The big idea
Most decisions you practise for are solitary: solve the problem, write the code, run the race. But many of the decisions that shape a life are strategic. What you should do depends on what other people will do, and what they should do depends on you. A salary negotiation, a group project, two companies setting prices, a goalkeeper guessing where a penalty will go.
Game theory is the mathematics of these interdependent decisions. A "game" is any situation with players, the options each one has, and payoffs, meaning how much each possible outcome is worth to each player. Payoffs are not necessarily money. They measure whatever people actually care about, including fairness and other people's wellbeing. This is the point that gets lost most often.
Three lessons come up again and again:
- Individually sensible choices can add up to a collective mess. Everyone doing what is best for themselves can leave everyone worse off.
- Repetition changes everything. When you will deal with someone again, cooperating can be the selfish choice.
- The rules of the game often matter more than the players. Who moves first, what can be seen, and what can be punished shape behaviour more than personalities do.
Fifty years of experiments add a fourth: real people are not the cold calculators of textbooks. They care about fairness, punish cheats at their own expense and think only a step or two ahead. Game theory works best as a lens for structure, combined with evidence about how people actually behave.
A short history
- 1944 The field is born
- 1950 Nash equilibrium
- 1950 The prisoner's dilemma
- 1960 Focal points and commitment
- 1980 Axelrod's tournaments
- 1982 The ultimatum game
- 1994 Nobel prize
The building blocks
Four ideas carry most of the weight.
- Zero-sum versus positive-sum. In a zero-sum game, one player's gain is exactly another's loss: poker, a penalty kick, splitting a fixed bonus pool. In a positive-sum game, the total can grow, so cooperation can create value. Most of life, including trade, teamwork and most negotiations, is positive-sum.
- Dominant strategy. A move that is best no matter what the others do. If you have one, play it.
- Nash equilibrium. A combination of choices where no player can do better by changing only their own choice [2Primary studyEquilibrium points in n-person games]. It is a stable resting point, not necessarily a good one.
- Pareto efficiency. An outcome where nobody can be made better off without making someone else worse off. The central tension in game theory is that stable outcomes are not always efficient ones.
Four games worth knowing by heart
The lab below lets you explore four classic two-player games. Each player chooses at the same time. In each cell, the left number is your payoff and the right number is the other player's. Turn on best responses to see why certain cells are stable, then try changing the numbers.
Find the equilibrium
Two players each pick a move at the same time. Each cell shows the payoff to You (left number) and to Them (right number). Turn on best responses to see why some cells are stable. Edit any payoff to see how the answer changes.
The prisoner's dilemma. Take the payoffs from Axelrod's tournaments: both cooperate and each gets 3; both defect and each gets 1; if one defects while the other cooperates, the defector gets 5 and the cooperator 0 [11Primary studyEffective choice in the Prisoner's Dilemma]. Check what you should do. If the other player cooperates, defecting gives you 5 instead of 3. If they defect, defecting gives you 1 instead of 0. Defecting is better either way, so it is a dominant strategy, for both players. The only equilibrium is mutual defection, with 1 each, even though mutual cooperation would give both 3 [3ReviewPrisoner's Dilemma]. Individual logic produces a collective loss.
Real versions are everywhere: two colleagues who both hoard information, two companies locked in a price war, countries that overfish a shared sea.
The stag hunt. Two hunters can chase a stag together (big payoff, but only if both commit) or each catch a hare alone (smaller but safe). Both "everyone hunts stag" and "everyone hunts hare" are stable. The problem here is not temptation but trust: hunting stag only makes sense if you believe the other person will too. This is the game of start-ups, joint ventures and new teams.
Chicken. Two drivers race toward each other. Each wants the other to swerve. If both go straight, both lose badly. The stable outcomes are the ones where exactly one backs down. This game explains why credible commitment matters: a driver who visibly throws the steering wheel out of the window wins, because the other now knows they must swerve [6BookThe Strategy of Conflict].
Coordination with conflict. Two people want to do the same thing rather than split up, but each prefers a different shared plan. There are two stable outcomes, one favouring each player. If they try to guess randomly, they miscoordinate often and both do worse than if either one simply led. The lesson: a convention, a focal point or a first mover is very valuable, even one that favours the other side.
Focal points: coordinating without talking
How do people coordinate when they cannot communicate? Schelling noticed they often converge on whatever stands out [6BookThe Strategy of Conflict]. In a controlled experiment, when people tried to match a partner's choice of "heads or tails", 86.7% chose heads, compared with 76.1% when simply picking one [8Primary studyThe nature of salience: an experimental investigation of pure coordination games]. Labels that formal theory treats as irrelevant help real people coordinate.
Mixed strategies: why being unpredictable is rational
In games of outguessing, any predictable choice can be exploited. If a penalty taker always shoots to one side, the goalkeeper dives that way. The answer is to randomise, in exactly the proportions that leave your opponent with no better option. This is the logic von Neumann proved for zero-sum games, a special case of Nash's result.
A strange consequence: your best mix is set by your opponent's payoffs, not your own. And theory makes two testable predictions. First, a player's scoring rate should be the same whichever side they choose. Second, their choices should show no detectable pattern.
Professional footballers play the equilibrium
About 80% of penalties were scored. Kickers chose the centre only 7.5% of the time. For the players with enough kicks, scoring rates were statistically equal across sides and choices showed no serial patterns, just as the theory predicts [9Primary studyProfessionals play minimax]. A separate study of 459 French and Italian kicks found results consistent with equilibrium too [10Primary studyTesting mixed-strategy equilibria when players are heterogeneous: the case of penalty kicks in soccer].
Moves in sequence: threats and promises
When players take turns, you can draw the game as a tree and solve it from the end: at each step, ask what the person moving would actually do. This is backward induction. Reinhard Selten's idea of subgame perfection requires strategies to make sense at every step, including steps never reached, which rules out empty threats [5Primary studyReexamination of the perfectness concept for equilibrium points in extensive games].
Take the ultimatum game. One person proposes how to split 10 coins; the other accepts or rejects, and if they reject, nobody gets anything. A purely money-driven responder should accept any positive offer, since something beats nothing. Knowing that, the proposer should offer 1 coin and keep 9. A threat like "I'll reject anything below 5" should not be believable.
Real people break this prediction, as we will see. And in the centipede game, where two players take turns either grabbing a growing pot or passing it on, backward induction says the first player should grab immediately. In an experiment, only 37 of 662 games ended that way [38Primary studyAn experimental study of the centipede game]. People trust each other more than the cold logic predicts, and often do better for it.
How cooperation survives
Axelrod's tournaments
If the prisoner's dilemma makes defection rational, why does so much cooperation exist? In 1980 Robert Axelrod ran an unusual experiment. He invited game theorists, economists and others to submit computer programs that would play a repeated dilemma against each other, 200 rounds per match, with the 5, 3, 1, 0 payoffs [11Primary studyEffective choice in the Prisoner's Dilemma].
The winner was the simplest entry: tit for tat, by Anatol Rapoport. It cooperates on the first move and then copies whatever the other player did last. It averaged 504.5 points per 200-round game, where 600 would be perfect mutual cooperation and 200 steady mutual defection. All eight top-ranked programs were "nice": never the first to defect.
Here is the remarkable part: tit for tat won zero head-to-head matches. It can never outscore the player it faces, because it only defects after being defected on. It ranked last by number of wins and first by total points [14Primary studyIs tit-for-tat the answer? On the conclusions drawn from Axelrod's tournaments]. It won by drawing cooperation out of others, not by beating anyone.
A second tournament drew 62 entrants who had studied the first results. Tit for tat won again [12Primary studyMore effective choice in the Prisoner's Dilemma]. Axelrod summarised the winning traits:
- Nice: never be the first to defect.
- Provocable: respond to defection, so you are not exploited.
- Forgiving: return to cooperation once the other side does.
- Clear: be easy to read, so others can learn that cooperating with you pays.
The shadow of the future
Why does repetition help? Because today's defection costs you tomorrow's cooperation. Axelrod called this the shadow of the future [13Primary studyThe evolution of cooperation]. With the 5, 3, 1, 0 payoffs, a strategy that cooperates until crossed and then defects forever can sustain cooperation as long as there is at least a 50% chance of meeting again. When the next encounter becomes uncertain, cooperation becomes fragile. Biologist Martin Nowak showed that reciprocity, reputation, networks, family ties and group competition are five distinct routes by which cooperation can beat defection [20ReviewFive rules for the evolution of cooperation].
A meta-analysis of repeated-game experiments confirms that repetition raises cooperation, with a catch: people reliably cooperate only when doing so is not too risky, meaning the cost of being exploited by a partner who defects is manageable [19Meta-analysisOn the determinants of cooperation in infinitely repeated games: a survey].
Noise: why tit for tat is not the final answer
Axelrod's tournaments had no mistakes. Real life does: emails are misread, deadlines slip, a favour goes unnoticed. In a noisy world, tit for tat performs badly. One accidental defection triggers retaliation, which triggers retaliation, an echo that can run for many rounds [15Primary studyThe optimal level of generosity in a selfish, uncertain environment]. Axelrod later wrote that two tit-for-tat players in a noisy world do no better than two random players, and that he regretted not appreciating this sooner [16ReviewLaunching "The Evolution of Cooperation"].
Two fixes work better. Generous tit for tat forgives some defections at random [15Primary studyThe optimal level of generosity in a selfish, uncertain environment]. Win-stay, lose-shift repeats its last move after a good result and switches after a bad one, which lets it recover from mistakes and still punish unconditional cooperators [17Primary studyA strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game]. Human players seem to know this: in a lab study of noisy repeated games, people were lenient and forgiving, and those strategies earned high payoffs. The authors titled the paper "Slow to anger and fast to forgive" [18Primary studySlow to anger and fast to forgive: cooperation in an uncertain world].
Run your own cooperation tournament
Every strategy plays every other strategy (and a copy of itself) for many rounds, using the payoffs from the dilemma above. Add or remove strategies, then add noise: a chance that any move comes out as the opposite of what was intended, like a misread email.
Scores are averaged over five full tournaments with the same random seed, so results are repeatable. Press Run again for a new seed.
Try three experiments. First, with no noise, retaliating strategies such as tit for tat and grim trigger sit at or near the top. Second, set noise to 2%: the forgiving strategies (win-stay, lose-shift, generous tit for tat and tit for two tats) usually climb, because they recover from accidents instead of feuding. Third, push noise to 10% with Always cooperate and Random still in the field: Always defect can now reach the top, because when most moves are noise and there are easy targets to exploit, cooperating stops paying. Then switch off Always cooperate and Random and run it again. Watch, too, how a single accidental D echoes through the match below. These are results of this simulation, not data from real people, but they show the key lesson: which strategy wins depends on the noise and on who else is playing.
How real people play
Fairness: the ultimatum game
Theory says a responder should accept any positive offer. People do not. Across 37 papers, proposers offered about 40% of the pie on average, and about 16% of offers were rejected [22Meta-analysisCultural differences in ultimatum game experiments: evidence from a meta-analysis]. People pay to punish unfairness.
But fairness is not identical everywhere. A team of anthropologists and economists ran the game in 15 small-scale societies, from hunter-gatherers to herders, with stakes of about one or two days' wages [23Primary studyIn search of Homo economicus: behavioral experiments in 15 small-scale societies].
How much a society's daily life depended on cooperating with non-family and on market trade explained much of the variation. Fairness norms are learned from the games people play every day. This also matters for how we read research: most experiments use Western university students, who turn out to be unusual compared with most of humanity [25ReviewThe weirdest people in the world?].
Stakes matter too. In villages in India where the stakes ranged up to about 1,600 hours of work, rejections almost disappeared at the highest stakes: only 1 of 24 responders rejected [24Primary studyStakes matter in ultimatum games]. Fairness is real, but it has a price.
Punishment, and its dark side
In a public goods game, each person in a group decides how much to put into a shared pot, which is multiplied and split equally. Everyone does best if all contribute, but each individual does best by contributing nothing and taking a share of what others put in.
In a classic experiment with groups of four, contributions collapsed toward zero over ten rounds without punishment. When players could pay to fine low contributors, contributions stayed high [27Primary studyCooperation and punishment in public goods experiments].
People punish even strangers they will never meet again, at a cost to themselves [28Primary studyAltruistic punishment in humans]. Over 50 rounds, punishment clearly pays for itself [29Primary studyThe long-run benefits of punishment], and a meta-analysis found both punishment and rewards raise cooperation [31Meta-analysisReward, punishment, and cooperation: a meta-analysis].
But when the same game was run in 16 participant pools around the world, some groups punished generous contributors as much as free riders. In those places, this antisocial punishment wiped out the benefit of sanctions. It was most common where norms of civic cooperation and the rule of law were weak [30Primary studyAntisocial punishment across societies]. Sanctions work when the surrounding culture supports cooperation.
Talking works, even when theory says it should not
In standard theory, non-binding talk is "cheap" and should not matter. In reality, it is one of the strongest tools available. A meta-analysis found that communication raises cooperation in social dilemmas by a large amount (d = 1.01), more face to face than in writing [32Meta-analysisCommunication and cooperation in social dilemmas: a meta-analytic review].
Governing the commons
Economist Elinor Ostrom studied fisheries, forests and irrigation systems that communities had managed sustainably for generations, without a central authority or private ownership [33BookGoverning the Commons: The Evolution of Institutions for Collective Action]. She identified design principles: clear boundaries, rules made locally, monitoring, graduated sanctions and ways to resolve conflict. A review of 91 later studies found these principles well supported [34ReviewA review of design principles for community-based natural resource management]. The lesson for any team: design the rules of the game rather than blaming the players.
How many steps ahead do people think?
Before reading on, play this game.
Guess two thirds of the average
Everyone in a large group picks a number from 0 to 100. The winner is whoever comes closest to two thirds of the group's average. What do you pick? Decide before you look at the ladder.
The ladder of reasoning appears after you lock in a guess, so it cannot anchor you.
In the original experiments, the average first guess for "two thirds of the average" was about 37, with a median of 33, and nobody chose 0 [35Primary studyUnraveling in guessing games: an experimental study]. Choices clustered at one or two steps of reasoning. When newspapers ran the game, about 7,900 readers showed the same spikes [36Primary studyOne, two, (three), infinity, ...: newspaper and lab beauty-contest experiments]. A model fitted across many games suggests people think about 1.5 steps ahead on average [37Primary studyA cognitive hierarchy model of games]. The practical rule: model other people as thinking one or two steps deep, and aim one step beyond them.
Game theory in your life and career
Signals
When employers cannot see your ability directly, a credential, portfolio or track record can work as a signal, as long as it is harder to obtain for people without the ability [39Primary studyJob market signaling]. A signal works whether or not it makes you more productive; what matters is that it is costly to fake. How much of the real pay gain from education comes from signalling rather than skill is still disputed, so be wary of strong claims either way.
Markets designed by game theory
Game theory does not only describe games; it can design them. In a second-price auction, the highest bidder wins but pays the second-highest bid, which makes bidding your true value the best strategy [40Primary studyCounterspeculation, auctions, and competitive sealed tenders]. The deferred acceptance algorithm always produces a stable matching, where no two parties would both rather be paired with each other [41Primary studyCollege admissions and the stability of marriage]. A version runs the US medical residency match [42Primary studyThe redesign of the matching market for American physicians], and similar ideas power kidney-exchange programs that match incompatible donor pairs [43Primary studyKidney exchange]. If you ever apply through a system like this, rank your true preferences: gaming your list can only hurt you.
Negotiation
Your BATNA, the best alternative to a negotiated agreement, is your walk-away option [48BookGetting to Yes: Negotiating Agreement Without Giving In]. In bargaining models it is your fallback payoff, and improving it shifts the deal in your favour. Look for positive-sum trades as well: a review of 32 experiments found negotiators often fail to notice interests they share with the other side, and sometimes settle for deals that are worse for both [47Meta-analysisLose-lose agreements in interdependent decision making].
Your playbook, graded
- Lengthen the shadow of the futureStrong evidence
- Be nice, provocable, forgiving and clearModerate evidence
- Assume noise before maliceModerate evidence
- Talk, ideally face to faceStrong evidence
Communication is one of the strongest levers for cooperation [32Meta-analysisCommunication and cooperation in social dilemmas: a meta-analytic review].
- Do not lowballStrong evidence
Very low offers get rejected even when rejecting is costly [22Meta-analysisCultural differences in ultimatum game experiments: evidence from a meta-analysis]. How strongly depends on culture and stakes [23Primary studyIn search of Homo economicus: behavioral experiments in 15 small-scale societies, 24Primary studyStakes matter in ultimatum games].
- Know and improve your walk-away optionModerate evidence
A better BATNA shifts the deal toward you [48BookGetting to Yes: Negotiating Agreement Without Giving In]. Strong logic; limited direct experimental testing of the advice.
- Look for the positive-sum tradeModerate evidence
People often miss shared interests [47Meta-analysisLose-lose agreements in interdependent decision making].
- Design the rules, not just the peopleModerate evidence
Legitimate rules, monitoring and graduated sanctions sustain cooperation [34ReviewA review of design principles for community-based natural resource management, 31Meta-analysisReward, punishment, and cooperation: a meta-analysis], but beware cultures that punish high performers [30Primary studyAntisocial punishment across societies].
- Choose games where cooperation is easyModerate evidence
Pick teams and workplaces where interactions repeat, effort is visible and fairness norms are strong [19Meta-analysisOn the determinants of cooperation in infinitely repeated games: a survey, 30Primary studyAntisocial punishment across societies]. It is easier to find a good game than to win a bad one.
Myths and what the evidence says
Payoffs can include fairness and care for others. It is experiments that show money alone predicts behaviour badly: people offer about 40% and reject unfair offers [22Meta-analysisCultural differences in ultimatum game experiments: evidence from a meta-analysis], and give money away when they do not have to [26Meta-analysisDictator games: a meta study].
It won two tournaments without winning a single match [14Primary studyIs tit-for-tat the answer? On the conclusions drawn from Axelrod's tournaments]. With noise it struggles, and forgiving strategies do better [15Primary studyThe optimal level of generosity in a selfish, uncertain environment, 17Primary studyA strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game].
Nice strategies took all eight top places in the first tournament [11Primary studyEffective choice in the Prisoner's Dilemma]. But niceness without the willingness to respond gets exploited [17Primary studyA strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game].
The well-known study behind this claim did not replicate in 21 labs [46Primary studyRegistered Replication Report: Rand, Greene, and Nowak (2012)].
Check your understanding
Words to know
- Game
- Any situation where your best choice depends on what others choose.
- Payoff
- How much an outcome is worth to a player. Not necessarily money.
- Zero-sum game
- A game where one player's gain is exactly another's loss.
- Dominant strategy
- A move that is best whatever the others do.
- Nash equilibrium
- A set of choices where nobody gains by changing only their own.
- Pareto efficient
- An outcome where no one can be made better off without making someone worse off.
- Prisoner's dilemma
- A game where defecting is individually best but mutual cooperation beats mutual defection.
- Mixed strategy
- Choosing randomly between moves in set proportions.
- Backward induction
- Solving a turn-by-turn game by reasoning from the last move backwards.
- Credible commitment
- A promise or threat that it will really be in your interest to carry out.
- Shadow of the future
- The weight of future interactions, which makes cooperation pay today.
- Focal point
- An option people converge on because it stands out.
- Public goods game
- A group game where everyone benefits from contributions but each is tempted to free ride.
- Signal
- A costly action that reveals hidden qualities because it is harder for others to fake.
- BATNA
- Best alternative to a negotiated agreement: your walk-away option.
- Level-k thinking
- Reasoning a limited number of steps about what others will do.
- Stable matching
- A pairing where no two parties would both rather be with each other.
Sources
Every claim on this page links to one of these. Primary studies and meta-analyses carry the most weight; books and secondary sources are used for history and context.
- 1von Neumann J, Morgenstern O (1944). Theory of Games and Economic Behavior. Princeton University Press.The book that founded game theory as a field.
- 2Nash JF (1950). Equilibrium points in n-person games. PNAS 36:48-49.Proof that every finite game has at least one equilibrium.
- 3Kuhn S (1997, revised 2025). Prisoner's Dilemma. Stanford Encyclopedia of Philosophy.History of the dilemma (Flood, Dresher and Tucker) and its interpretation.
- 4Nobel Prize Outreach (1994). The Prize in Economic Sciences 1994: Harsanyi, Nash, Selten. NobelPrize.org.Nobel for the analysis of equilibria in non-cooperative games.
- 5Selten R (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4:25-55.Subgame perfection: strategies must make sense at every step, ruling out empty threats.
- 6Schelling TC (1960). The Strategy of Conflict. Harvard University Press.Focal points, threats and credible commitment.
- 7Nobel Prize Outreach (2005). The Prize in Economic Sciences 2005: Aumann, Schelling. NobelPrize.org.Nobel for game-theory analysis of conflict and cooperation.
- 8Mehta J, Starmer C, Sugden R (1994). The nature of salience: an experimental investigation of pure coordination games. American Economic Review 84:658-673.86.7% chose heads when trying to match a partner, 76.1% when just picking.
- 9Palacios-Huerta I (2003). Professionals play minimax. Review of Economic Studies 70:395-415.1,417 penalty kicks: players randomise much as theory predicts.
- 10Chiappori PA, Levitt S, Groseclose T (2002). Testing mixed-strategy equilibria when players are heterogeneous: the case of penalty kicks in soccer. American Economic Review 92:1138-1151.459 French and Italian kicks consistent with equilibrium play.
- 11Axelrod R (1980). Effective choice in the Prisoner's Dilemma. Journal of Conflict Resolution 24:3-25.First computer tournament; tit for tat wins with 504.5 points per game.
- 12Axelrod R (1980). More effective choice in the Prisoner's Dilemma. Journal of Conflict Resolution 24:379-403.Second tournament with 62 entrants; tit for tat wins again.
- 13Axelrod R, Hamilton WD (1981). The evolution of cooperation. Science 211:1390-1396.Why reciprocity can be evolutionarily stable.
- 14Rapoport A, Seale DA, Colman AM (2015). Is tit-for-tat the answer? On the conclusions drawn from Axelrod's tournaments. PLOS ONE 10:e0134128.Tit for tat won no head-to-head match; its success depends on tournament design.
- 15Molander P (1985). The optimal level of generosity in a selfish, uncertain environment. Journal of Conflict Resolution 29:611-618.Noise wrecks tit for tat; some generosity repairs it.
- 16Axelrod R (2012). Launching "The Evolution of Cooperation". Journal of Theoretical Biology 299:21-24.Axelrod's retrospective, including the noise problem.
- 17Nowak M, Sigmund K (1993). A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game. Nature 364:56-58.Win-stay, lose-shift beats tit for tat in evolving populations with errors.
- 18Fudenberg D, Rand DG, Dreber A (2012). Slow to anger and fast to forgive: cooperation in an uncertain world. American Economic Review 102:720-749.People in noisy repeated games are lenient and forgiving, and it pays.
- 19Dal Bó P, Fréchette GR (2018). On the determinants of cooperation in infinitely repeated games: a survey. Journal of Economic Literature 56:60-114.Repetition raises cooperation, but only when cooperating is not too risky.
- 20Nowak MA (2006). Five rules for the evolution of cooperation. Science 314:1560-1563.Five mechanisms that let cooperation beat defection.
- 21Güth W, Schmittberger R, Schwarze B (1982). An experimental analysis of ultimatum bargaining. Journal of Economic Behavior & Organization 3:367-388.The first ultimatum game experiment.
- 22Oosterbeek H, Sloof R, van de Kuilen G (2004). Cultural differences in ultimatum game experiments: evidence from a meta-analysis. Experimental Economics 7:171-188.Across 37 papers: average offer about 40%, about 16% of offers rejected.
- 23Henrich J, Boyd R, Bowles S, Camerer C, Fehr E, Gintis H, McElreath R (2001). In search of Homo economicus: behavioral experiments in 15 small-scale societies. American Economic Review 91:73-78.Mean offers ranged from 26% to 58% across societies.
- 24Andersen S, Ertaç S, Gneezy U, Hoffman M, List JA (2011). Stakes matter in ultimatum games. American Economic Review 101:3427-3439.At very high stakes, almost nobody rejects an offer.
- 25Henrich J, Heine SJ, Norenzayan A (2010). The weirdest people in the world?. Behavioral and Brain Sciences 33:61-83.Typical lab participants are unusual compared with most of humanity.
- 26Engel C (2011). Dictator games: a meta study. Experimental Economics 14:583-610.People given money to share freely give away a substantial share on average.
- 27Fehr E, Gächter S (2000). Cooperation and punishment in public goods experiments. American Economic Review 90:980-994.Contributions collapse without punishment and stay high with it.
- 28Fehr E, Gächter S (2002). Altruistic punishment in humans. Nature 415:137-140.People pay to punish free riders even when they gain nothing from it.
- 29Gächter S, Renner E, Sefton M (2008). The long-run benefits of punishment. Science 322:1510.Over 50 rounds, punishment clearly pays for itself.
- 30Herrmann B, Thöni C, Gächter S (2008). Antisocial punishment across societies. Science 319:1362-1367.In some societies people punish cooperators, which wipes out the benefit.
- 31Balliet D, Mulder LB, Van Lange PAM (2011). Reward, punishment, and cooperation: a meta-analysis. Psychological Bulletin 137:594-615.Both punishment (d = 0.70) and reward (d = 0.51) raise cooperation.
- 32Balliet D (2010). Communication and cooperation in social dilemmas: a meta-analytic review. Journal of Conflict Resolution 54:39-57.Talking raises cooperation strongly (d = 1.01), face to face most of all.
- 33Ostrom E (1990). Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge University Press.How communities govern shared resources without a central authority.
- 34Cox M, Arnold G, Villamayor Tomás S (2010). A review of design principles for community-based natural resource management. Ecology and Society 15(4):38.A review of 91 studies supports Ostrom's design principles.
- 35Nagel R (1995). Unraveling in guessing games: an experimental study. American Economic Review 85:1313-1326.Beauty-contest data: people reason one or two steps deep.
- 36Bosch-Domènech A, Montalvo JG, Nagel R, Satorra A (2002). One, two, (three), infinity, ...: newspaper and lab beauty-contest experiments. American Economic Review 92:1687-1701.About 7,900 newspaper readers show the same one- and two-step spikes.
- 37Camerer CF, Ho TH, Chong JK (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics 119:861-898.People think about 1.5 steps ahead on average.
- 38McKelvey RD, Palfrey TR (1992). An experimental study of the centipede game. Econometrica 60:803-836.Only 37 of 662 games ended where backward induction predicts.
- 39Spence M (1973). Job market signaling. Quarterly Journal of Economics 87:355-374.A costly credential can reveal hidden ability.
- 40Vickrey W (1961). Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance 16:8-37.In a second-price auction, bidding your true value is best.
- 41Gale D, Shapley LS (1962). College admissions and the stability of marriage. American Mathematical Monthly 69:9-15.The deferred acceptance algorithm always finds a stable matching.
- 42Roth AE, Peranson E (1999). The redesign of the matching market for American physicians. American Economic Review 89:748-780.Game theory used to redesign the US medical residency match.
- 43Roth AE, Sönmez T, Ünver MU (2004). Kidney exchange. Quarterly Journal of Economics 119:457-488.Matching theory applied to kidney donation.
- 44Nobel Prize Outreach (2012). The Prize in Economic Sciences 2012: Roth, Shapley. NobelPrize.org.Nobel for stable allocations and market design.
- 45Maynard Smith J, Price GR (1973). The logic of animal conflict. Nature 246:15-18.Introduces the evolutionarily stable strategy.
- 46Bouwmeester S, Verkoeijen PPJL, et al. (2017). Registered Replication Report: Rand, Greene, and Nowak (2012). Perspectives on Psychological Science 12:527-542.21 labs, 3,596 people: time pressure did not increase cooperation.
- 47Thompson L, Hrebec D (1996). Lose-lose agreements in interdependent decision making. Psychological Bulletin 120:396-409.Negotiators often miss interests they actually share.
- 48Fisher R, Ury W (1981). Getting to Yes: Negotiating Agreement Without Giving In. Houghton Mifflin.Origin of the term BATNA.
- 49Press WH, Dyson FJ (2012). Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent. PNAS 109:10409-10413.Zero-determinant strategies that can extort a partner.
- 50Stewart AJ, Plotkin JB (2013). From extortion to generosity, evolution in the Iterated Prisoner's Dilemma. PNAS 110:15348-15353.In evolving populations, generous strategies beat extortion.