Math! Science! History! The Birth of Game Theory

Gabrielle Birchak/ June 10, 2026/ Modern History/ 0 comments

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Game the­o­ry is every­where, from the moves you make in chess to the way coun­tries nego­ti­ate treaties, from the strate­gies in our favorite video game to the deci­sions we make every day. But how did this field come to be? Who were the bril­liant minds behind it, and what math­e­mat­i­cal break­throughs made it possible?

Wel­come to Math! Sci­ence! His­to­ry!, I’m Gabrielle Bir­chak and today I’m talk­ing about the birth of game theory.

Wel­come back it’s been awhile! I took a few weeks off to cel­e­brate my birth­day and I had a cou­ple of fun things that I real­ly want­ed to do dur­ing my break. One of them was to play the game risk. It’s a long game and I for­got how much I did­n’t like it but I went all in and lost as usu­al. That’s OK. I still love play­ing games and I love the con­cept of risk because it uti­lizes game the­o­ry on so many dif­fer­ent levels.

In today’s episode, we’ll explore:

• The his­tor­i­cal con­text that led to the birth of game theory.
• The key fig­ures: John von Neu­mann and John Nash, and their ground­break­ing contributions.
• The math behind the mag­ic: How con­cepts like the min­i­max the­o­rem and Nash equi­lib­ri­um work, and why they matter.

So, let’s roll the dice and shuf­fle the deck. It’s time to play the game of game theory.

THE HISTORICAL CONTEXT

To under­stand the birth of game the­o­ry, we need to step back to the ear­ly 20th cen­tu­ry. At the time, math­e­mat­ics was under­go­ing a rev­o­lu­tion. Fields like prob­a­bil­i­ty, log­ic, and set the­o­ry were being for­mal­ized, and math­e­mati­cians were start­ing to apply these ideas to real-world problems.

But what exact­ly is a “game” in the con­text of game the­o­ry? It’s not just chess or pok­er, it’s any sit­u­a­tion where two or more play­ers make deci­sions that affect each oth­er’s out­comes. Think of it as a strate­gic inter­ac­tion, where the best move for one play­er depends on what the oth­er play­ers do. [1]

Game the­o­ry emerged as a way to mod­el these inter­ac­tions math­e­mat­i­cal­ly. It gave us tools to ana­lyze sit­u­a­tions where:

• Play­ers have dif­fer­ent goals.
• The out­come depends on what every­one does.
• There’s uncer­tain­ty or risk involved.

Ear­ly influ­ences on game the­o­ry came from eco­nom­ics, mil­i­tary strat­e­gy, and even phi­los­o­phy. But it was two math­e­mati­cians, John von Neu­mann and John Nash, who laid the foun­da­tion for the field as we know it today.

JOHN VON NEUMANN AND THE MINIMAX THEOREM

Let’s start with John von Neu­mann, a Hun­gar­i­an-Amer­i­can math­e­mati­cian who is often called the “father of game the­o­ry.” [2] In 1928, von Neu­mann pub­lished a ground­break­ing paper titled “On the The­o­ry of Games of Strat­e­gy.” [3] This paper intro­duced the min­i­max the­o­rem, a cor­ner­stone of game theory.

What is the Min­i­max Theorem?

The min­i­max the­o­rem applies to zero-sum games, games where one play­er’s gain is exact­ly equal to the oth­er play­er’s loss. Think of pok­er, chess, or even rock-paper-scis­sors. In these games, the best strat­e­gy is to min­i­mize your max­i­mum pos­si­ble loss.

Here’s how it works:

1. Play­er A wants to max­i­mize their min­i­mum gain (the best worst-case scenario).
2. Play­er B wants to min­i­mize their max­i­mum loss (the worst-case sce­nario for them).
3. The min­i­max the­o­rem proves that in zero-sum games, there’s always a sta­ble solu­tion where both play­ers can’t do bet­ter by chang­ing their strat­e­gy. [4]

Von Neu­mann him­self under­scored how foun­da­tion­al this the­o­rem was, say­ing: “As far as I can see, there could be no the­o­ry of games with­out that the­o­rem … I thought there was noth­ing worth pub­lish­ing until the Min­i­max The­o­rem was proved.” [5]

The Math Behind It

Imag­ine Annie and Bob are play­ing a sim­ple game. If Annie goes with her first strat­e­gy and Bob goes with his, Annie wins three points, but Bob los­es three. If they both switch strate­gies, Annie los­es a point and Bob gains one. The num­bers flip and shift depend­ing on what each play­er picks. So Annie looks at all her pos­si­ble out­comes and asks: ‘What’s the worst that could hap­pen with each choice?’ She picks the option where her worst case is least bad. Bob does the exact same thing from his side. And here’s the remark­able part, the min­i­max the­o­rem proves that both play­ers doing this inde­pen­dent­ly will land on the same sta­ble solu­tion. Nei­ther can do bet­ter by switching.

Using the min­i­max the­o­rem, we can find the opti­mal strat­e­gy for both play­ers. In this case, Annie might choose Strat­e­gy 1 50% of the time and Strat­e­gy 2 50% of the time, while Bob does the same. This ensures nei­ther play­er can exploit the oth­er’s strat­e­gy. [4]

Why It Matters

Von Neu­man­n’s work showed that even in com­pet­i­tive sit­u­a­tions, there’s a ratio­nal way to play. This idea was­n’t just the­o­ret­i­cal, it had real-world appli­ca­tions in eco­nom­ics, mil­i­tary strat­e­gy, and even the Cold War, where game the­o­ry was used to mod­el nuclear deter­rence. [6]

JOHN NASH AND THE NASH EQUILIBRIUM

Fast-for­ward to 1950. Enter John Nash, a bril­liant but trou­bled math­e­mati­cian whose life sto­ry was famous­ly told in the book and movie A Beau­ti­ful Mind. [7] Nash took game the­o­ry to the next lev­el by intro­duc­ing the Nash equi­lib­ri­um, a con­cept that rev­o­lu­tion­ized the field.

Nash was a young doc­tor­al stu­dent at Prince­ton when he pub­lished his foun­da­tion­al work. [8] In a brief 1950 com­mu­ni­ca­tion to the Pro­ceed­ings of the Nation­al Acad­e­my of Sci­ences, Nash for­mu­lat­ed the notion of equi­lib­ri­um that bears his name. [9]

What is the Nash Equilibrium?

The Nash equi­lib­ri­um is a sit­u­a­tion where no play­er can ben­e­fit by uni­lat­er­al­ly chang­ing their strat­e­gy, assum­ing the oth­er play­ers keep their strate­gies unchanged. [10] Unlike von Neu­man­n’s zero-sum games, Nash’s equi­lib­ri­um applies to any game, includ­ing those with coop­er­a­tion or mixed motives. [8]

The Math Behind It

Let’s take a clas­sic exam­ple: the Pris­on­er’s Dilemma.

Pic­ture this: Annie and Bob are both sit­ting in sep­a­rate inter­ro­ga­tion rooms. They can’t talk to each oth­er. If they both stay silent, they each get one year in prison, not great, but man­age­able. If one of them talks and the oth­er stays silent, the one who talked walks free and the loy­al one gets three years. And if they both talk? They each get two years. Now think about it from Annie’s per­spec­tive. She has no idea what Bob will do. But if she stays silent and Bob betrays her, she gets the worst out­come, three years. If she betrays him regard­less of what he does, she either goes free or gets two years. Betray­ing is always the safer bet for her. Bob is doing the exact same math. So they both betray each oth­er, and both end up with two years, even though they would have been bet­ter off if they’d just trust­ed each other.“In this case, the Nash equi­lib­ri­um is for both to defect, even though they’d both be bet­ter off if they coop­er­at­ed. Why? Because if Annie defects, she gets 0 years if Bob coop­er­ates, or 2 years if Bob defects. Either way, defect­ing is her best move. The same goes for Bob.

Why It Matters

The Nash equi­lib­ri­um explains why ratio­nal indi­vid­u­als might end up in sub­op­ti­mal sit­u­a­tions, like traf­fic jams, arms races, or even price wars in busi­ness. It’s a pow­er­ful tool for under­stand­ing real-world strate­gic inter­ac­tions, from auc­tions to inter­na­tion­al diplo­ma­cy. [10]

Nash’s work earned him the Nobel Prize in Eco­nom­ics in 1994, shared with John Harsanyi and Rein­hard Sel­ten, for their pio­neer­ing analy­sis of equi­lib­ria in the the­o­ry of non-coop­er­a­tive games. [11] His ideas have been applied to every­thing from evo­lu­tion­ary biol­o­gy, how ani­mals com­pete for resources, to auc­tion design, struc­tur­ing bid­ding to max­i­mize rev­enue. [12]

GAME THEORY IN THE REAL WORLD

Now that we’ve cov­ered the math and his­to­ry, let’s talk about how game the­o­ry shows up in our every­day lives.

1. Chess and Poker

• Chess: Every move in chess is a strate­gic deci­sion where play­ers try to antic­i­pate their oppo­nen­t’s moves. The min­i­max the­o­rem applies here, play­ers aim to max­i­mize their advan­tage while min­i­miz­ing their risk. [4]
• Pok­er: Pok­er is a mix of skill and chance. Play­ers use prob­a­bil­i­ty to cal­cu­late odds, bluff­ing to manip­u­late oppo­nents, and game the­o­ry to decide when to fold, call, or raise.

2. Traf­fic Patterns

Ever won­der why traf­fic jams form even when there’s no acci­dent? It’s a clas­sic exam­ple of the Nash equi­lib­ri­um. If every­one tries to take the fastest route, they end up con­gest­ing the same roads, mak­ing every­one worse off. [10]

3. Busi­ness and Economics

• Price Wars: Com­pa­nies like air­lines or fast-food chains often engage in price wars, where low­er­ing prices might seem like a good idea, but ends up hurt­ing every­one. Price wars are a real-world Pris­on­er’s Dilem­ma, every com­pa­ny has an incen­tive to under­cut the com­pe­ti­tion, so every­one does, and the whole indus­try ends up with thin­ner mar­gins, cheap­er prod­ucts, and low­er per­ceived val­ue than if nobody had blinked in the first place.
• Auc­tions: Game the­o­ry helps design auc­tions, like those for wire­less spec­trum licens­es, to ensure fair com­pe­ti­tion and max­i­mize rev­enue for the sell­er. Econ­o­mists Paul Mil­grom and Robert Wil­son won the 2020 Nobel Prize in Eco­nom­ics for their work design­ing new auc­tion for­mats, includ­ing the simul­ta­ne­ous mul­ti­ple-round auc­tion used by the FCC to allo­cate wire­less spec­trum. [13]

4. Pol­i­tics and Inter­na­tion­al Relations

• Nuclear Deter­rence: Dur­ing the Cold War, the U.S. and Sovi­et Union were in a game where nei­ther could strike first with­out risk­ing total destruc­tion. This doc­trine, Mutu­al­ly Assured Destruc­tion, or MAD, is itself a form of Nash equi­lib­ri­um, in which both sides had no incen­tive to ini­ti­ate con­flict nor to dis­arm. [14]
• Vot­ing Sys­tems: Game the­o­ry helps ana­lyze how dif­fer­ent vot­ing sys­tems (like first-past-the-post or ranked-choice) influ­ence vot­er behav­ior and elec­tion outcomes.

THE LEGACY OF GAME THEORY

Game the­o­ry has come a long way since von Neu­mann and Nash laid its foun­da­tions. Today, it’s used in:

• Arti­fi­cial Intel­li­gence: Deep­Mind’s Alpha­Go and Alp­haZe­ro pro­grams use rein­force­ment learn­ing, a close cousin of game-the­o­ret­ic self-play, to mas­ter games like Go and chess, and Alp­haZe­ro taught itself from scratch to achieve super­hu­man play in both games with­in hours. [15]
• Biol­o­gy: Evo­lu­tion­ary game the­o­ry, pio­neered by John May­nard Smith and George R. Price in 1973, explains how ani­mals and even bac­te­ria com­pete for resources, treat­ing species as play­ers in a game com­pet­ing for sur­vival and repro­duc­tion. [16]
• Cyber­se­cu­ri­ty: Game the­o­ry helps mod­el attacks and defens­es in com­put­er networks.
• Social Sci­ences: It’s used to study every­thing from mar­riage mar­kets to social norms.

But per­haps the most excit­ing fron­tier is quan­tum game the­o­ry, where researchers are explor­ing how quan­tum mechan­ics could rev­o­lu­tion­ize strate­gic inter­ac­tions. [17] In quan­tum games, play­ers can employ strate­gies that take advan­tage of quan­tum prop­er­ties like super­po­si­tion and entan­gle­ment, mean­ing your moves can exist in mul­ti­ple states at once until observed. [17]

REFLECTIONS AND TAKEAWAYS

So, what can we learn from the birth of game theory?

1. Strat­e­gy is every­where: Whether you’re play­ing a game, nego­ti­at­ing a deal, or just decid­ing what to have for lunch, you’re engag­ing in strate­gic thinking.
2. Math can make sense of chaos: Game the­o­ry shows how math­e­mat­i­cal tools can bring order to seem­ing­ly unpre­dictable situations.
3. Coop­er­a­tion and con­flict are two sides of the same coin: The Pris­on­er’s Dilem­ma reminds us that some­times, the best out­come for every­one requires trust and collaboration.

As John Nash once said: “The best play­ers are those who can adapt to any situation.”

So, the next time you’re play­ing a game, whether it’s chess, pok­er, or just a friend­ly debate, remem­ber: you’re not just play­ing. You’re doing math. You’re doing sci­ence. And you’re par­tic­i­pat­ing in a tra­di­tion that’s been unfold­ing for centuries.

Thank you for lis­ten­ing to math sci­ence his­to­ry and until next time carpe diem!

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BIBLIOGRAPHY

[1] Kuhn, H. W., and A. W. Tuck­er, eds. Con­tri­bu­tions to the The­o­ry of Games, Vol. 4. Annals of Math­e­mat­ics Stud­ies, 40. Prince­ton, NJ: Prince­ton Uni­ver­si­ty Press, 1959. As cit­ed in: Uni­ver­si­ty of Wash­ing­ton, CSE 490H. “John Von Neu­man­n’s Con­tri­bu­tions to Com­put­er Sci­ence.” https://courses.cs.washington.edu/courses/cse490h1/19wi/exhibit/john-von-neumann‑0.html

[2] Pri­vat­dozent. “The von Neumann–Morgenstern Col­lab­o­ra­tion (1938–43).” August 21, 2024. https://www.privatdozent.co/p/the-von-neumann-morgenstern-collaboration

[3] von Neu­mann, John. “Zur The­o­rie der Gesellschaftsspiele” [On the The­o­ry of Games of Strat­e­gy]. Math­e­ma­tis­che Annalen 100 (1928): 295–320. Trans­lat­ed by S. Bargmann in Con­tri­bu­tions to the The­o­ry of Games, Vol. 4, eds. A. W. Tuck­er and R. D. Luce. Prince­ton Uni­ver­si­ty Press, 1959.

[4] Weis­stein, Eric W. “Min­i­max The­o­rem.” Math­World. Wol­fram Research. https://archive.lib.msu.edu/crcmath/math/math/m/m254.htm

[5] Wikipedia. “Min­i­max The­o­rem.” Wiki­me­dia Foun­da­tion. https://en.wikipedia.org/wiki/Minimax_theorem (quot­ing von Neu­mann, as cit­ed in Casti, J. L. “Five Gold­en Rules.” New York: Wiley, 1996.)

[6] EBSCO Research. “Cold War and Math­e­mat­ics.” Research Starters: His­to­ry. https://www.ebsco.com/research-starters/history/cold-war-and-mathematics

[7] Nasar, Sylvia. A Beau­ti­ful Mind: The Life of Math­e­mat­i­cal Genius and Nobel Lau­re­ate John Nash. New York: Simon & Schus­ter, 1998. Ref­er­enced in: The Con­ver­sa­tion. “The Lega­cy of John Nash and His Equi­lib­ri­um The­o­ry.” May 2015. https://theconversation.com/the-legacy-of-john-nash-and-his-equilibrium-theory-42343

[8] The Nobel Prize. “Sveriges Riks­bank Prize in Eco­nom­ic Sci­ences in Mem­o­ry of Alfred Nobel 1994, Press Release.” https://www.nobelprize.org/prizes/economic-sciences/1994/press-release/

[9] Nash, John F. “Equi­lib­ri­um Points in N‑Person Games.” Pro­ceed­ings of the Nation­al Acad­e­my of Sci­ences 36 (1950): 48–49. Sum­ma­rized in: Myer­son, Roger B., and Philip J. Reny. “The Nash Equi­lib­ri­um: A Per­spec­tive.” PNAS 101, no. 10 (2004): 3999–4002. https://www.pnas.org/doi/10.1073/pnas.0308738101

[10] The Con­ver­sa­tion. “John Nash and His Con­tri­bu­tion to Game The­o­ry and Eco­nom­ics.” https://theconversation.com/john-nash-and-his-contribution-to-game-theory-and-economics-42355

[11] The Nobel Prize. “Sveriges Riks­bank Prize in Eco­nom­ic Sci­ences in Mem­o­ry of Alfred Nobel 1994, Press Release.” https://www.nobelprize.org/prizes/economic-sciences/1994/press-release/

[12] The Con­ver­sa­tion. “The Lega­cy of John Nash and His Equi­lib­ri­um The­o­ry.” May 2015. https://theconversation.com/the-legacy-of-john-nash-and-his-equilibrium-theory-42343

[13] The Con­ver­sa­tion. “Nobel Eco­nom­ics Prize: Wil­son and Mil­grom’s Insights into Auc­tions Could Dri­ve Down Car­bon Emis­sions.” Octo­ber 2020. https://theconversation.com/nobel-economics-prize-wilson-and-milgroms-insights-into-auctions-could-drive-down-carbon-emissions-148019

[14] Medi­um / Intel­lec­tu­al­ly Yours (IGTS DTU). “Under­stand­ing the Cold War Through Game The­o­ry.” August 2020. https://medium.com/intellectually-yours/understanding-the-cold-war-through-game-theory-44b6754266a9

[15] Google Deep­Mind. “Alpha­Go at 10: How AI Inno­va­tion Is Paving the Path to AGI.” March 2026. https://deepmind.google/blog/10-years-of-alphago/ See also: Google Deep­Mind. “Alp­haZe­ro: Shed­ding New Light on Chess, Sho­gi, and Go.” https://deepmind.google/discover/blog/alphazero-shedding-new-light-on-chess-shogi-and-go/

[16] Wikipedia. “Evo­lu­tion­ary Game The­o­ry.” Wiki­me­dia Foun­da­tion. https://en.wikipedia.org/wiki/Evolutionary_game_theory See also: May­nard Smith, John, and George R. Price. “The Log­ic of Ani­mal Con­flict.” Nature 246 (1973): 15–18. Ref­er­enced in: Stan­ford Ency­clo­pe­dia of Phi­los­o­phy. “Evo­lu­tion­ary Game The­o­ry.” https://plato.stanford.edu/entries/game-evolutionary/

[17] CSIRO Research. “Quan­tum Game The­o­ry.” https://research.csiro.au/quantumbattery/research/quantum-game-theory/ See also: Springer Nature. “Map­ping the Fron­tier: A Review of Quan­tum and Evo­lu­tion­ary Game The­o­ry for Com­plex Deci­sion-Mak­ing.” Quan­tum Infor­ma­tion Pro­cess­ing (2025). https://link.springer.com/article/10.1007/s11128-025–04913‑4