1 Provide the normal and the reduced normal forms of the centipede game (which I ran as an experiment). Normal form: Player (...

1 Provide the normal and the reduced normal forms of the centipede game (which I ran as an experiment). Normal form: Player (...

1 Provide the normal and the reduced normal forms of the centipede game (which I ran as an experiment). Normal form: Player (...

1 Provide the normal and the reduced normal forms of the centipede game (which I ran as an experiment). Normal form: Player (...

Inf2C Computer Systems Tutorial 1, Week 3 Solutions Boris Grot, Paul Jackson, Stratis Viglas 1. Two’s complement. What decimal number doe...

Inf2C Computer Systems Tutorial 1, Week 3 Solutions Boris Grot, Paul Jackson, Stratis Viglas 1. Two’s complement. What decimal number doe...

Inf2C Computer Systems Tutorial 1, Week 3 Solutions Boris Grot, Paul Jackson, Stratis Viglas 1. Two’s complement. What decimal number doe...

1 M produces a good which is durable and indivisible in consumption to C , who values immediate ownership of the good at v . C is private...

1 M produces a good which is durable and indivisible in consumption to C , who values immediate ownership of the good at v . C is private...

Inf2C Computer Systems Tutorial 1, Week 3 Solutions Boris Grot, Paul Jackson, Stratis Viglas 1. Two’s complement. What decimal number doe...

1 Provide the normal and the reduced normal forms of the centipede game (which I ran as an experiment). Normal form: Player (6 6) (0 5) (10 3) (0 5) Player (1 1) (1 1) (1 1) (1 1) ( ) is equivalent to ( ) ! merge into . No other equivalent strategies 1 Reduced normal form: Player (6 6) (0 5) Player (10 3) (0 5) (1 1) (1 1) Payoffs: ( ) 2 2.(a) Find the normal form of the following game (which is known as ‘Battle of the Sexes’): Players and each choose whether to go to a football match ( ) or to a movie ( ) without observing the other player’s choice. Both prefer to go to an event together; but differ in their preferences over these events. If both players choose then earns 3 and earns 1; if both players choose then earns 3 and earns 1; and both earn 0 if they go to different events. 3 Player (3 1) (0 0) Player (0 0) Payoffs: ( ) 4 (1 3) (b) Provide the normal and the reduced normal forms of the following game, which is again played by and . Player starts the game by deciding whether to burn ( ) or not to burn ( ) one unit of utility. After has observed ’s decision, the two players play a Battle of the Sexes game. If has chosen then payoffs are the same as in part a) above; if has chosen then her payoff is one unit less than in Battle of the Sexes at every terminal node. (Player ’s payoffs are unaffected by ’s decision.) 5 Normal form: ’s strategy: means , followed by after and after , etc; ’s strategy: means after and after , etc Order of payoffs: ( ) (3 0) (3 0) (0 ¡1) (0 ¡1) (3 1) (3 1) (0 0) (0 0) 6 (3 0) (3 0) (0 ¡1) (0 ¡1) (0 0) (0 0) (1 3) (1 3) (0 ¡1) (0 ¡1) (1 2) (1 2) (3 1) (3 1) (0 0) (0 0) (0 ¡1) (0 ¡1) (1 2) (1 2) (0 0) (0 0) (1 3) (1 3) is equivalent to ! ; is equivalent to ! ; is equivalent to ! ; is equivalent to ! Reduced normal form: (3 0) (0 ¡1) (3 1) (0 0) (3 0) (0 ¡1) (0 0) (1 3) 7 (0 ¡1) (1 2) (3 1) (0 0) (0 ¡1) (1 2) (0 0) (1 3) 3. Consider the following game of “divide the dollar”. There is a dollar to be split between two players. Player 1 can offer either 25 cents or 50 cents to player 2, where an offer is the amount of the original dollar that player 1 would like player 2 to have. After player 2 gets an offer, she has the option of either accepting or rejecting the offer. If she accepts, she gets the offered amount and player 1 keeps the remainder. If she rejects, neither player gets anything. Each player’s payoff is the money she earns. Draw the game tree and the normal form. 8 Normal = reduced normal form: means accept 25 and reject 50, etc Player 1 25 50 (75 25) (5050) (75 25) (0 0) Player 2 (0 0) (5050) (0 0) (0 0) 9