What is ‘Game theory’?

Game theory can be described as the mathematical study of decision-making, of conflict and strategy in social situations.

The “game” is the interaction between two or more parties, and relies on people acting rationally, knowing the boundaries of the “game”, and knowing that the other party is equally cognisant of the rules. These strategic interactions form the crux of game theory. “Sometimes we use it knowingly, sometimes we do it intuitively,”

The theory has entered popular culture, perhaps most notably through Russell Crowe’s portrayal of Nobel laureate John Nash in the film A Beautiful Mind.

A pioneer of the theory, John D Williams, wrote a 1954 study – The Compleat Strategyst – which attempted to bring it to the masses. He said society “would benefit from having more persons informed regarding its nature; and that the knowledge would benefit the persons”.

Now it’s used by many different people across a broad spectrum of interests. “The major reason for the success was that in a variety of settings people began to realise they had to think formally and systematically about strategic interactions,” explains Rakesh Vohra, an economics professor at the University of Pennsylvania and senior member of the Game Theory Society. “Game theory revolutionised the study of economics.”

Auctions for infrastructure projects or Premier League TV rights deploy game theory. Dating applications and services rely on it. Companies selling consumer goods use game theory to predict how their competitors – and customers – would react in a price war.

Away from the decisions made by retailers, commercial negotiators and so on, quiz shows often use game theory. The Weakest Link is a notable example, where partnerships are formed and strategic decisions are made about who to cut from the team.

Some of the first codified uses of game theory were in war. Both the British and American military used early computers to run models that would utilise game theory to help commanders decide whether, where and when to attack the enemy.

Since then, the concept has evolved. As Vohra explains, “when game theory was first born, there was a group of people who thought that if we build a model large and complex enough and we crank that handle we will know what to do.”

Poker hand and chips

That was seen as too ambitious, and the theory has changed. “Instead what we’re trying to do is inform judgement,” says Vohra. “We cannot tell you what to do, except in very limited circumstances. But what we can do is tell you the important things you have to make a judgement about. In a complex world where there are many things you have to pay attention to, this is still enormously useful in terms of focusing your attention.”

The concept is not solely based in conflict and combat, though – it can also help co-operation. “In a zero-sum game, you can think about chess, where one person’s win means immediately another player loses,” argues Schweinzer. “There are other games like joint production. If the two of us write something together, we can both gain from that. There’s no winner and no loser, but the act of playing together generates something we can both benefit from – a win-win game.”

Ethicist Carissa Veliz, of the Oxford Uehiro Centre for Practical Ethics, agrees. “While game theory may appear to be essentially about situations involving opposed self-interests, it needn’t be.

“Selfishness need not be among the assumptions of game theory. In the classical Prisoner’s Dilemma, it is often assumed that each prisoner only values his or her own well-being. But we can imagine the case where both prisoners are genuinely disinterested activists, and each wants to leave prison as soon as possible because they sincerely believe they will do the most good in the world by furthering the respective cause they are committed to.”

The negotiations currently taking place between Greece and its creditors are a prime place to deploy game theory – not least because of Varoufakis’s past as a theorist in the field. “If you think about the renegotiation of the loans to Greece, this is a very good example of where you have a tension between competition and co-operation,” says Vohra.

Not everybody agrees. Sean Hargreaves Heap, a professor of political economy at King’s College London, who co-authored a critical introduction to game theory in the 1990s, believes that game theory is of little use to Greece’s financial negotiations.

“If you think the talks are like a game of chicken, it’s a case of who’s going to blink first – the Greek government or the Germans? That’s useful, but game theory merely tells you there are three different things you should expect in such a game of chicken,” he says.

“One is the Germans blink, the other is the Greeks blink, the third is that both sides toss a coin as to whether they blink or not. Game theory is a useful way of characterising the problem, but in terms of telling you what someone is going to do in a game of chicken, it’s completely hopeless.”

Hargreaves Heap wrote his book on game theory with a young academic born in Athens and educated in Essex and Birmingham. His co-author’s name? Yanis Varoufakis.

In biology, game theory has been used as a model to understand many different phenomena. It was first used to explain the evolution (and stability) of the approximate 1:1 sex ratios. (Fisher 1930) suggested that the 1:1 sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their number of grandchildren.

Additionally, biologists have used evolutionary game theory and the ESS to explain the emergence of animal communication. The analysis of signalling games and other communication games has provided insight into the evolution of communication among animals. For example, the mobbing behaviour of many species, in which a large number of prey animals attack a larger predator, seems to be an example of spontaneous emergent organization. Ants have also been shown to exhibit feed-forward behaviour akin to fashion (see Paul Ormerod’s Butterfly Economics).

Biologists have used the game of chicken to analyse fighting behaviour and territoriality.

According to Maynard Smith, in the preface to Evolution and the Theory of Games, “paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed”. Evolutionary game theory has been used to explain many seemingly incongruous phenomena in nature.

One such phenomenon is known as biological altruism. This is a situation in which an organism appears to act in a way that benefits other organisms and is detrimental to itself. This is distinct from traditional notions of altruism because such actions are not conscious, but appear to be evolutionary adaptations to increase overall fitness. Examples can be found in species ranging from vampire bats that regurgitate blood they have obtained from a night’s hunting and give it to group members who have failed to feed, to worker bees that care for the queen bee for their entire lives and never mate, to Vervet monkeys that warn group members of a predator’s approach, even when it endangers that individual’s chance of survival.[28] All of these actions increase the overall fitness of a group, but occur at a cost to the individual.

Evolutionary game theory explains this altruism with the idea of kin selection. Altruists discriminate between the individuals they help and favour relatives. Hamilton’s rule explains the evolutionary rationale behind this selection with the equation c<b*r where the cost (c) to the altruist must be less than the benefit (b) to the recipient multiplied by the coefficient of relatedness (r). The more closely related two organisms are causes the incidences of altruism to increase because they share many of the same alleles. This means that the altruistic individual, by ensuring that the alleles of its close relative are passed on, (through survival of its offspring) can forgo the option of having offspring itself because the same number of alleles are passed on. Helping a sibling for example (in diploid animals), has a coefficient of ½, because (on average) an individual shares ½ of the alleles in its sibling’s offspring. Ensuring that enough of a sibling’s offspring survive to adulthood precludes the necessity of the altruistic individual producing offspring.[28] The coefficient values depend heavily on the scope of the playing field; for example if the choice of whom to favor includes all genetic living things, not just all relatives, we assume the discrepancy between all humans only accounts for approximately 1% of the diversity in the playing field, a co-efficient that was ½ in the smaller field becomes 0.995. Similarly if it is considered that information other than that of a genetic nature (e.g. epigenetic, religion, science, etc.) persisted through time the playing field becomes larger still, and the discrepancies smaller.

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