Prove that every 2 times 2 game has a nash equilibrium in, Management Theories

Prove that every 2 times 2 game has a nash equilibrium in

Prove that every 2 × 2 game has a Nash equilibrium (in either pure or mixed strategies). Do this by considering the following general game and breaking the analysis into two categories:

(a) one of the pure-strategy profiles is a Nash equilibrium, and

(b) none of the pure-strategy profiles is a Nash equilibrium.

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