Graphical Method For 2 x n Game (Game Theory)

Graphical Method For 2 x n Game (Game Theory):-

Graphical method to solve those games which have 2 rows and n columns.

Algorithm to solve :-

STEP 1. Reduce the size of the pay-off matrix by applying Dominance property, if exists.

STEP 2. Let "x" be the probability of selection of alternative 1 by player A  & 1-x be the probability of selection of Alternative 2 by player A.

Derive the expected gain function of player A with respect to each of the alternative of  player B.

STEP 3. Find the value of the gain when "x=0" & "x=1".

STEP 4. Plot the gain function on a graph ,by assuming a suitable scale . ( keep X on x-axis & gain in y-axis).

STEP 5. Find the highest intersection point in the lower boundary of the graph i.e. Maximin Point.

STEP 6. If the number of lines passing through the maximin  points is only two from the 2x2 pay-off matrix , go to step 8, else go to STEP 7.

STEP 7. Identify any two lines with opposite slopes passing through that point then form a 2x2 matrix.

STEP 8. Solve the 2x2 game using odments and find the strategies for player A+B & also value of the game.

For more understanding you can download the Handouts by clicking here, for more numerical practice.
else
you can go to the
web.- https://drive.google.com/file/d/1bO5XBBPOckFaOUZJfGwVwLnlW3On6Qz2/view?usp=sharing

Thank you.