This feature was first published in September 2024 in My Mensa Weekly, our exclusive newsletter for Mensa members. Find out more about becoming a Mensa member here.

Words: Nicola More

Game theory is the science of strategy. It seeks to understand conflict and co-operation by studying quantitative models and hypothetical experiments. We explore what game theory is, who developed it and how it applies to our lives; from social behaviour and morality to economics and democracy. Does game theory hold the key to world peace?

Imagine yourself a hardened criminal gang lord, arrested by police and held for questioning along with one of your ‘associates’. A detective enters the room and admits he does not have enough evidence to prosecute. Instead, he intends to charge you both for a lesser crime, which will attract a one-year prison sentence. If you testify against your associate you will walk free, while he will serve three years. Your associate is offered the same deal. The catch? If you each throw the other under the bus, you will both get two years.

This is known as the Prisoner’s Dilemma, and it’s one of the most famous examples of game theory. Game theory uses mathematical modelling to better understand human and animal behaviour, and the strategies we employ to achieve success.

Tit-for-tat

Game theoretic thought can be traced right back to the principle of ‘know thy enemy’ in the ancient Chinese text The Art of War. Modern game theory emerged as a field of study in 1928 with the work of mathematician John van Neumann, who analysed two-person, zero-sum games, such as chess. Later scholars explored a much broader application, and today game theory is an umbrella term for decision-making strategies by humans, animals and computers.

Perhaps the most famous everyday examples are ‘chicken’ and ‘tit-for-tat’. Chicken pits opponents against each other in a high-risk situation, where the person who yields first is the ‘chicken’ or coward.

Meanwhile tit-for-tat is a highly effective strategy based on equivalent retaliation. At its worst, it can play out in violence (e.g. tit-for-tat bombings) but when the ‘players’ choose co-operation it can be a powerful agent for peace – more on that below.

A beautiful mind and its powerful applications

One of the most influential game theorists was John Nash, winner of the 1994 Nobel Prize for Economics and the subject of the movie The Beautiful Mind. His so-called ‘Nash equilibrium’ is a solution concept for non-co-operative games. If each player in a game has a strategy and cannot increase their payoff by changing that strategy, then the players have a Nash equilibrium.

This concept had a seismic impact on game theory, allowing for detailed analysis of how decisions are made in a range of situations, from economic trading to political negotiation.

Despite the complexity of the maths, game theory plays out in all our lives, in surprising and interesting ways:

Nuclear disarmament

Game theory has powerful applications to military strategy and nuclear disarmament. The Cold War brought considerable advances in the study, with models such as the Prisoner’s Dilemma and tit-for-tat providing a framework to analyse the stakes, deterrents and strategy of both sides.

Crucially, the repercussions of nuclear war could only be understood by looking at the long-term outcomes for both the Soviet Union and the United States, rather than exploring strategies in isolation. Similarly, visibility of threat is as important as threat itself. Or as Dr Strangelove observed: “The whole point of the doomsday machine is lost if you keep it a secret!”

WW1 Christmas truce

A more positive example of game theory in action was the historic Christmas Day football match played in No-Man’s Land during the First World War. This was tit-for-tat at its best, where each side reciprocated the ceasefire.

Nature ‘red in tooth and claw’

The Darwinian view of violent nature is at odds with some aspects of evolutionary biology, such as apparent acts of altruism among animals. The development of evolutionary game theory by John Maynard Smith in 1973 provided a breakthrough. While game theory posits that all ‘players’ have a rational strategy, evolutionary game theory points to non-rational, inherited strategies. Kin selection – favouring relatives over individuals – is one such built-in strategy that motivates animals to help others at their own expense.

Economics

Game theory has expansive applications in economics and business, including auctions, mergers and acquisitions pricing, fair division, duopolies and voting systems. The 2020 Nobel Prize for Economic Sciences went to game theorists Paul Milgrom and Robert Wilson for the development of simultaneous, multi-round auctions. Their advances in the field of ‘auctionomics’ had a profound effect on the functions of the stock market.

Game theory on screen

We have established that game theory is not really about games. Yet its principles have also been adopted by game designers to ensure their games are fair, and don’t offer advantage to any particular player. Look to huge online games such as Fortnite to see game theory in action.

Or, staying with popular culture, watch Heath Ledger’s ‘Joker’ set up his own memorable Prisoner’s Dilemma, when he tells passengers in two different ferries to bomb each other to save themselves. You just never know when game theory could save the day.

Play the game

Want to try out some game theory strategies for yourself? Explore the role of trust in game theory in this 30-minute game.