheld from those who fail to return it.

Relative-rank dilemma Game

Also: relative rank game, positional competition, rank-order dilemma

A dilemma can be manufactured out of nothing but relative ranking, because when rewards are handed out by position the gain from getting ahead is the same event as somebody else falling behind.

Repeated game

Also: repeated games, supergame, iterated game

The same game played by the same players again and again, so that what someone does today can be answered tomorrow.

Repeated prisoner's dilemma Game

Also: repeated prisoner's dilemma, iterated prisoner's dilemma, infinitely repeated prisoner's dilemma

The same stage game stops being a dilemma once the relationship is likely to continue.

Replicator dynamics

Also: replicator equation, replicator dynamic, selection dynamics

A rule under which the ways of behaving that do better than the population average become more common over time.

Reputation

Also: reputation effects, building a reputation, reputational equilibrium

Being thought likely to behave in a particular way is worth having in itself, because others respond to the belief rather than to the act.

Reserve price

Also: reserve, reservation price, minimum bid

The minimum the seller will accept, below which the object goes unsold, set strictly above the seller's own valuation because a higher reserve extracts more from the bidders who would have won anyway.

Revelation principle Result

Also: revelation principle for mechanisms

Anything achievable by any set of rules at all can also be achieved by rules under which participants just report honestly.

Revenue equivalence Result

Also: revenue equivalence theorem, RET, revenue equivalence principle

Any two auctions that end up giving the object to the same bidder and leave the lowest possible type with the same payoff raise the same expected revenue.

Risk dominance

Also: risk dominant equilibrium, risk-dominant, risk-dominant strategy

Of two equilibria, the risk dominant one is the equilibrium a player would choose if they thought the other side equally likely to do either thing, which in a stag hunt can point to the outcome both players like less.

Rock paper scissors Game

Also: rock paper scissors, roshambo, rock-scissors-paper

Best responses can run in a circle, so no choice is safe and the only stable play is to be equally unpredictable across three options rather than two.

Rubinstein alternating-offer bargaining Game

Also: Rubinstein bargaining, alternating offers bargaining, alternating offer game

Patience is bargaining power, and the entire split is settled before anyone speaks by how much each side loses from one more round of delay.

Screening

Also: self-selection, screening contract, menu of contracts

The uninformed side offers a menu of terms built so that which one you choose gives away what you are.

Second mover advantage

Also: second mover advantage, late mover advantage, follower advantage

Moving second pays when seeing what the other side has done is worth more than tying their hands would have been.

Second-price sealed-bid auction Game

Also: second price auction, second-price auction, Vickrey auction

Paying the runner-up's bid rather than your own severs the link between what you say and what you pay, so bidding your true value is weakly dominant and you need know nothing about your rivals to play it.

Selfish mining

Also: block withholding, selfish mining attack, block withholding attack

Withholding a newly found block and releasing it only to orphan honest work, which earns a coalition more than its share of the hash power and so shows that honest mining is not a Nash equilibrium.

Selten's chain store paradox Game

Also: chain store paradox, chain-store paradox, Selten's chain store paradox

A reputation for fighting cannot be built when the final fight would be pointless, because that pointlessness travels back through every market until it reaches the first.

Separating equilibrium

Also: separation, separating outcome, fully revealing equilibrium

Different types end up behaving differently, so watching what someone does tells you which type they are.

Sequential equilibrium

Also: sequential equilibria, Kreps-Wilson equilibrium, consistent assessment equilibrium

A perfect Bayesian equilibrium whose beliefs off the expected path are additionally required to be the limit of beliefs derived from strategies that tremble.

The shadow of the future

Also: shadow of the future, continuation value, continuation payoff

Cooperation survives only while the relationship is likely enough to continue.

Shapley value

Also: Shapley allocation, Shapley payoff, average marginal contribution

The unique way of dividing the spoils that gives each player their average contribution to the group, taken over every order in which the group could have assembled.

Signalling

Also: signaling, costly signalling, costly signaling

The informed side spends something that a weaker type could not afford to spend, in order to prove which type it is.

Spence education signalling Game

Also: job market signalling, education signalling, the sheepskin game

A signal is believed only because it would cost the liar more than the truth-teller, so the thing that makes it work is waste rather than anything the signal produces.

Stable matching

Also: stability, stable match, no blocking pair

A matching with no blocking pair, meaning no two agents on opposite sides of the market both prefer each other to the partners they were assigned.

Stackelberg competition Game

Also: Stackelberg duopoly, Stackelberg model, quantity leadership

Fixing your output before your rival chooses theirs is worth more than the flexibility you give up, because the move they are now responding to can no longer be changed.

Stag hunt Game

Also: stag hunt game, the stag hunt, Rousseau's stag hunt

When cooperation is not dominated, the obstacle is not greed but doubt about the other.

Strategic ambiguity

Also: deliberate ambiguity, calculated ambiguity, constructive ambiguity

Saying deliberately little about what you would do, so that an opponent cannot plan around your response and an ally cannot take it for granted.

Strategic complements and substitutes

Also: strategic complements, strategic substitutes, strategic complementarity

Choices are complements when one side doing more makes the other want to do more as well, and substitutes when it makes them want to do less.

Strategy versus action

Also: complete contingent plan, contingent plan, plan of action

A strategy is a complete plan saying what a player would do in every situation they could face, while an action is a single move made at one of them.

Strict dominance

Also: strictly dominant strategy, strictly dominated strategy, dominant strategy

One strategy pays more than another against every possible choice by the others.

Subgame perfect equilibrium

Also: subgame perfect equilibrium, SPE, SPNE

A plan that is a Nash equilibrium not only in the game as a whole but in every part of it that could still be reached.

Superadditivity

Also: superadditive game

The property that two groups with no members in common can always do at least as well by merging as by working separately.

Tennis serve direction Game

Also: tennis serve game, serve direction, serve and return game

The two players' equilibrium frequencies need not match each other, because each one is fixed by the other player's payoffs rather than by their own.

Tit-for-tat

Also: tit for tat, TFT, copycat strategy

Start by cooperating and from then on simply repeat whatever the other player did in the previous round.

Top trading cycles

Also: TTC, top trading cycles mechanism, Gale's top trading cycles

The procedure in which every agent points at the holder of its favourite object and each cycle so formed trades, giving the unique core allocation of a housing market and a mechanism that is both Pareto efficient and strategy-proof.

Tragedy of the commons

Also: the commons, commons problem, common-pool resource problem

A resource that everyone may draw on and nobody may exclude others from is used past the point that would suit the users collectively, because each one bears only a share of the damage they do.

Transferable utility

Also: TU, TU game, side payments

The assumption that a group's winnings come in a single divisible good that members can pass between themselves at a one for one rate.

Traveller's dilemma Game

Also: traveller's dilemma, traveler's dilemma, travelers dilemma

An argument that is irresistible one step at a time can walk both players all the way down to an outcome neither would ever have proposed, which is why unravelling arguments predict badly in practice.

Trembling hand perfection

Also: trembling hand perfect equilibrium, trembling-hand perfect equilibrium, perfect equilibrium

An equilibrium counts only if it survives the possibility that every player makes each mistake with some small probability, which rules out plans that rely on a move never being tried.

Trust game Game

Also: investment game, the trust game, trust and reciprocity game

Returning a favour is never in the returner's interest at the moment it falls due, so the value is destroyed one step earlier when nobody extends the favour in the first place.

Type space

Also: player type, type set, private information structure

The list of private situations a player might be in, together with what each of those situations tells them about everyone else.

Ultimatum game Game

Also: ultimatum bargaining, the ultimatum game, take it or leave it offer

Proposing first in a one-shot split lets you keep nearly all of it, and the fact that real responders turn such offers down is the plainest evidence that payoffs are not money.

Uniform-price auction

Also: uniform price auction, single-price auction, market-clearing auction

A multi-unit auction in which every winner pays the same market-clearing price rather than their own bid, which removes the need to guess rivals' bids but invites demand reduction by bidders large enough to move the clearing price.

VCG mechanism

Also: VCG, Vickrey-Clarke-Groves, Vickrey-Clarke-Groves mechanism

A mechanism that picks the outcome maximising total reported value and charges each participant the loss their presence imposes on everyone else.

Volunteer's dilemma Game

Also: volunteer dilemma, volunteers dilemma, bystander game

Only one person needs to bear the cost for everyone to be saved, and that is exactly why the chance that nobody bears it goes up as more people are watching.

War of attrition

Also: attrition contest, waiting game, who blinks first

A contest in which both sides pay for every period they stay in, so the prize goes to whoever is willing to keep paying longest.

War of attrition in continuous time Game

Also: continuous time war of attrition, attrition in continuous time, waiting contest

When the cost of holding out is paid continuously by both sides and only the one who stays wins, any predictable stopping time invites the rival to wait exactly that long, so the contest can only end at a random moment and the prize is eaten entirely by the waiting.

Weak dominance

Also: weakly dominant strategy, weakly dominated strategy, weak dominance

One strategy never pays less than another and sometimes pays more.

Winner's curse

Also: winner's curse, the winner's curse, common value overbidding

Winning a contest for something of uncertain value means you were the most optimistic bidder, which is itself evidence that you bid too much.

Zermelo's theorem Result

Also: Zermelo's theorem, Zermelo theorem, determinacy of finite games

In a finite two-player game of perfect information with no chance, either one player can force a win or both can force at least a draw.

A zero-sum 2x3 game Game

Also: zero sum 2x3, 2x3 zero-sum game, dominance then mixing

Deleting a strategy one side would never use can shrink a game down to a size that mixing can handle, so dominance and mixing are two stages of one method rather than rival ones.

A zero-sum game with a saddle point Game

Also: saddle point, saddle point game, strictly determined game

Pure conflict does not always force you to randomise: when the most each side can guarantee itself is the same number, that number is the value of the game and a pure pair of strategies delivers it.