Game Theory – An Introduction

Game theory, as with most logical and mathematical disciplines has interested me for a long time but until recently I haven’t had time or the motivation to look in to it very far. On my reading list from Christmas I have a small introduction to Game Theory. So far it’s been really quite interesting, I’ve lost the plot a few times and not understand one of the very basic concepts because of some of the wording, but it’s got all the information and there are no hard to understand formula.

Game Theory then, from what I understand of it so far, is the maths that can be used to determine what a ‘rational’ thing (or things) would do in a given situation. It’s applied across the board from the decisions animals and insects make and why they should make one decision over another all the way to what I should do in a game of poker.

In a basic game like Matching Pennies you can explain the very basics of Game Theory. The game involves two players, each has to choose either Heads or Tails on a penny and when they reveal their choice the first player wins if both pennies are the same (Heads, Heads/Tails, Tails) and the second player wins if the pennies are missmatched (Heads, Tails/Tails, Heads). It is known as a Zero-Sum Game because one player wins and the other player loses, i.e both players ‘payoffs’ are balanced, I win, you lose, visa versa, or a draw occurs in which all players get 0 payoff. A Zero-Sum game is therefore a game of pure-conflict, to maximize my payoff I have to try and make you lose by winning and visa versa. You could change Matching Pennies so that it was no longer Zero-Sum by giving some of the options benefit for both parties or the opposite. If we say that anything with a Tail in it means that both players win then it might be beneficial, if you know your opposition will play Heads, to always play Tails.

Game Theory is used to demonstrate what the best strategy is for both players, should the first player always go Heads, choose Heads two-thirds, one-half, one-quarter of the time, or maybe not at all? A decision matrix can be drawn up for the Matching Pennies game whereby if you win you get 1 and if you lose you get -1, that way the payoffs are balanced at a round 0.

Player 1
Heads
Player 1
Tails
Player 2
Heads
+1
-1
-1
+1
Player 2
Tails
-1
+1
+1
-1

In the top left you can see that if both player choose Heads then player one gets +1 and player two gets -1. We can understand from simple common sense that there isn’t really a best strategy unless you know what the other player is going to do, so I’m best off choosing Heads/Tails with an equal probability of 50%. This is called a mixed strategy as opposed to a pure strategy which will determine what a rational person should do in any situation of a Game.

Game Theory seems like it could be very useful in lots of situations where one should make a decision, the more I think about it the more I believe I’m going to start pondering options I take in terms of Game Theory.

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