50 Fun Facts About Game Theory

Which Kubrick film, made with advice from game theorist Thomas Schelling, features a Soviet doomsday machine?

Dr. Strangelove turns on a deterrent nobody was told about. As the title character protests, a doomsday machine only deters an enemy who knows it exists.

Which Best Picture-winning film stars Russell Crowe as game theory pioneer John Nash?

A Beautiful Mind won four Academy Awards. In its best-known scene, classmates debating how to approach a group of women at a bar give Nash his breakthrough idea.

Which game theory model is named after a dare in which two drivers speed head-on until one swerves?

Chicken brands whoever swerves first a coward. The philosopher Bertrand Russell compared the nuclear standoff between East and West to the same deadly dare.

In game theory, how should a rock paper scissors player pick moves so that no opponent can gain an edge?

Uniformly at random, with every throw equally likely, leaves an opponent no pattern to exploit. Against anyone more predictable, a player can gain an edge by spotting patterns in past throws.

In the one-shot prisoner's dilemma, which choice leaves each suspect better off whatever the accomplice decides?

Betraying the partner always shortens your own sentence, so it is the dominant strategy. The catch is that when both suspects reason this way, both end up worse off than if they had kept quiet.

Which pencil-and-paper game is 'solved' in game theory, always ending in a draw when both sides play perfectly?

Tic-tac-toe is simple enough that best play always draws. In the 1983 film WarGames, nuclear war is likened to the game: with the best strategies on all sides, nobody wins.

Which phrase, the title of a Garrett Hardin essay, describes self-interested users ruining a shared resource?

Tragedy of the commons echoes an 1833 pamphlet by William Forster Lloyd, who pictured herders each adding extra cattle to shared grazing land until it was ruined.

In Thomas Schelling's puzzle, where in New York City did most students say they would meet a stranger?

Grand Central Terminal at noon was the most frequent reply. Schelling called such a stand-out choice a focal point: with no way to talk, people coordinate on whatever seems obvious.

Which restaurant habit creates game theory's 'diner's dilemma', tempting every guest to order a pricier dish?

Splitting the bill evenly means friends cover most of whatever extra you order. In a 2004 field experiment, diners sharing the cost consumed more than those paying their own way.

Advertising of which product, banned from US television in 1971, is sometimes cited as a real prisoner's dilemma?

Cigarettes are the classic case: each maker's adverts largely cancelled out its rival's, so both paid heavily just to stand still, and both stood to gain when the spending stopped.

In the ultimatum game, what happens to the money on offer if the responder rejects the proposer's split?

Both players get nothing, so cold logic says accept any offer. Real people disagree: offers of less than 30% are often rejected, at the rejecter's own expense.

John Maynard Smith's model of animal conflict names its aggressive and peaceful strategies after which two birds?

Hawk and dove stand for escalating a fight and backing down. The biologist set the model out with George Price in a 1973 paper titled 'The logic of animal conflict'.

John Maynard Keynes likened stock picking to which newspaper competition, won by guessing what others choose?

A beauty contest, in his telling, asked readers to pick the six prettiest faces from a hundred photographs, with a prize for whoever matched the most popular choices.

Which game theory term describes a game such as chess, where one side's gain is exactly the other's loss?

Zero-sum also describes cutting a cake: a bigger slice for one person leaves exactly that much less for everybody else.

In game theory's public goods problem, which term describes someone who enjoys a benefit without paying for it?

Free rider fits the ships that steer by a lighthouse they never helped to fund, or a crowd watching a fireworks display that somebody else paid for.

Which illness, first apparent in 1959, kept game theory pioneer John Nash from academic work for years?

Schizophrenia put Nash in psychiatric hospitals for several years. After 1970 his condition slowly improved, and he was back at academic work by the mid-1980s.

Studies of which soccer set piece found that players vary their choices much as game theory predicts?

Penalty data fit the theory closely: kickers and keepers mix left and right unpredictably, in proportions that do not deviate significantly from a Nash equilibrium.

Which standoff between Kennedy and Khrushchev is a standard game theory example of nuclear brinkmanship?

The Cuban Missile Crisis was a 13-day confrontation in which each superpower edged toward nuclear war, betting that the other would back down first.

Which philosopher's Discourse on Inequality supplied the hunting story behind game theory's stag hunt?

Jean-Jacques Rousseau pictured hunters who can only bring down a stag together, each tempted to slip away after a hare he could catch alone. It is also called the assurance game.

Which Richard Dawkins bestseller devotes a chapter on aggression to game theory's evolutionarily stable strategy?

The Selfish Gene defines the idea as a strategy that, once most of a population adopts it, cannot be bettered by any alternative, so selection penalises every deviation.

Which Hungarian-born mathematician founded game theory as a discipline, proving his minimax theorem in 1928?

John von Neumann showed that when two players' interests are flatly opposed, the best each can guarantee is equal and opposite, so the game has a definite value.

Which economist, raised in Vienna, co-wrote the founding 1944 text Theory of Games and Economic Behavior?

Oskar Morgenstern was visiting America in 1938 when Hitler took over Vienna, so he chose to stay, and wrote the book there with a mathematician colleague.

At which university did John Nash write the short doctoral thesis that introduced his famous equilibrium?

Princeton took Nash on after his old professor sent a recommendation letter stating 'He is a mathematical genius.' The thesis that made his name ran to fewer than 30 pages.

Which think tank employed Merrill Flood and Melvin Dresher when they devised the prisoner's dilemma in 1950?

RAND Corporation researchers built the puzzle as bare payoffs. The prison story came afterwards, when another mathematician reframed the rewards as jail sentences.

Which strategy, entered by Anatol Rapoport, won both of Robert Axelrod's repeated prisoner's dilemma tournaments?

Tit for tat was the simplest entry both times: cooperate first, then repeat whatever the opponent did on the previous move.

In a Vickrey auction the top sealed offer wins, but which amount does the successful buyer actually pay?

The second-highest bid sets the price, which makes honesty the best policy: bidding exactly what the item is worth to you is the dominant strategy. Stamp collectors used the format from 1893.

Game theory's 'normal form' sets out the players' strategies and payoffs in which kind of layout?

A matrix does the job: one player picks a row, the other a column, and the cell where they meet holds a payoff for each. The rival 'extensive form' is drawn as a graph instead.

In a Nash equilibrium, no player can do better by taking which step while all the others stay put?

Switching strategy alone never helps at such a point, so nobody has a reason to budge. Nash proved in 1950 that every finite game has one once mixed strategies are allowed.

In which poker variant, a classic game of imperfect information, did the AI Libratus beat four top professionals?

Texas hold 'em, in its two-player no-limit form, was the battleground. After 120,000 hands over 20 days in 2017, Libratus was more than $1.7 million in chips ahead of the human team.

Which term, first applied to oil-lease auctions, describes the tendency of the top bidder to have overpaid?

Winner's curse was first analysed in 1971 by three Atlantic Richfield engineers, who noticed oil companies kept winning offshore drilling leases and then earning unexpectedly low returns.

Which British game show ended each episode with 'Split or Steal?', a prisoner's dilemma played for the jackpot?

Golden Balls finalists each secretly chose Split or Steal. Two splitters shared the jackpot, a lone stealer took it all, and two stealers both left with no money.

Which Italian economist gives his name to an outcome where nobody can gain unless somebody else loses out?

Vilfredo Pareto trained as a civil engineer. The prisoner's dilemma unsettles people precisely because its only equilibrium fails his test: both players could do better.

Game theory's stable matching algorithm is used in the United States to pair medical students with what?

Residency programs were being filled this way from 1952, a decade before two mathematicians published the method and showed that a stable set of matches always exists.

Which US agency has sold radio spectrum licences since 1994 in auctions shaped by game theorists?

The FCC used to hand out licences through drawn-out hearings or by lottery. Its auctions, shaped by theorists such as Paul Milgrom, have since raised tens of billions of dollars.

Which French mathematician's 1838 model of two rival spring-water sellers anticipated the Nash equilibrium?

Antoine Cournot pictured two owners of mineral springs each deciding how much water to sell. At his solution, neither can raise profit by changing output alone.

Which result, named after a German mathematician, shows that adding a road to a network can slow traffic down?

Braess's paradox arises because the equilibrium drivers settle into is not the best overall flow. Seoul saw the reverse: traffic sped up after an expressway was torn down.

Which field, nicknamed reverse game theory, starts from a desired outcome and works backwards to the rules?

Mechanism design earned Leonid Hurwicz, Eric Maskin and Roger Myerson the 2007 economics Nobel. Its questions cover how best to set up auctions, wages and other incentives.

Which mathematics award did John Nash collect from Norway's king in 2015, days before he died in a taxi crash?

The Abel Prize honoured Nash's work on partial differential equations, not his game theory. He and his wife were killed on the New Jersey Turnpike on their way home from the airport.

Which nuclear doctrine is a Nash equilibrium in which neither superpower gains by striking first or disarming?

Mutual assured destruction got its acronym from strategist Donald Brennan, who spelled out MAD on purpose to argue that holding such arsenals was irrational.

Nobel laureate Alvin Roth used game theory's matching methods to arrange swaps between donors of which organ?

Kidney exchange helps patients whose willing donors are incompatible with them: two such pairs swap, so each donor gives to the other's patient. Roth co-founded New England's program.

Which Canadian mathematician, John Nash's doctoral adviser, gave the prisoner's dilemma its name and jail-term story?

Albert Tucker took a bare payoff model devised by two colleagues and retold it as suspects weighing prison terms, creating game theory's best-known puzzle.

Which 1994 Nobel laureate devised game theory's 'trembling hand' test, which allows for players' slips?

Reinhard Selten was Germany's first economics Nobel laureate. A keen Esperantist, he met his wife through the Esperanto movement.

Which Israeli-American game theorist, a 2005 Nobel laureate, showed that rational people cannot 'agree to disagree'?

Robert Aumann showed that two rational people who begin with the same prior beliefs cannot knowingly differ in their opinions. His family fled Germany in 1938, two weeks before Kristallnacht.

Which mathematician, namesake of a famous 'value' in game theory, shared the 2012 economics Nobel?

Lloyd Shapley was the son of astronomer Harlow Shapley. As a young serviceman in wartime China, he earned a Bronze Star for breaking the Soviet weather code.

Game theory's El Farol problem, about a bar that is only fun when uncrowded, is named after a venue in which city?

Santa Fe is home to the real El Farol. W. Brian Arthur gave the puzzle its bar-room form in 1994: the night is enjoyable only if fewer than 60% of people decide to turn up.

Which reptile's three male throat-colour types play out an evolutionary game of rock paper scissors?

Side-blotched lizard males have orange, blue or yellow throats. Each type's mating tactics do well against one rival but lose to the other, so no colour ever takes over for good.

Which game theory result says an endlessly repeated game can sustain a huge range of outcomes as equilibria?

Folk theorem got its name because game theorists widely knew the result in the 1950s, even though nobody had published it.

Which two composers name the concert-going version of the 'battle of the sexes' coordination game?

Bach or Stravinsky recasts the 1957 original as a choice between two concerts, for authors who would rather not assign sexes to the players. Either way, coordination is mixed with conflict.

Which German logician gives his name to a game theory theorem that he proved for chess in 1913?

Ernst Zermelo's theorem says that in chess either White can force a win, Black can force a win, or both sides can force at least a draw.

In Martin Shubik's dollar auction, which unusual rule keeps rival bidders raising their offers long past good sense?

The runner-up pays too, yet walks away empty-handed, so whoever is trailing always has a reason to raise the bid again. The economist used it to show short-sighted logic turning irrational.