1. Game theory is the study of the best play–safe strategy to adopt if 2 players are playing a game where decisions affect each other. Ex Two men are caught with forged £20 notes. They are interrogated separately and as there is no evidence as whether one of them is the counterfeiter the following proposition is put to each of them separately. 1) If neither of you confess to counterfeiting then you will be charged with possession and receive 1  years. 2) If you both confess then you will each receive 3 years. 3) If one of you confesses then you will receive a free pardon and the other one will receive 7 years. This is the Prisoners Dilemma. Neither prisoner knows how the other will plead - interrogated separately Game theory

2. If he does not confess the best is that he will receive 1  years and the worst is 7 years. If he does confess the best is that he will receive a pardon and the worst is 3 years. B confesses B does not confess Worst outcome for A A confesses (–3, –3) (0, –7)–3 A does not confess (–7, 0)(–1 , –1  )–7 Worst outcome for B –3 –7 To minimise the worst outcome A should confess. B has exactly the same choices and he to should confess. So the both confess and the police get the glory!!!

3. Each player looks for the worst that can happen if he makes each choice in turn. He then picks the choice that results in the least, worst option The minimum value in each row (for player A) and each column (for player B) is listed at the end of the row/column. We then select the maximum of these minimums which tells us which option the player should choose. Note: If A chooses option 1 we say that A plays 1. B confesses B does not confess Worst outcome for A A confesses (–3, –3) (0, –7) –3 A does not confess (–7, 0)(–1 , –1  ) –7 Worst outcome for B –3 –7

4. B Plays 1 B Plays 2 B plays 3Worst outcome for A A plays 1(8, 2)(0, 9)(7, 3)0 A plays 2(3, 6)(9, 0)(2, 7)2 A plays 3(1, 7)(6, 4)(8, 1)1 A plays 4(4, 2)(4, 6)(5, 1)4 Worst outcome for B201 In the pay–off matrix below player A has a choice of four options, player B three. The outcomes are given as ordered pairs, (A's winnings, B's winnings) For player A the worst outcome if he chooses option 1 is a win of 0, if he chooses option 2 his worst outcome is a win of 2, and so on. Similarly for player B. We now look at A's worst outcomes and choose the option that gives him the best result. In this case A should play 4. Looking at B's best worst outcomes, we can see that B should play 1.

5. By playing safe the outcome is (4, 2) – A wins 4 and B wins 2. A play safe strategy is to choose the option whose worst outcome is as good as possible. In the example above it would certainly pay the players to collaborate Eg If A plays 3 and B plays 2 the result is (6, 4) and both players increase their winnings. Also if the game were played many times it would pay each player to vary their strategy, for example if A knew that B would play 1, he could play 1 himself on occasion scooping a win of 8. Similarly if B were sure that A would play 4 he could play 2 on occasion scooping a win of 6. B Plays 1B Plays 2B plays 3Worst outcome for A A plays 1(8, 2)(0, 9)(7, 3)0 A plays 2(3, 6)(9, 0)(2, 7)2 A plays 3(1, 7)(6, 4)(8, 1)1 A plays 4(4, 2)(4, 6)(5, 1)4 Worst outcome for B201