Let a 2 x n game where the payoff matrix will have 2 twos and n columns. Player A will choose two separate strategies. If there is no saddle point of the payoff matrix, this problem can be solved by:

  1. By using the rule of dominance, reduce the size of payoff matrix (wherever applicable)
  2. Let probability of strategy I be p and probability of strategy II be 1 – p. and write down expected gains of player A w.r.t to each strategies
  3. Now, plot the gain functions of the graph. p will be on the x-axis and gain function will be on the y-axis where p will vary between 0 and 1
  4. Player A is the maximum player. So after finding the highest intersection point in lower envelope or lower boundary of graph, mark this point as maximum point.
  5. If these numbers of lines are only two, then you have to obtain payoff matrix of 2 x 2 that contains the columns of these lines. If not, then move to step ‘6’ or else go to step ‘4’.
  6. If there are more than two lines passing through this highest point, then identify only two lines with opposite slope. With this, you can obtain a 2 x 2 payoff matrix as explained in step ‘5’
  7. Now, solve this 2 x 2 game.

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