Robin and Cathy play a game of matching fingers. On a predetermined signal, both players simultaneously extend 1, 2, or 3 fingers from a closed fist. If the sum of the number of fingers extended is even, then Robin receives an amount in dollars equal to that sum from Cathy. If the sum of the numbers of fingers extended is odd, then Cathy receives an amount in dollars equal to that sum from Robin. (a) Construct the payoff matrix for the game. (Assume Robin is the row player and Cathy is the column player.)

Determine whether the two-person, zero-sum matrix game is strictly determined.   4 5   2 −4 If the game is strictly determined, answer the following. (If the game is not strictly determined, enter DNE for each.)(b) Find the optimal strategy for each player. The optimal strategy for the row player is to play row  .The optimal strategy for the column player is to play column  . (c) Find the value of the game.(d) Determine whether the game favors one player over the other. It favors the row player.It favors the column player.    It is fair.It is not strictly determined. (DNE)

Matching Pennies: Players 1 and 2 each put a penny on a table simultaneously. If the twopennies come up the same side (heads or tails) then player 1 gets both pennies; otherwiseplayer 2 gets both pennies. Represent this game as a matrix and find pure- and mixedstrategies equilibria.

The matrix for a strictly determined game is given. Find the value of the game. Is the game fair? -2 -1 - 3 2 0 2 -2 -3 -1 Select the correct choice below and fill in the answer box within your choice. (Type an integer or a decimal.) O The value of the game is O The value of the game is The game is fair. The game is not fair.