Game Theory

In: Business and Management

Submitted By DenEd
Words 2617
Pages 11
Maths Presentation 21/01/09
Start with a brief timeline, including when applications to different areas were first used.
Game Theory
(i) Game Theory Introduction We begin with a simple, informal example of a game. Rousseau, in his Discourse on the Origin and basis of equality among men, comments:
“If a group of hunters set out to take a stag, they are fully aware that they would all have to remain faithfully at their posts in order to succeed, but if a hare happens to pass near one of them, there can be no doubt that he pursued it without qualm, and that once he had caught his prey, he cared very little whether or not he had made his companions miss theirs”
To make this into a game, we need to fill out a few details.
Suppose that there are only two hunters, and that they must decide simultaneously whether to hunt for a stag or for hare. Each player has a choice between two strategies: (hunt stag, hunt hare).
If both hunt stag, each gets half a stag
If both hunt hare, each gets one hare
If one hunts for hare while the other tries to take a stag, the former will catch a hare and the latter will catch nothing.
If we suppose that the utility of catching a stag is 4 and for a hare is 1, then the payoff matrix for the players can be summarised as follows: Stag Hare (2,2)
(0,1)

(1,0)
(1,1)

Game theory is concerned with what outcomes arise in equilibrium. An equilibrium outcome is one which consists of a strategy for each player which is that player’s best response to the strategies of all players. An equilibrium is a stable state which holds because no rational player has an incentive to deviate from that state, where a rational player is one who always attempts to maximise their utility from any situation which requires a choice between alternatives.
In the…...

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