This game theory problem will change the way you see the world

On September 3, 1949, US weather monitoring planes detected radioactive material over Japan, revealing the Soviet Union had developed nuclear weapons through isotope analysis.

• American military supremacy from the Manhattan Project was fading • Some military leaders advocated for unprovoked nuclear strikes while the US was still ahead • Game theory founder John von Neumann questioned timing: why bomb tomorrow instead of today?

In 1950, the RAND Corporation began studying nuclear weapons strategy using game theory approaches.

The crisis demonstrated that solving the nuclear weapons dilemma required finding the best strategy quickly.

Two players choose between cooperating or defecting. A banker awards coins based on outcomes: both cooperate (3 coins each), one defects (5 coins for defector, 0 for cooperator), both defect (1 coin each).

• If opponent cooperates: defecting gives 5 coins vs 3 coins from cooperating • If opponent defects: defecting gives 1 coin vs 0 coins from cooperating • Therefore, defection is the rational choice regardless of opponent's action

When both players act rationally and defect, they each get only 1 coin when they could have gotten 3 coins if both cooperated.

The US and Soviet Union both developed massive nuclear arsenals costing around $10 trillion combined, yet neither could use them, resulting in mutual vulnerability instead of security.

Impalas in African woodlands need mutual grooming to remove ticks that cause disease and death, but grooming costs saliva, electrolytes, time, and attention under predatory conditions.

Each impala faces the decision: should they groom each other (cooperate) or refuse to pay the cost (defect)?

Unlike a single prisoner's dilemma, impalas interact repeatedly, creating a different strategic landscape where past behavior influences future interactions.

The prisoner's dilemma appears everywhere in nature and human society, making understanding solutions crucial.

• Political scientist Robert Axelrod invited leading game theorists to submit computer programs as strategies • Each strategy played against every other strategy and copies of itself for 200 rounds • Received 14 strategies plus one random strategy (15 total) • Tournament was repeated five times to ensure robust results

• Friedman: Cooperates initially, defects permanently after one opponent defection • Joss: Copies opponent's last move but defects randomly 10% of the time • Graaskamp: Like Joss but defects specifically on round 50 to probe weaknesses • Name Withheld: Most elaborate strategy with 77 lines of code

Tit for Tat, the simplest strategy with just 3 lines of code, won the tournament. It starts with cooperation and then copies exactly what the opponent did in the previous move.

Contrary to expectations, simplicity and clarity outperformed complexity and sophistication in the strategic competition.

• Nice strategies never defect first; they only retaliate • All top 8 strategies were nice; all 7 nasty strategies were inferior • Even the worst nice strategy outscored the best nasty strategy

• Forgiving strategies retaliate but don't hold grudges beyond the last round • Tit for Tat is forgiving: it retaliates immediately but returns to cooperation if opponent does • Friedman is unforgiving: it defects forever after one opponent defection, which performs poorly

Always cooperate is a total pushover that gets exploited. Effective strategies must strike back immediately when defected upon, like Tit for Tat does.

Opaque, random-like strategies are hard for opponents to understand, making trust impossible and causing default defection behaviors.

Tit for Two Tats only defects after the opponent defects twice in a row, being more forgiving than Tit for Tat.

Tit for Two Tats would have won the first tournament if submitted, but it only placed 24th in the second tournament.

This reveals that there is no universally best strategy; performance always depends on what other strategies are present.

When Tit for Tat plays against nothing but always-defect strategies, it finishes in last place.

Axelrod announced a second tournament with 62 entries, keeping everything the same except varying the number of rounds to avoid the endgame problem.

• In the first tournament, knowing the last round arrives means no reason to cooperate that round (defection is better) • If both players defect in round 200, neither cooperates in round 199, or 198, cascading back to round 1 • Solution: Use random end rounds so players don't know when the last interaction occurs

• One camp submitted nice, forgiving strategies based on first tournament results • Another camp anticipated this and submitted nasty strategies to exploit the forgiving ones • Tester defects first to probe reactions, apologizes if opponent retaliates, then exploits if opponent doesn't

Tit for Tat won again. Nice strategies dominated the top 15; nasty strategies dominated the bottom 15.

• Successful strategies in one generation increase in population • Unsuccessful strategies decrease in numbers • Strategies compete in an ecological environment, not a single tournament

Harrington, the only nasty strategy in the top 15, initially grew quickly but collapsed as its prey strategies went extinct, then Harrington itself declined.

After 1000 generations, only nice strategies survive. Tit for Tat represents 14.5% of the stable population.

• A small cluster of Tit for Tat players surrounded by always-defect strategies can build up points and grow • This island of cooperation can spread and eventually take over the entire population • Cooperation can emerge from pure self-interest without altruism or conscious choice

The prisoner's dilemma may explain how cooperation emerged in a world of completely selfish organisms concerned only with themselves.

• Impalas grooming each other • Fish cleaning parasites from sharks • Many life forms experiencing prisoner's dilemma conflicts repeatedly

• Because organisms interact repeatedly, not just once, cooperation becomes beneficial • Strategies can be encoded in DNA without requiring conscious thought or trust • Strategies performing better than alternatives can take over populations through natural selection

Cooperation doesn't require altruism; it emerges naturally when organisms interact multiple times and successful behaviors spread through populations.

• Random errors occur constantly in real systems • One player intends to cooperate but it's perceived as defection • Example: 1983 Soviet early warning system confused sunlight reflecting off clouds with a ballistic missile

• When Tit for Tat plays itself with noise, a single cooperation misperceived as defection triggers retaliation • This creates an echo effect of alternating mutual defections • Additional errors lock both players into constant mutual defection for the rest of the game

Tit for Tat goes from performing excellently in perfect environments to performing poorly with noise, earning only one-third of perfect points.

Generous Tit for Tat: Retaliate only 9 out of 10 times instead of always. This breaks echo cycles while maintaining retaliation to prevent exploitation.

By design, Tit for Tat can never win against any individual opponent; it can only lose or draw. Yet when results are tallied, it comes out ahead of all other strategies.

Always defect can never lose; it can only draw or win. Yet overall it performs extremely poorly against varied opponents.

• In chess and poker, one person's gain is another's loss (zero sum) • In most of life, this is not true • Most situations are non-zero sum where both players can gain together

• To win, you don't need to beat the other person • Get rewards from the environment (the banker), not from your opponent • In real life, the banker is the world and everything around you

From 1950 to 1986, the US and Soviet Union continued developing nuclear weapons, unable to cooperate effectively.

From the late 1980s onward, both countries started reducing their nuclear stockpiles, learning how to resolve conflict.

• Rather than agreeing to abolish all nukes at once (risky single prisoner's dilemma) • They disarmed slowly with a small number of weapons reduction each year • Both sides checked that the other had cooperated • The process repeated year after year with verification of mutual cooperation

Repeated interaction with verification allowed the Tit for Tat strategy to work in the real world.

For more than 40 years since Axelrod's tournaments, researchers have studied which strategies perform best in various environments.

• Different payoff structures • Varied strategy types • Errors and noise in the system • Strategies with mutations allowed

While Tit for Tat or Generous Tit for Tat don't always win in all contexts, Axelrod's core principles still hold: be nice, forgiving, retaliatory, and clear.

The research shows that optimal strategies balance multiple values rather than maximizing any single factor.

Axelrod had specifically asked Anatol Rapoport to submit Tit for Tat, not the other way around.

Rapoport, a peace researcher, expressed doubt about the strategy, preferring to be more forgiving and less provokable.

• Axelrod's four winning principles (nice, forgiving, provokable, clear) resemble the evolved morality worldwide • Often summarized as an eye for an eye, not Christian turning the other cheek • Rather, it's an older philosophy of reciprocal justice

The effectiveness of these strategies suggests they align with deep principles of human and natural morality.

What sets life apart from non-living things is that life gets to make decisions and choices.

• Choices change your own future • Choices change the future of those you interact with • Impact of choices may reach further than expected

• In the short term, the environment determines who does well • In the long run, players shape the environment through their repeated choices

In the game of life, choose strategies wisely because the consequences extend beyond immediate interactions.