Notes for Class: Thursday, 28 January

Game Theory

Game theory is widely regarded as having its origins in the mid-nineteenth century with the publication in 1838 of Augustin Cournot's Researches into the Mathematical Principles of the Theory of Wealth, in which he attempted explain the underlying rules governing the behaviour of duopolists. However, it was with the publication in 1944 ofJohn von Neumann and Oskar Morgenstern's The Theory of Games and Economic Behaviour that the modern principles of game theory were formulated.  Game theory has been widely applied to the behaviour of producers with a few or only one competitor.

What is a game?

All games have the following:

1. Rules, which govern conduct of the players
2. Pay-offs, such as win, lose or draw
3. Strategies, which influence the decision making process.

In applying game theory to the behaviour of firms we can suggest that firms face a number of strategic choices which govern their ability to achieve a desired pay-off, including:

Decisions on price and output, such as whether to:

·       Raise

·       Lower

·       Hold

Decisions on products, such as whether to:

·       Keep existing products

·       Develop new ones

Decisions on promoting products, such as whether to:

·       Spend more on advertising

·       Spend less

·       Keep spending constant

Firms could derive a range of possible pay-offs from their strategy choices, including:

·       More profits for shareholders

·       Greater market share

·       Improved chances of survival

·       Getting rid of a rival

The Prisoner’s Dilemma

The Prisoner's Dilemma is a simple game which illustrates the choices facing oligopolies. As you read the scenarios, you can play the part of one of the prisoners.

The scenario

Robin and Tom are prisoners:

They have been arrested for a petty crime, of which there is good evidence of their guilt – if found guilty they will receive a 2 year sentence.

During the interview the police officer becomes suspicious that the two prisoners are also guilty of a serious crime, but is not sure he has any evidence.

Robin and Tom are placed in separate rooms and cannot communicate with each other. The police officer tries to get them to confess to the serious crime by offering them some options, with possible pay-offs.

The options

Each is told that if they both confess to the serious crime they will receive a sentence of 3 years. However, each is also told that if he confesses and his partner does not, then he will get a light sentence of 1 year, and his partner will get 10 years. They know that if they both deny the serious offence they are certain to be found guilty of the lesser offence, and will get a 2 year sentence.