Two department heads are fighting over six new engineers. Each wants all six; each is sure that whatever the other gets, they lose, so they brief against each other, hide information, and inflate forecasts until the numbers mean nothing. The trap is that nobody is being irrational. Given how each one reads the situation, fighting dirty is the smart move. The problem isn't the players. It's the game, and the game has been misdiagnosed.

The quick version

  • Most fights that feel zero-sum ("my win is your loss") are really repeated, positive-sum games where both sides can come out ahead.
  • When you're losing, playing harder usually backfires. The high-leverage move is to change the game, its payoffs, information, sequencing and whether it repeats.
  • Repetition is the secret weapon: once people expect to deal with each other again, cooperation becomes the rational choice, not a soft one.
  • So your first question is never "how do I win?", it's "what game am I actually in?"

The idea in depth

Game theory is the study of decisions where your best move depends on what other people do, and theirs depends on what you do. John von Neumann and Oskar Morgenstern set it out formally in Theory of Games and Economic Behavior (1944), but their cleanest results covered two-person zero-sum games, the pure-conflict case where one side's gain is exactly the other's loss. That starting point did something unfortunate: it trained a couple of generations to picture strategy as zero-sum by default.

The correction came in 1950, when a 21-year-old John Nash showed that every finite game, zero-sum or not, has at least one equilibrium: a combination of strategies where no player can do better by changing theirs alone. That sounds reassuring until you notice the catch managers live with daily: an equilibrium can be stable and collectively terrible. Both managers hoarding and briefing against each other is a Nash equilibrium. Neither can improve by being the only one to stop. That is exactly why it feels stuck. Which makes the first job diagnostic, not tactical. Before you negotiate harder, work out who the players really are, what each one actually gets under each choice, and whether the pie is genuinely fixed or you've just decided it is.

quadrantChart
    title Diagnose the game before you play it
    x-axis "One-shot" --> "Repeated"
    y-axis "Zero-sum (fixed pie)" --> "Positive-sum (pie can grow)"
    quadrant-1 "Build the relationship: cooperation pays"
    quadrant-2 "Trade fairly: protect future rounds"
    quadrant-3 "Compete cleanly: a true contest"
    quadrant-4 "Change the game: make it repeat"
    "Headcount fight (as seen)": 0.18 0.18
    "Headcount fight (as it is)": 0.78 0.74
    "Vendor one-off auction": 0.22 0.30
    "Long-term supplier": 0.80 0.78
The first question is never "how do I win?", it's "what game am I in?" The headcount fight feels like the bottom-left; it usually lives in the top-right. Leaders Loop

Why repetition flips the maths

The cleanest model of the headcount fight is the prisoner's dilemma. Two parties each choose to cooperate or defect. If both cooperate, both do well; if both defect, both do badly; but if one cooperates while the other defects, the defector cleans up and the cooperator is exploited. Whatever the other person does, your safest individual move is to defect, so both defect, and both end up worse off than if they'd trusted each other.

quadrantChart
    title "Prisoner's dilemma: the trap of one-shot logic"
    x-axis "They cooperate" --> "They defect"
    y-axis "You defect" --> "You cooperate"
    quadrant-1 "You exploited (worst for you)"
    quadrant-2 "Both win (the prize)"
    quadrant-3 "Both lose (the trap)"
    quadrant-4 "You exploit them (best for you)"
Mutual cooperation is best for the pair, yet one-shot self-interest pulls each player toward "both lose." Leaders Loop

If that were the whole story, cooperation would be a mug's game. But almost nothing at work happens only once. In the early 1980s the political scientist Robert Axelrod ran tournaments in which strategies played the prisoner's dilemma repeatedly against each other. The winner, twice, was the simplest entry: tit-for-tat, which cooperates first, then copies whatever the other player did last time. In The Evolution of Cooperation (1984), Axelrod distilled why the strongest strategies won: they were nice (never the first to defect), provocable (retaliating at once when crossed), and forgiving (returning to cooperation the moment the other side did).

Repetition changes everything because it changes the payoffs. In a one-shot game, defection is banked and there's no tomorrow to pay for it. In a repeated game, today's defection poisons every future round, and once the future matters enough, cooperation becomes the genuinely rational choice. The lever, then, is to make the game visibly repeat. The two managers behave differently the instant they know they'll carve up headcount together every quarter for three years, with a shared record of who played straight. You don't appeal to their better natures. You change the structure so self-interest and cooperation point the same way.

flowchart LR
    A("One-shot framing
defection is rational") --> B("Make it repeat
shared future, visible record")
    B --> C("Add reciprocity
nice, provocable, forgiving")
    C --> D("Cooperation is now
the rational choice")
The leader's lever isn't willpower, it's structure. Turn a one-shot into a repeated game and the rational move flips from defect to cooperate. Leaders Loop

The levers you actually have

"Change the game" sounds like a slogan until you list the levers, and there are only a handful. Thomas Schelling, who shared the 2005 Nobel in economics for this work, showed in The Strategy of Conflict (1960) that your power often comes not from your options but from credibly removing some of them: a commitment you can't walk back from changes how the other side plays. Schelling also named the focal point, the obvious, salient option people converge on when they can't coordinate by talking, which means a leader who names a fair, legible default can pull a group toward it before the fight starts. Adam Brandenburger and Barry Nalebuff turned all of this into a manager's toolkit in Co-opetition (1996): the game is something you can redesign, not just a board you're handed. Concretely, that comes down to four edits:

Four levers to change the game

Payoffs
Reward the joint outcome, not the individual win. If you only bonus the manager who grabbed the headcount, you've built a defection machine.
Information
Defection thrives in the dark. Make each side's contribution and history visible, and reciprocity has something to work with.
Sequencing
Who moves first, and who sees what before deciding, can flip the result. Sometimes moving second, and being seen to react fairly, beats moving first.
Repetition & commitment
Turn one-shots into repeated games with a shared future; then make a credible, visible commitment to play straight (Schelling).

"The best-performing strategies were nice, never the first to defect, yet provocable and forgiving." , after Robert Axelrod, The Evolution of Cooperation (1984)

One honest limit before the example: classical game theory assumes players are rational optimisers who share a clear view of the payoffs. Real people aren't, and don't. They act on fairness, spite and loss-aversion; they misread the payoffs and each other. Decades of experimental work show people reject "rational" splits they find unfair and cooperate where pure self-interest says they shouldn't. So use the theory the way a navigator uses a chart, indispensable for seeing the structure, useless as a substitute for looking out of the window.

A worked example

Take the headcount fight and move it to the top-right quadrant, one lever at a time. Payoffs: tie part of each leader's review to the division's combined result, not their own unit's. Information: put both teams' demand forecasts and last quarter's actuals in one shared document, so inflated numbers are visible to everyone. Sequencing: have each manager state what they'd give up before they state what they want. Repetition: announce that allocation is now a standing quarterly process with a published record of past rounds.

None of this needs new budget or authority, each is a structural edit a manager can make this week. Together they convert a fight over a fixed six into a negotiation about how to grow the whole org's output. The same logic scales to a vendor relationship: a single hard-nosed auction invites the supplier to cut corners and walk, but framing it as a multi-year partnership with transparent scorecards and repeat business on the line makes playing straight the supplier's most profitable move too.

Frequently asked questions

What if my situation really IS zero-sum?

Sometimes it is, a fixed redundancy pool, one promotion two people want, a one-off auction you'll never revisit. Run the test honestly: a game is closer to truly zero-sum only when the total really is fixed, you won't deal with this counterparty again, and there's no audience whose trust you carry into the next game. Most workplace situations fail at least one of those. And even in a genuine one-off, how you play is watched, your reputation for playing straight is itself a repeated game.

Isn't "changing the game" just manipulation?

No, manipulation hides the rules; changing the game makes them clearer and more symmetric. Publishing the forecasts, rewarding the joint outcome, committing to a fair default in the open: these work precisely because everyone can see them. If a lever only works while the other side doesn't know about it, that's the manipulation tell, and it won't survive a repeated game anyway.

Does tit-for-tat actually work in real teams?

The principles do, even though people aren't the tidy optimisers the model assumes. Start cooperative, respond proportionately when someone defects, and forgive quickly once they return to good faith, that beats both being a pushover (which invites exploitation) and holding permanent grudges (which kills the cooperation you need next quarter). The one adjustment for humans: be a little more forgiving than strict tit-for-tat, because real signals are noisy and a misread can spiral.

What's a focal point?

It's the obvious answer people gravitate to when they have to coordinate without negotiating, Schelling's classic example is two strangers told to meet in New York with no time or place agreed, who often converge on Grand Central at noon. For a leader, naming a fair, legible default ("we split new headcount by each team's revenue contribution") gives everyone a focal point to rally around before positions harden.

Where do I even start?

With diagnosis, not tactics. Name the players (including the ones not in the room), write down what each actually gets under each choice, and ask whether the pie is genuinely fixed. That question is most of the edge, it pairs naturally with how you weigh the moves themselves under uncertainty, which we cover in decision theory and expected value, and it's the same instinct behind leaders who win quietly, as in our profile of Rob Alford.

Where to go next

The sticky version, the one to repeat to a colleague who's bracing for a fight: when you're losing the game, stop playing it harder, and ask whether you're playing the wrong game.

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