GAME THEORY by Harry Spratt

This week in Economics Society, Harry addressed the topic of Game Theory, discussing the impact this has on behaviour of economic agents in the real world.

The questions that Harry addressed were the following:

  • What is Game Theory?
  • Why is it useful?
  • What is the future of game theory?

 

What is Game theory?

Game theory is a rapidly advancing subject area within behavioural economics; eight game-theorists have won the Nobel prize for economic sciences despite it being a relatively new subject area. It has also now been applied to areas other than economics involving decision making, such as biology, political sciences, and psychology.

The following quote by Roger B. Myerson, an American economist and Nobel Laureate, accurately captures the essence of game theory:

the study of mathematical models of conflict and cooperation between intelligent rational decision-makers”

At its core, it is just about strategic decision making, or how a decision is made by a “player” (the intelligent, rational decision-maker) in a “game” when he/she has to also take into account the decisions of others. Game theorists study many different types of games and try to find the equilibrium point where most games end up and the optimal strategies. They often represent the games through a pay-off matrix or through trees.

It is important to highlight that both the terms, ‘player’ and ‘game’, are used loosely – the player can be anyone capable of making a decision and the game doesn’t only refer to typical games like board games – although they are covered – but also to things like business and military decisions.

Game theory is also known as the Interactive Decision Theory, reflecting that the decisions involve considerations of other economic agents involved, making the process interactive.

History of development of Game theory

The first known discussion was by James Waldegrave in 1713. He wrote a letter discussing the optimal strategies for a card game known as le Her. However, it only really became accepted as its own unique field after a paper by John van Neumann was released in 1928 proving his Minimax theorem. This theorem in essence says that in a two-person, zero-sum game (where one’s gain is another’s loss), a player will try to minimise the maximum payoff for the other player, while maximising his own minimum payoff.

Game theory then started to become increasingly popular and  the Prisoner’s Dilemma first appeared in 1950. The Prisoner’s Dilemma is the most well-known example of game theory and describes the situation where there are two prisoners convicted of a crime. They are examined separately by the police and are not allowed to talk to each other. They have the choice to either confess or stay quiet about the crime they committed. If both confess, they are given 6 years each, but if they both stay quiet they only get 2 years each as the court does not have enough evidence to give them a longer sentence. However, if one confesses and the other stays silent, the confessor is allowed to go free whilst the other prisoner gets 10 years. Now the obvious optimal strategy for the two of them is to both stay silent as they only get 2 years each. But each prisoner is self-interested, and regardless of the other person’s choice confessing is the best option since if prisoner A remains silent, the best result for B is to confess, and if prisoner A confesses, the best result is again for B to confess. Therefore we arrive at what is known as the Nash Equilibrium where both prisoners confess.

Pay-off Matrix

Pay-off Matrix

The theory of Nash Equilibrium was developed by John Nash, perhaps one of the most famous game theorists. It is the equilibrium point, or the “solution”, in a non-cooperative game where the players are forced to change their decision based on what the other players will do, even if, for example, in the prisoner’s dilemma both prisoners wanted to stay quiet, they had to confess as they do not trust each other.

The RAND corporation who first pursued the prisoner’s dilemma wanted to apply it to global nuclear weapons strategies during the Cold War. Like the prisoner’s dilemma, countries had the choice of developing nuclear weapons or not developing them. The optimal strategy is of course to not have nuclear weapons, however, as countries did not trust each other, they feel compelled to develop nuclear weapons as a defence mechanism should another country try to attack them, resulting in the Nash equilibrium where most countries have nuclear weapons.

Types of games

Though there are countless different types of games, each involving its own game theory, in the world, most of them can be categorised. The following is an effective way to categorise them:

  • Cooperative and non-cooperative games – Cooperative games are where the players are allowed to work together and form legally-binding contracts whereas the other is where they are not allowed to cooperate. It is implied that there is communication in the former and none in the latter.
  • Simultaneous and Sequential – Simultaneous games are those where everybody has to make their decisions at the same time, or in other words, the decisions of others are not revealed until everybody has decided. Sequential games are those when turns are taken by the players in making a decision. Simultaneous games are the most interesting as it requires a player to predict what other players will do and adjust their own decision accordingly.
  • Perfect Information and imperfect information –  Perfect information is when every player in the game knows exactly what everyone else is doing or has done, whereas with imperfect information they do not. This is an important distinction as in games with imperfect information decision making needs to be more careful and is more risky as all the details about other players’ strategies are not known.
  • Zero sum games and non-zero sum games – Zero-sum games are where outcome values of a game added together sum to zero (where benefits to a player are positive values and costs are negative). This is easiest to explain with games where bets are involved. For example, Poker – assuming the dealer isn’t taking a cut of the bets – is a zero-sum game because the gains and losses of each player add up to zero. I.e. if one player win £100, all the other players collectively must have lost £100, so the gains and losses sum to zero.

Why is Game Theory useful?

There are many areas of life where game theory comes into practice. The following are some examples of the application of the Prisoner’s Dilemma:

  • Pricing and advertising
  • Nuclear strategy (described above)
  • Environmental policies
  • Investment in recessions

The future of Game Theory

Game theory is a rapidly progressing subfield of economics. Many of the ideas brought about by game theory are relevant in real world situations and can be applied to predict outcomes. But it is by no means perfect as human behaviour cannot be reduced simply to mathematical equations used in modelling given the complexity of human behaviour.  Also, game theory needs to account for other factors than just other players’ decisions that can and do affect decision making. Also, Harry proposed that the name ‘Interactive Decision Theory’ is better than ‘Game theory’ given the nature of decision making and its application to decisions outside the sphere of games to the real world.

The talk ended with several questions stimulating discussion on whether the Nash Equilibrium could be avoided in the market without this being a consequence of collusion and whether self-interest could involve considerations of our moral obligations. Any further questions and discussions on this topic are welcomed. Thank you to all those who attended.

Next Economics Society will take place in January, after the Christmas holiday. Hope you all have a relaxing break!

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