Question

Consider a subtraction game with subtraction set S= {1,4} starting with 6 chips. Player 1 goes first, and if Player 1 is the last to remove a chip, then Player 2 pays one dollar to Player 1; if Player 2 is the last to remove a chip, then Player 1 pays one dollar to Player 2. a) Find the payoff matrix for the game (create matrix)  b) Find v+ and v-

Answer 1

SOLUTION:

Given That data Consider a subtraction game with subtraction set S= {1,4} starting with 6 chips. Player 1 goes first, and if Player 1 is the last to remove a chip, then Player 2 pays one dollar to Player 1; if Player 2 is the last to remove a chip, then Player 1 pays one dollar to Player 2.

So

(a)

Player 1 goes first,

S = {1 , 4} stating with 6 chips.

Player 1 is the last to remove a chip.

Player 2 pays one dollar to player 1.

If player 2 is the last to remove a chip

Than player 1 pays one dollar to player 2.

PAYOFF MATRIX:

Player 1 player 2

Chips dollar

Player 1 chips (0,4) (1,2)

Player 2 dollar (2,1) (1.4)

The payoff matrix there basic parts.==>[Opponents , Strategists, Outcome].