Question

1. Assume a simple 2 player, sequential move game occurs as follows:
   1. Play rotates back and forth between players- player 1 moves first, then player 2, then player 1 again……and so on.
   2. Each time a player gets a chance to move, they choose a number 1 through 5 inclusive (so that 1,2,3,4, & 5 are the five choices they have).
   3. Every time a number gets selected, the number is added to a running tally of all numbers that have been selected.
   4. The game ends when a player selects a number that places the running tally at 36. The player that selected the final number wins and receives a positive payoff, the other player losses- and receives nothing.

Questions:

a. What is the specific technique that game theory suggests be used to formally analyze the nature of this game?

b. If you could choose to play this game, would you choose to play first or second?  

c. Assuming you could choose to play from the position of movement you identified above- write out the strategy you would follow to play the game.

d. How would you try to play this game if you were forced to move in the position you DID NOT select in part ii? Describe the strategy you would you follow in this case.

Answer 1

1. Backward induction technique and rational assumption with the belief that everyone has full information and every player is rational, is the technique to be used to solve this game.

2. I would chose to play second.

3. I would repeat the number chosen by the player 1, till it reaches some close (within the range of 1-5) from 36.

4. If I am forced to play first, I'll try to confuse the player by playing 1 for multiple times, and then between somewhere i select 2, to get the game in my court.