Game Theory and Its Applications

Game Theory examines our interactions and decisions in social contexts through the lens of ‘games’. It explores the outcomes of the different strategies available to their participants (known as either ‘players’ or ‘agents’) and looks to find the most ‘rational’ option, which means maximizing the payoff in terms of their own self-interest). Game Theory has been labeled a “descriptive” theory, as opposed to an “explanatory one”: it doesn’t explain why players act in a certain way, nor does it forecast the definite course of action they will take. Instead, it lends insight into how agents will act if they play rationally and consistently throughout. A ‘game’ can be broadly defined as a strategic scenario involving multiple participants: as Binmore asserts in Game Theory: a very short Introduction, games are in action “whenever human beings interact”. Therefore, because games need to involve more than one player, although many conventional games such as Risk, Volleyball, Spit, and Catan, are still mathematically classed as ‘games’, others such as Patience, crosswords, and the once-popular single-player version of Crossy Road, however enjoyable, are not technically games. Through games, game theory can be used to explain everyday phenomena and has applications in many fields Game Theory’s applications are ever-expanding, and there now exist many different types of games, from non-zero games to asymmetric games to combinatorial games, all of which describe are slightly different: some games have a winner, others don’t, etc., accommodating almost every type of social interaction there is.

History

Game Theory, remains in its infancy, at less than a century old, especially compared with other famous theorems (such as Pythagoras’ Theorem) which have aged millennia. Although the first recorded discussion of a game was in 1713 (within a letter of James Waldegrave’s), and underwent some scrutiny in the 19th and early 20th centuries, Game Theory as we know it today was only truly born in the early- to mid-20th Century with the publication of a paper titled On the Theory of Games of Strategy in 1928. This work, written by the allegedly-mad Hungarian mathematician John von Neuman, although not wholly exceptional in itself, led to the collaboration of von Neuman and Oskar Morgenstern, an eminent Austrian economist, and ultimately facilitated the publication of Theory of Games and Economic Behaviour in 1944. It was the later published, to a much greater extent than the former, which truly revolutionized the field, described decades later by the Princeton University Press as the “classic work upon which modern-day game theory is based”. When it was first invented, the theory could only be applied to specific circumstances, but since then, the scaffold has been “deepened and generalized”, growing in its complexity and applications. It really is a ‘living’ theory, continually evolving and adapting, changing with the world; I think that is partly what makes it so captivating, that there is so much more to learn about it and learn from it, for example, Game Theory has become a major source of novel concepts in Microeconomics.

Both silent: departmental each= 0.5h total

Both blame: school detention each= 2h total

One blames, One is silent: Blamer is let off, blame is given a Saturday= 3h total

Prisoner’s Dilemma

Undoubtedly the most widely-known toy game is the Prisoner’s Dilemma, a scenario which beautifully demonstrates how Game Theory can help us to choose the mathematically ‘sensible’ option while bringing to light the paradox that the algebraically-correct choice is often far from the optimal solution. Ordinarily, the infamous game is modeled using criminals and jail sentences, but in order to make it more resonant, ‘prison sentence’ will be exchanged for school detention and the game’s two criminals for two ill-behaved pupils. The - albeit minorly modified - the game goes like this: two students have breached the school’s Code of Conduct, but the teacher sanctioning them does not have enough evidence to convict them. Consequently, in order to obtain the truth, the teacher places them in separate rooms (likely somewhere in the ominously-named ‘Dungeons’) and offers them a choice: they can either remain silent or tell on their associate. The Prisoner’s Dilemma (or rather the Schoolchild’s Dilemma) is a textbook example of a non-zero-sum, non-cooperative game of complete information: the gains of a player do not necessarily counteract the losses of the other, both pupils cannot collaborate, yet each knows the full terms of the game and that their counterpart also answers to the same terms. The teacher sets out the conditions: if both students tell on one and other, they both receive a School Detention (one hour after school on a Friday); if one tells, but their loyal companion doesn’t, the informant suffers no penalty, while the betrayed friend weathers 3 hours in a Saturday Detention; whilst if they one tell on their accomplice, and the pythey each receive departmental detention lasting 15 minutes. What should they do? Obviously, the ideal option is that both remain silent: with this course of action, their combined sentence is a mere 30 minutes. However, because the players cannot communicate, a prisoner is no way of ensuring their accomplise will stay mute. Therefore, the rational (from a purely mathematical perspective) option is that they both give up their associate. This is known as the dominant strategy (it is the best tactic regardless of the other player’s actions): the player either suffers a 1-hour sentence or a no sentence at all, rather than the possibility of a 3-hour sentence. If both players, reason alike, the outcome is known as a Nash Equilibrium, which is simply a situation when both players employ the dominant strategy.

Vague applications (inc telecoms)

• Covid
• Evolutionary biology

Games don’t simply exist on the whiteboard, but also in reality. MAD (Mutually Assured Destruction) during the Cold War, awkward dodges in the street (a desperate attempt to maintain social distancing), and …….. are all examples of games which were and are played out in actuality.

The American, and later British, auctions, are a fantastic example of….

Philosophy and Ethics

From a philosophical perspective, Game Theory is intriguing. It imposes an algorithm on our decisions, making one wonder if you really can ‘win’ the game of life. In some ways, Game Theory can be restricting and liberating: in certain instances, one realizes that choices are finite, and questions the extent to which one really does have Free Will, but, on the other hand, in many cases, it can rid of us of indecision, help us to make more sensible choices, from which we gain the most. However, ethically speaking, the mathematically correct option, does not necessarily correspond with what we consider to be the morally ‘right’ one, introducing an ethical dilemma: the conflict of the benefits of the individual versus societal benefit. But morality is at the center of our society, it is the base of our religions: we need to be able to distinguish between the inherently ‘right’ and the inherently ‘wrong’, and the answers are given by game theory such as, in the Prisoner’s Dilemma, to tell on your friend, do not, to many seem morally right (although, for that matter, neither is disobedience in the first place). As Ethicist Carissa Veliz argues, in Game Theory assumes that the players only care about the best outcome for them, but in reality, this is often not true; in the prisoner’s dilemma. This brings to light one of the biggest caveats in game theory: it assumes that we play the game rationally, but humans have emotions, (hopefully) a moral compass, and common sense; they are neither robots nor slaves to algebra and calculations. Alternatively, the fact that game theory, especially during the Cold War time, through the eyes of game theorists, continues to build up a nuclear arsenal in order to compete ….the issue of nuclear weapons… Over time, this conflict could become increasingly problematic as people increasingly turn to mathematics for ‘moral’ justification.

Conclusion

Game theory and its uses are ever-expanding; it is a constantly blossoming, not static, theorem, something which makes it truly intriguing: there is such potential for discovery. Indeed, there is something so satisfying about whittling a series of options down to the rational one, although at times, game theory can become very complex, if not messy, when you introduce a multitude see Binmore. Game Theory, partly due to its recent founding unearths many deep-seated moral questions which have yet to be resolved, fact ethicists and philosophers will debate for years to come.