Question

Remember the game of Matching Pennies: First, Player 1 chooses the side ofher penny (Heads or Tails) and conceals her choice from Player 2. Player 2then chooses a side of his penny. If they match, Player 1 takes a dollar fromPlayer 2; if they mismatch, Player 1 gives a dollar to Player 2.

1. Now consider the following variation of that game. After the coins areuncovered, Player 1 can choose to veto the game or not. If Player 1chooses to veto, then no transfer gets made (both players get $0).

(a) (5 points)Write this game in extensive form

(b) (5 points) How many strategies does Player 1 have?

2. Now consider a different variation: Player 1 has to choose to veto or notbefore picking a side of her penny. If she chooses not to veto, then thegame proceeds as regular Matching Pennies.

(a) (5 points) Write this game in extensive form.

(b) (5 points) Write this game in normal form.

Answer 1

1)

Player 1 can choose Head or Tail. Then player 2 can also choose Head or Tail. Now Player 1 has the option to veto or not to veto.

(a) the extensive form can be drawn as -

(b)

Lets consider player 1 strategy. Player 1 can choose Head at the start. Player 1 one can veto when she(player 1) choose Head and player 2 guess Head. Player 1 can also veto when she choose Head and player 2 guess Tail. Player 1 can veto when she choose Tail and player 2 guess head. Player 1 can veto when she choose tail and player 2 guess tail.We can denote this plan by (H, V, V, V, V). Now we can see that player 1 has 5 contingencies and has 2 option for each. Therefore she has 2⁵ strategies.

(2) In this variation, Player 1 has option to veto at the beginning.

(a) Extensive form can be drawn as -

(b)

In this scenerio player 1 has 3 strategies - (i)Veto, (ii) Not to veto and Head, (iii)Not to veto and Tail

and player 2 has 2 strategies - (i) Head (ii) Tail

This normalform can be drawn as -