Games & Strategic Interaction

Two Bayesian agents with a common prior and common knowledge of each other's posteriors cannot agree to disagree.

Aumann proved in 1976 that agents with a common prior whose posteriors are common knowledge must hold equal posteriors, even where their private information differs. Persistent disagreement therefore shows that one of the assumptions fails; it does not by itself say which.

In practice

• Two analysts with the same data and the same model who still disagree have learned that one of the theorem's assumptions does not hold, and not yet which one.
• Two forecasters both saying 30% who cannot converge after comparing notes are not disagreeing about the world but about what counts as evidence.

Attributed to

Robert Aumann

Further reading

Wikipedia

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Given money to divide with no possibility of retaliation, most people still give some away.

Kahneman, Knetsch and Thaler's 1986 design removes every strategic motive: the recipient cannot retaliate or reciprocate. Giving falls sharply when the framing changes, so the effect is real but highly context-sensitive.

In practice

• A team dividing an unexpected budget surplus gives some to the group with no claim on it and no way to reciprocate.
• A departing employee hands over documentation nobody will check, to colleagues who cannot reward them.

Attributed to

Kahneman, Knetsch & Thaler

Standing

Giving falls sharply when anonymity and framing change, so the effect is context-sensitive.

Further reading

Wikipedia

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In indefinitely repeated interaction almost any outcome above the minimum can be sustained as an equilibrium, so theory alone cannot predict which.

Friedman's 1971 result, called folk because it circulated for years before anyone published it. Its consequence is deflating: repeated-game theory explains why cooperation is possible, not why it happens.

In practice

• A long-running supplier relationship could settle at almost any split of the margin, and which split it settled at is history rather than theory.
• Two departments sharing a budget line reach a stable convention that neither could derive from first principles.

Attributed to

James Friedman

Further reading

Wikipedia

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Altruism spreads when relatedness times benefit to the recipient exceeds cost to the actor.

Hamilton's 1964 rule, rB > C. It explains why sterile worker castes exist in bees and why people take larger risks for siblings than for strangers, without requiring anyone to compute anything.

In practice

• An employee covers a sibling's shift at real cost and would not cover a stranger's for the same money.
• A family firm tolerates a level of underperformance from a cousin that no hiring process would have accepted.

Attributed to

W. D. Hamilton

Also called

Kin selection

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Optimising against the rules as implemented rather than the activity the rules were meant to constitute.

The player's version of Goodhart's law. Any competitive system produces a metagame, and design that ignores it treats optimisation as cheating rather than as the predictable response.

In practice

• A chess club whose ratings determine seeding sees players choosing opponents rather than improving.
• A university that ranks on research income finds departments buying grants that produce nothing they wanted.

Attributed to

Game-playing culture

Also called

The meta; rules lawyering

Standing

Goodhart's law as observed by players rather than by economists.

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In any finite two-person zero-sum game there is a strategy pair from which neither side can profitably deviate.

Von Neumann's 1928 proof, which founded game theory. Its guarantee holds only for zero-sum games, and finding a value at all required allowing mixed strategies.

In practice

• A goalkeeper who always dives right is beaten; the strategy is to be genuinely unpredictable.
• A negotiator with a predictable concession pattern is read after two rounds, and randomising the pace is worth more than any argument.

Attributed to

John von Neumann

Further reading

Wikipedia

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A split is the unique fair settlement if it is efficient, symmetric, and unchanged by irrelevant alternatives or rescaling.

Nash's 1950 solution, and its axioms are the contested part — independence of irrelevant alternatives in particular. Kalai and Smorodinsky's alternative drops it and yields a different split.

In practice

• Two departments splitting a shared saving find a settlement that is efficient, symmetric, and independent of the third proposal nobody wanted.
• A divorce settlement that would change if an irrelevant third option were introduced has failed one of the axioms, which is usually where mediation stalls.

Attributed to

John Nash

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Outcomes stabilize when no actor can benefit by unilateral change.

Nash's 1950 result, and the reason it matters is existence: every finite game has one in mixed strategies, so there is always something to solve for. Whether it is good for anyone is a separate question.

In practice

• Two firms in a price standoff both hold, because either moving alone is worse for the mover.
• A team's meeting culture is stable because no individual can shorten meetings unilaterally without appearing disengaged.

Attributed to

John Nash

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A small additional demand made after agreement is usually conceded, because the other side will not reopen a settled deal.

Karrass's term. The defence is procedural rather than rhetorical: agree in advance that nothing is settled until everything is, which removes the settled-deal leverage the nibble depends on.

In practice

• A supplier who agrees terms and then asks for the delivery charge to be added usually gets it.
• A candidate who accepts an offer and then asks for an extra week's holiday is rarely refused, because the offer is settled.

Attributed to

Chester Karrass

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Voluntary contribution collapses over repeated rounds unless participants can punish free riders, at which point it stabilises.

Fehr and Gächter's 2000 experiments. Contributions collapse over ten rounds without punishment and stabilise high with it, even though punishing costs the punisher. It is the experimental case for costly enforcement.

In practice

• A street where somebody will knock on the door about the bins keeps its pavements clear, and the knocking costs the knocker.
• A shared workspace where anyone may challenge a mess stays clean; one where challenge is discouraged does not, and the cleaning rota is not the difference.

Attributed to

Fehr & Gächter

Standing

The experimental case for costly enforcement in commons governance.

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Under standard conditions, very different auction formats yield the same expected revenue, so format matters only where those conditions fail.

Vickrey's 1961 result, generalised by Myerson and independently by Riley and Samuelson in 1981. It is why auction design focuses on conditions rather than format: risk aversion, correlated values or collusion each break the equivalence and change which format is better.

In practice

• A charity that switches from a silent auction to an open one raises about the same, and is surprised.
• A procurement that runs a sealed bid and one that runs an open auction get the same price only where the bidders are symmetric and independent, which they rarely are.

Attributed to

Vickrey; generalised by Myerson and Riley–Samuelson

Further reading

Wikipedia

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A canonical axiomatic division of a joint surplus, giving each member their average marginal contribution across all orders of joining.

Shapley's 1953 value assigns each player their average marginal contribution across all orders of coalition formation, and is the unique rule satisfying efficiency, symmetry, the null-player property and additivity.

In practice

• Attributing revenue to marketing channels, and features to model predictions, both use it as the allocation satisfying those axioms.
• A three-person team splitting a bonus by average marginal contribution across every order of joining is doing arithmetic rather than negotiation.

Attributed to

Lloyd Shapley

Further reading

Wikipedia

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People pay costs to punish norm violations that did not harm them, which sustains cooperation that direct reciprocity cannot reach.

Fehr and Fischbacher's 2004 experiments gave observers the option to spend their own money reducing the payoff of someone who had treated a third party unfairly. A substantial share did. The finding matters because reciprocity between the parties involved cannot explain cooperation among strangers, and disinterested punishment can.

In practice

• A colleague who reports a rule breach that cost him nothing and may cost him standing is the mechanism the policy depends on.
• A stranger who challenges queue-jumping gains nothing from the queue and sustains it for everyone behind.

Attributed to

Ernst Fehr & Urs Fischbacher

Also called

Altruistic punishment; disinterested sanctioning

Further reading

Wikipedia

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One party sends resources hoping for voluntary return; the amount sent measures trust and the amount returned measures trustworthiness.

Berg, Dickhaut and McCabe's 1995 design. Senders typically send about half and receivers return slightly more than was sent, which is enough to make trust profitable and not enough to make it safe.

In practice

• A supplier ships before payment on a new account, is paid slightly early in return, and neither party could have written that into the contract.
• A landlord returns a deposit in full without an inspection, and the tenant recommends the flat to two colleagues.

Attributed to

Berg, Dickhaut & McCabe

Also called

Investment game

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Offered a split by another party, people reject unfair offers even at cost to themselves, so fairness norms constrain bargaining.

Güth's 1982 design. Offers below about 20% are routinely rejected, which is money refused to punish unfairness — the most replicated evidence that people are not narrowly self-interested.

In practice

• A contractor offered 5% of a joint windfall walks away from the money rather than accept the split.
• A team told their bonus pool is a tenth of the department's next door declines the pool, and the money goes back unclaimed.

Attributed to

Güth, Schmittberger & Schwarze

Possible explanations

Explanations include fairness norms, in which an unfair offer is worth paying to punish; anger as a proximate mechanism; and reputation, since in repeated life refusing signals that one cannot be exploited.

In its favour

It is among the most replicated results in experimental economics, holding across many countries and stake sizes, and it is the clearest evidence that people are not narrowly self-interested.

Against it

Offers and rejections vary considerably across cultures, and behaviour in a laboratory with a stranger and one round may not transfer to the repeated bargaining people mostly do.

Standing

The most replicated evidence that people are not narrowly self-interested.

Further reading

Wikipedia

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In a sealed-bid auction where the winner pays the second-highest bid, bidding your true value is optimal.

Vickrey's 1961 result, and eBay's proxy bidding is the everyday implementation. Truthful bidding is optimal because your bid determines whether you win and not what you pay.

In practice

• A bidder who would pay £400 enters £400, wins at £310, and gains nothing from having guessed what the others would do.
• A council procuring by sealed bid and paying the second price stops receiving the strategic underbids that used to decide its contracts.

Attributed to

William Vickrey

Also called

Second-price sealed-bid auction

Further reading

Wikipedia

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In common-value auctions the winner is the bidder who most overestimated the prize.

Capen, Clapp and Campbell's 1971 finding from offshore oil leases. The winner is whoever most overestimated the reserves, which is why disciplined bidders lose most auctions and profit on the ones they win.

In practice

• Nine firms value a licence between £8m and £22m, the £22m bid wins, and the asset turns out to be worth about £12m.
• A hiring panel that beat four rivals to a candidate at 30% above band discovers what the four rivals had priced in.

Attributed to

Capen, Clapp & Campbell

Further reading

Wikipedia

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Treating a divisible-surplus situation as fixed-pie produces conflict that the underlying structure does not require.

Von Neumann and Morgenstern's framing, and the negotiation consequence is direct: parties who assume a fixed pie stop searching for trades, so the surplus that would have existed never gets found.

In practice

• A buyer and a seller who each assume price is the only variable never find that one needs delivery in March and the other has spare capacity in February.
• Two departments arguing over a budget line never discover that one values timing and the other values total, which is a trade both would take.

Attributed to

von Neumann & Morgenstern

Also called

Fixed-pie bias

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Two parties want to coordinate more than they want their preferred option, so any convention beats none.

Luce and Raiffa's 1957 example was a couple choosing between two evenings out. Driving conventions are the pure institutional case: which side is arbitrary, agreeing is everything.

In practice

• Two departments each prefer a different project management tool and both prefer either tool to the current state, where half use each.
• Two teams argue about the naming convention for six weeks; the convention chosen matters far less than the six weeks.

Attributed to

Luce & Raiffa

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Open with your final terms and refuse to move; efficient when credible, and corrosive of the relationship when not.

Named for Lemuel Boulware of General Electric, who used it against unions in the 1950s. GE's broader Boulware system was held inconsistent with the duty to bargain in good faith under US labour law; a firm final offer is not by itself unlawful in ordinary private negotiation.

In practice

• A landlord issues a final offer, means it, and lets the flat in a week; the same tactic from a landlord who always blinks costs three months.
• A supplier who says "this is our price" and holds keeps the contract and loses the relationship, and finds out which mattered at renewal.

Attributed to

Named for Lemuel Boulware

Also called

Take it or leave it

Further reading

Wikipedia

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Creating risk can force concessions despite mutual harm.

Schelling's insight is that a threat too terrible to carry out can still work if you can credibly hand over partial control to chance. Deliberately going to the edge is the strategy; the risk is the instrument.

In practice

• A negotiator schedules the deadline for the day before a shareholder meeting, so that neither side fully controls whether talks collapse.
• A union announces a strike date it cannot easily cancel, which is what makes the threat worth answering.

Attributed to

Thomas Schelling

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Costless statements can still coordinate behaviour when interests partly align, but cannot convey information when they conflict.

Crawford and Sobel showed in 1982 that when interests align, mere assertion coordinates; when they conflict, only costly signals carry information. It explains why "we're committed to quality" conveys nothing.

In practice

• Two teams whose bonuses depend on the same launch date can coordinate by saying "we'll be ready Thursday" and be believed.
• A supplier saying "we're confident about capacity" during a price negotiation conveys nothing, because they would say it either way.

Attributed to

Crawford & Sobel

Standing

The formal counterpart to costly signalling.

Further reading

Wikipedia

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Both sides prefer conceding to mutual disaster, so the advantage goes to whoever can credibly refuse to concede.

Maynard Smith and Price's 1973 model. In the Cuban Missile Crisis both sides understood that whoever could appear less able to back down held the advantage — which is why visibly limiting your own options can be a move.

In practice

• Two departments both refuse to move their deadline, each believing the other will blink, and the release slips for everyone.
• Two cars meet on a single-track lane and the one who has visibly folded their mirror in has already won the negotiation.

Attributed to

Maynard Smith & Price

Also called

Hawk-dove game; snowdrift game

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When fixed resources must be split across several contests won by local superiority, the weaker side wins by concentrating and randomising.

Borel's 1921 problem. It is why insurgents concentrate against isolated posts and why underdog electoral campaigns target a handful of districts rather than campaigning everywhere.

In practice

• A challenger party stands candidates in eleven marginal seats and ignores the other six hundred.
• A small brand buys every advertising slot in one city rather than a thin national campaign, and takes the city.

Attributed to

Émile Borel

Standing

Used to model electoral targeting, advertising, and military allocation.

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A fact is common knowledge only when all know it, all know that all know it, and so on without limit; coordination often turns on this rather than on the fact.

Everyone in a room may know the emperor is naked; the shout makes it common knowledge, and only then does behaviour change. Preference falsification and sudden regime collapse turn on exactly this distinction.

In practice

• Every manager privately knows the reorganisation is going badly, and nothing changes until someone says so in a meeting with all of them present.
• A queue forms because each person can see the others waiting; if they could not see each other, no queue would form.

Attributed to

David Lewis

Possible explanations

The explanation is coordination: acting together requires not only that each person knows the fact but that each can rely on the others knowing it. A public event creates that in one step, where private knowledge cannot.

In its favour

It is formalised in game theory and it explains what private belief cannot: why a shout, a broadcast or a crowd in a square changes behaviour that everyone's silent knowledge did not.

Against it

The infinite hierarchy is an idealisation that no one can verify from inside, and experiments find people coordinating on rough approximations of it, so the condition is more useful as an analysis than as a measurement.

Standing

Distinguished from mutual knowledge, which is weaker and often insufficient.

Further reading

Wikipedia

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Where players gain from matching and lose from mismatching, the problem is not conflict but selecting among equally good conventions.

The choice of railway gauge, keyboard layout or date format matters only in that everyone makes the same choice. Schelling's focal points are the mechanism by which one is selected without negotiation.

In practice

• Whether meetings start on the hour or five past matters far less than whether everyone uses the same rule.
• Two teams agreeing to write dates one way, either way, saves more than a year of argument about which way is better.

Attributed to

Thomas Schelling

Further reading

Wikipedia

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Credible commitments and focal points shape strategic outcomes.

Cortés scuttling his ships is the archetype: removing your own option to retreat is what makes the commitment believable. Legislated deadlines and escrow arrangements do the same work institutionally.

In practice

• A supplier signs a contract with a penalty clause they cannot escape, and the buyer believes the delivery date for the first time.
• A government legislates a deficit rule that binds its own successor, which is the point.

Attributed to

Thomas Schelling

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When the bill is split evenly, each person orders more expensively than they would alone, so everyone ends up worse off.

Glance and Huberman's 1994 model. Each diner rationally orders the more expensive dish since they bear only a fraction of its cost, and all end up paying more for a meal none of them chose.

In practice

• Six colleagues at a team dinner order the wine list's middle range rather than the house wine, and everyone pays more than they wanted.
• A shared departmental budget produces requests nobody would make from their own.

Attributed to

Glance & Huberman

Also called

Unscrupulous diner's dilemma

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When everyone forecasts the same congestion from the same information, the forecast defeats itself and no shared rule can be right.

Arthur's 1994 problem, modelled on a Santa Fe bar with live music. If everyone predicts it will be crowded, nobody goes and it is empty; the absence of a stable rule is the result, not a failure of the modelling.

In practice

• Every team schedules its deploy for the quiet Tuesday window, and Tuesday becomes the busiest deploy day.
• Everyone leaves for the beach on the bank holiday Monday because Sunday will be busy, and Monday is worse.

Attributed to

W. Brian Arthur

Further reading

Wikipedia

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In a repeated game where mistakes happen, a strategy that sometimes forgives a defection does better than strict retaliation, which locks players into mutual punishment.

Axelrod's tournaments made tit-for-tat famous, but they assumed that no one ever made an error. Nowak and Sigmund's 1992 paper in Nature, on heterogeneous populations and with random variation built in, found that tit-for-tat players are needed mainly to pave the way for a more generous strategy. In the generous version a player answers some defections with cooperation, around one in three for the standard payoffs. A single error between two strict reciprocators sets off an echo of retaliation in which each punishes the other's last move, and generosity ends it. Nowak and Sigmund's 1993 paper described win-stay, lose-shift, which beat tit-for-tat in noisy contests, and Wu and Axelrod's 1995 study of noise found that both contrition and generosity helped.

In practice

• Two colleagues each read a missed message as a snub and reply in kind, and the small insults escalate until one of them absorbs the next.
• A forum moderator who restores a member's access after a first offence may end more feuds than a rule of permanent bans would.

Attributed to

Martin Nowak & Karl Sigmund

Also called

GTFT; forgiving tit-for-tat

Possible explanations

In a noisy world a kind move can be misread as a defection, and a cooperator can slip. Strict reciprocity treats each such error as a real defection and returns it, and the partner returns that in turn. Occasional forgiveness breaks the chain at small cost.

In its favour

Fudenberg, Rand and Dreber's 2012 experiments with noisy repeated prisoner's dilemmas found that strategies and subjects that were slower to retaliate and quicker to forgive earned more.

Against it

Generosity can be exploited, since against a player who defects every time a forgiving strategy loses a little in each round. The results come from simulations and games with fixed payoffs and symmetric moves, whereas real offences differ in size and often cannot be undone. Nowak and Sigmund's own later work found win-stay, lose-shift outperformed generous tit-for-tat in some settings.

Standing

Extends Tit-for-Tat. Compare Strong Reciprocity and the Incivility Spiral. The online counterpart is Rule 5 of the Rules of the Internet.

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A strategy of permanent retaliation after a single defection sustains cooperation, at the cost of being unable to forgive error.

Effective at sustaining cooperation and brittle in practice, because it cannot distinguish defection from error. Tit-for-tat outperforms it precisely by forgiving.

In practice

• A supplier dropped permanently after one late delivery loses a decade of good service to one bad week.
• A friendship ended over one unreturned favour cannot recover, and tit-for-tat would have.

Attributed to

Repeated-games literature

Further reading

Wikipedia

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Once a party has invested in a relationship-specific asset, the other can renegotiate, so the investment is never made.

Klein, Crawford and Alchian's case was Fisher Body and General Motors: dies built for one buyer's cars have no other use, so the buyer can renegotiate afterwards. GM eventually bought the supplier outright, which is the standard remedy.

In practice

• A supplier who retools a factory for one customer's specification discovers the price is renegotiated once the tooling is installed.
• A contractor who buys equipment for a single client's site finds the day rate revised at the first renewal.

Attributed to

Klein, Crawford & Alchian

Further reading

Wikipedia

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Where value depends on what others will value, rational players stop reasoning about the thing and reason about each other's reasoning.

Keynes's 1936 image of picking not the prettiest face but the face others will pick — and then the face others expect others to pick. It is the standard account of bubbles and of fashion.

In practice

• A recruiter hires the candidate they believe the panel will approve, and the panel selects the candidate they believe the board expects.
• A fund buys a stock because it expects others to buy it, and the company's earnings enter nobody's reasoning.

Attributed to

John Maynard Keynes

Also called

Higher-order beliefs; guess two-thirds of the average

Standing

Explains asset bubbles, fashion, and hiring for prestige.

Further reading

Wikipedia

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In aimed-fire conflict, effective strength grows with the square of numbers, so concentration beats equal division.

Lanchester's 1916 square law. Two forces of 3 and 5 do not fight to a remainder of 2 — the larger wins with about 4 surviving, which is why splitting forces is usually fatal and why Nelson broke the line at Trafalgar.

In practice

• A challenger with a third of the marketing budget wins one city and cedes the rest, and beats a rival who spent evenly everywhere.
• A charity concentrating on two constituencies changes two votes; spread across forty it changes none.

Attributed to

Frederick Lanchester

Also called

Lanchester's square law

Further reading

Wikipedia

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Where one side's gain is exactly the other's loss, the only stable play is to be deliberately unpredictable.

Von Neumann's 1944 example. It is the cleanest case for randomisation: any detectable pattern is exploitable, so the optimal strategy is to be genuinely unpredictable rather than clever.

In practice

• A goalkeeper who always dives right is beaten; one who dives randomly is not, and the randomness is the strategy.
• A tax authority that audits on a predictable rule is gamed; one that audits partly at random is not.

Attributed to

von Neumann & Morgenstern

Also called

Zero-sum game with mixed strategy

Further reading

Wikipedia

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Work backwards from the outcome you want to the rules under which self-interested participants will produce it.

Hurwicz's field, sometimes called reverse game theory. Spectrum auctions, kidney exchange and school-matching systems are all built this way, and all three won Nobel prizes.

In practice

• A spectrum auction is designed so that truthful bidding is the bidder's best strategy, and the revenue follows from the design.
• A kidney exchange is built so that hospitals gain by entering their hardest cases rather than withholding them.

Attributed to

Leonid Hurwicz

Also called

Reverse game theory

Further reading

Wikipedia

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Competing actors are each forced to abandon a shared value to avoid being outcompeted, so all end up worse off with no one defecting.

Alexander's 2014 essay names it Moloch. Arms races, agricultural runoff and platform engagement optimisation are the same structure: each actor's defection is individually forced and collectively ruinous.

In practice

• Each publisher shortens its articles to hold attention, no publisher wants shorter articles, and none can lengthen alone.
• Each firm in a sector extends its working hours to compete, none wanted to, and the first to stop loses.

Attributed to

Scott Alexander, after Ginsberg

Also called

Moloch; race to the bottom

Standing

The generalised form of the arms race, the commons tragedy, and the regulatory race to the bottom.

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Individual rationality leads to collectively suboptimal outcomes.

Flood and Dresher's 1950 game, named by Tucker. The uncomfortable part is that defection is individually correct: both players reasoning perfectly reach the outcome both prefer least.

In practice

• Two firms in a price war both cut, both lose margin, and neither can stop alone.
• Two neighbours who could each save by sharing a skip both hire one, because neither will move first.

Attributed to

Flood & Dresher, named by Albert Tucker

Further reading

Wikipedia

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The neighbouring state is the natural enemy and the state beyond it the natural ally, so alignment follows position rather than affinity.

Book VII places the aspiring conqueror at the centre of concentric rings: the immediate neighbour is the enemy, the neighbour's neighbour the friend, with indifferent and neutral kings beyond. It is a positional theory of alliance, worked out independently of and long before the European balance of power, and with a sharper rule.

In practice

• Two firms competing for the same customers ally against a third that supplies them both.
• Two departments that share a budget line argue more than either does with the department upstairs.

Attributed to

Arthashastra, attributed to Kautilya

Also called

Mandala theory; the circle of states

Possible explanations

The explanation is geography and interest: neighbours compete over the same borders, resources and buffer states, while a state beyond the neighbour shares an interest in constraining it.

In its favour

Shared borders do raise the frequency of disputes in conflict datasets, and encirclement alliances are a recurring pattern in diplomatic history.

Against it

It describes rather than predicts, since alliances also follow ideology, trade and alliance systems, and long friendly borders are common. The text's date and authorship are disputed.

Standing

The Arthashastra's date and authorship are disputed. The framework describes a pattern rather than predicting it: shared borders raise the frequency of disputes without making enmity necessary.

Further reading

Wikipedia

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People coordinate by gravitating to salient solutions without communication.

Schelling asked students where they would meet a stranger in New York with no way to communicate; most said Grand Central information booth at noon. Nothing makes it correct except that others will think so too.

In practice

• Two colleagues separated in an unfamiliar airport both make for the departures board, having agreed nothing beforehand.
• A team with no agreed process defaults to the meeting everyone can see in the calendar, and the calendar became the coordination device.

Attributed to

Thomas Schelling

Also called

Focal point

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Advantage comes from the configuration of a situation rather than from force applied within it.

Sun Tzu compares shi to a round boulder on a steep slope: the energy is in the position, and the push that releases it is trivial. The practical instruction is to spend effort arranging circumstances rather than on the confrontation, because by the time the confrontation arrives its outcome is mostly set.

In practice

• A negotiator who has secured a second supplier before the meeting does not need to argue in it.
• A team that fixes its release process spends no heroism on release night.

Attributed to

Sun Tzu

Also called

Shi; strategic configuration; propensity

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Two hunters do better cooperating on large game, but each is safer defecting to small game, so trust rather than interest is the binding problem.

Rousseau's 1755 illustration. It is the core model of situations where everyone prefers cooperation and nobody dares go first, which makes it about assurance rather than about conflicting interests.

In practice

• Two neighbours would each rather share the cost of a fence than build their own, and each waits for the other to raise it.
• Two firms that would both gain from a shared standard each build their own, because being the only one who cooperated is the worst outcome.

Attributed to

Rousseau; formalised by game theory

Also called

Assurance game

Standing

The core model of situations where everyone prefers cooperation but nobody dares go first.

Further reading

Wikipedia

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A large irreversible investment can deter entry or force accommodation precisely because it cannot be undone, converting a threat into a fact.

Capacity built ahead of demand signals that the incumbent will fight rather than retreat, because retreating no longer saves anything. The commitment works by removing the incumbent's own option to be reasonable, which is why flexibility is a liability in this setting and why the investment must be visible to do its work.

In practice

• A firm that builds a plant at twice current demand has told entrants what a price war would look like.
• A publisher that signs a five-year exclusive has removed its own ability to be outbid, and is paid for it.

Attributed to

Thomas Schelling; developed in industrial organisation

Also called

Irreversible commitment as deterrence

Standing

Compare credible commitment, which is the same logic in bargaining rather than in market structure.

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Many people cooperate conditionally and punish defectors at their own expense, even with no prospect of future benefit.

The claim goes beyond self-interest with a long shadow of the future: strong reciprocators act the same way in one-shot anonymous settings where reputation cannot pay. Gintis and collaborators argued this is a stable human type rather than an error, and the counter-argument is that a subject in a laboratory has no way to switch off habits built for repeated life.

In practice

• A departing employee spends her last week documenting handovers she will never benefit from.
• A customer who will not return still leaves the review that warns the next one.

Attributed to

Herbert Gintis and colleagues

Also called

Conditional cooperation with costly punishment

Possible explanations

The explanation is a disposition to cooperate conditionally and to punish defection at personal cost, which would have been favoured where groups with such members outcompeted groups without them.

In its favour

The laboratory results are robust and repeated across societies, with punishment of defectors occurring in one-shot anonymous settings where reputation cannot pay.

Against it

Critics argue the results reflect everyday heuristics misapplied to an artificial setting rather than a distinct disposition, and that framing and experimenter presence account for much of the punishment observed.

Standing

Contested. Critics argue the laboratory results reflect misapplied everyday heuristics or experimental framing rather than a distinct disposition, and that the field evidence is thinner than the lab evidence.

Further reading

Wikipedia

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An equilibrium is credible only if the threats it relies on would actually be carried out at every point they might be needed.

Selten's 1965 refinement of Nash. It rules out equilibria sustained by threats the threatener would never carry out, which is why commitment devices matter — they make the incredible credible.

In practice

• A publisher threatening to pull a book a fortnight from print is not believed, because the printing is already paid for.
• A landlord threatening eviction over a week's arrears is not credible, and both sides know the threat costs more to execute than to abandon.

Attributed to

Reinhard Selten

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In repeated interaction a strategy that cooperates first, then mirrors the other side, performs robustly against sophisticated rivals.

Axelrod's 1980 tournaments. Tit-for-tat won twice against far more sophisticated entries, and its properties are nice, retaliatory, forgiving and clear — the forgiveness is what beats grim trigger.

In practice

• A supplier late once is warned once, delivers on time thereafter, and the relationship survives what a permanent penalty would have ended.
• Two departments that alternate covering each other's shortfalls keep it up for years, and the first to stop is copied within a month.

Attributed to

Robert Axelrod

Also called

Reciprocal altruism

Further reading

Wikipedia

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Someone must volunteer for the group's benefit, but individuals prefer others volunteer.

Diekmann's 1985 game. If everyone reasons the same way, nobody volunteers and all lose — which is why designating a specific person outperforms appealing to a group.

In practice

• An alarm sounds in an open-plan office and forty people look up; the one asked by name goes and checks.
• A committee asks for a volunteer to take the minutes and gets silence, then asks a specific member and gets minutes.

Attributed to

Andreas Diekmann

Further reading

Wikipedia

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Both sides burn resources until one quits, so the winner is whoever values the prize most or can bear loss longest.

Maynard Smith's 1974 model. The winner is not the stronger but the one who values the prize most or can bear loss longest, which is why patent litigation and strikes are decided by balance sheets.

In practice

• A small firm with a good patent settles for a tenth of its value because it cannot fund three more years of discovery.
• Two supermarkets on the same road hold a price war until one parent company loses patience, and the survivor raises prices within a month.

Attributed to

John Maynard Smith

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Agreement is possible only in the range between the two sides' reservation points, and most negotiation is discovering whether that range exists.

Fisher and Ury's term. Most negotiation is discovering whether the range exists at all, which is why early questions about constraints are more productive than early offers.

In practice

• A buyer who will pay up to £80,000 and a seller who will take nothing under £95,000 spend three meetings discovering there was never a deal.
• A candidate who asks about the band on the first call saves both sides four rounds of interviews.

Attributed to

Fisher & Ury

Also called

Zone of possible agreement; bargaining range

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Solve a sequential game by reasoning from the last move to the first, since only credible future actions constrain present ones.

Zermelo formalised it for chess in 1913. In negotiation it means working out what the other side will do in the last round, since only that constrains what they will accept now.

In practice

• A tenant deciding whether to accept a rent rise works out what the landlord will do in August with an empty flat, and only then answers the March letter.
• A team plans a launch by fixing the date customers must be able to buy, then working backwards to when the pricing page must be signed off.

Attributed to

Ernst Zermelo

Further reading

Wikipedia

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Bargaining power comes from the quality of your best alternative to agreement, not from your need or your rhetoric.

Fisher and Ury's central point in Getting to Yes, 1981: improve your alternative before you improve your arguments. A party with no alternative is negotiating terms, not price.

In practice

• A supplier holds firm not because their pitch is good but because they have three other buyers; the negotiation was decided before either side spoke.
• A tenant who has found somewhere else to live negotiates a rent increase very differently from one who has not looked.

Attributed to

Fisher & Ury

Also called

Best alternative to a negotiated agreement

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Seeking arrangements that benefit both parties is claimed to be more effective than competing, because most situations are not fixed-sum.

Covey's principle depends entirely on a prior judgement about the situation, which the principle itself does not help make. Distributive bargaining over a fixed sum exists, and a negotiator who assumes otherwise concedes. The useful discipline is checking whether the pie is fixed before assuming it is not.

In practice

• Two parties who discover complementary priorities trade them and both do better than splitting the difference.
• A buyer committed to win-win facing a seller committed to winning gets the outcome that predicts.

Attributed to

Stephen Covey

Also called

Think win-win

Possible explanations

The explanation is that most negotiations contain differences in what each side values, so trades exist that leave both better off, and searching for them beats dividing a fixed sum.

In its favour

Integrative bargaining is well supported in negotiation research, where parties who exchange information about priorities reach better joint outcomes than those who only concede.

Against it

It depends on a prior judgement about the situation that the principle itself does not help make, and prescribed universally it disarms the party that adopts it against one that does not, since distributive bargaining over a fixed sum is real.

Standing

Sound where the situation is genuinely positive-sum and misleading where it is not. Prescribed universally, it disarms the party that adopts it against one that has not. Compare zero-sum versus positive-sum framing.

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Backward induction says defect immediately, yet real players cooperate for many rounds, so the logic and the behaviour diverge.

Rosenthal's 1981 game. Rational play says take the money immediately; experimental subjects cooperate for many rounds and do better. It is the standard evidence that backward induction fails as a description of behaviour.

In practice

• Two firms in a renewable annual contract could each squeeze the other at any renewal and neither does, for eleven years.
• A landlord and tenant both know the tenancy will end eventually, and neither behaves as though the last month is the only one that counts.

Attributed to

Robert Rosenthal

Further reading

Wikipedia

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Deliberately destroying your own line of retreat to make commitment credible to the other side.

Caesar crossed in 49 BC knowing it made war unavoidable. The move is valuable precisely because it removes the option, which is what makes the commitment credible to the other side.

In practice

• A company announces the office closure date publicly, which is what stops the six-month internal argument about whether to close it.
• A negotiator books the return flight and tells the other side, converting a preference into a deadline.

Attributed to

Julius Caesar

Also called

Burning the boats

Standing

The historical instance of Schelling's credible commitment.

Further reading

Wikipedia

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Displayed weakness read as concealed strength, so an undefended position deters an attack it could not survive.

In the novel, Zhuge Liang faces a large army with an empty city, opens the gates and sits playing the lute on the wall. The opposing commander, who knows him as cautious, reads the display as a trap and withdraws. The strategy works only against someone who credits you with more prudence than you are showing.

In practice

• A startup publishes its roadmap in full, and a larger rival reads the openness as evidence of something held back.
• A negotiator who lets the other side see an empty diary is believed to have a better offer elsewhere, until they check.

Attributed to

Attributed to Zhuge Liang; from the Romance of the Three Kingdoms

Also called

The empty fort strategy

Possible explanations

The explanation is inference from reputation: an opponent who believes you are cautious reads an undefended position as evidence of a trap, so the display works only against someone who knows you.

In its favour

The logic is sound as a signalling problem, and the episode is among the most studied illustrations of deception in Chinese strategic writing.

Against it

The episode comes from a fourteenth-century novel rather than a chronicle, so the case may not have happened, and the stratagem fails badly against an opponent who simply attacks.

Standing

The episode comes from a novel rather than a chronicle; whether Zhuge Liang did any such thing is not established.

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Two games that each lose in the long run can be alternated to produce a winning sequence.

Parrondo demonstrated it in 1996 with a pair of simple gambling games whose rules depend on the player's current capital. Switching between them, at random or in a fixed pattern, keeps the capital in states where the second game is favourable, which neither game can do alone. It is not a way to beat a casino: the games have to be coupled through a shared state, and ordinary bets are not.

In practice

• A gambler told that two losing games make a winning one reads the rules and finds that the trick is the shared bankroll rather than the games.
• A manager alternates two unpopular policies and gets a result neither produces alone, because the second works only on the state the first leaves behind.

Attributed to

Juan Parrondo

Standing

Often quoted loosely as proof that two bad strategies can make a good one. Without the coupling, losing games stay losing. Compare Simpson's paradox, whose arithmetic it resembles.

Further reading

Wikipedia

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A win whose cost exceeds its value, which the winner's own framing makes hard to recognise.

Named for Pyrrhus, who beat the Romans at Asculum in 279 BC and reportedly said another such victory would undo him. The winner's own framing is what makes the cost hard to see.

In practice

• A litigant awarded £12,000 after three years has spent £40,000 getting there, and the judgment is reported as a win.
• A firm that wins a contract by underbidding staffs it at a loss for four years, and the win was reported as a win throughout.

Attributed to

Named for Pyrrhus of Epirus

Further reading

Wikipedia

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A catalogue of deception patterns, several of which have no single name in Western strategic writing.

The collection names manoeuvres compactly enough to be recognised in the field: besiege Wei to rescue Zhao, for striking the undefended thing your opponent must protect; borrow a corpse to return the soul, for reviving a dead institution under a new purpose. Naming a pattern is what lets it be spotted quickly.

In practice

• A competitor attacks the market that funds your main product rather than the product itself.
• A dormant charity is revived by a group who wanted its registration and none of its purpose.

Attributed to

Chinese military compilation

Also called

The Thirty-Six Stratagems

Possible explanations

The explanation for its usefulness is naming: a manoeuvre with a short name can be recognised, taught and discussed, which is the same reason military doctrine names formations.

In its favour

Several of the stratagems have no compact name in Western strategic writing, and the collection remains in active use in Chinese business and military education.

Against it

It is a catalogue rather than a theory, with no account of when each stratagem works, and its compilation date and authorship are unsettled.

Standing

Compilation date and authorship are unsettled; the collection is considerably later than the Warring States material it draws on.

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