Question

Two persons A and B without showing each other, place a coin each on the table. If the coin happens to be of the same denomination player A will take both of them. If they happen to be of different denominations, Player B will take both of them. Suppose Player A has a few one rupee coins and two rupee coins and suppose player B has few one – rupee, two-rupee and five-rupee coins. Write down the payoff matrix of A. Does the game have saddle point ? If so, write down the solution.

Answer 1

The pay off matrix of player A is

The minimum pay off in each row is Circled. The maximum pay off in each column is boxed. Here row minimums are repeated. 

The pay off ‘-1’ at (1, 3) is circled as well as boxed, which is the saddle point. The solution to the games is:.

The best strategies for player A is A₁, and for B is B₃ i.e., player A always use to play with 1 Re coin and player B with 5 Re. coin. 

Value of the game V = -1.