1. Game Theory and Applications following H. Varian Chapters 28 & 29

4. Defining a Nash Equilibrium The situation when Player A's choice is optimal for him given Player B's choice; and Player B's choice at the same time is optimal for him given Player A's choice. Or: A pair of strategies (r*,c*) such that c*=b c (r*) and r*=b r (c*), where c* is Player B's best response, and r* is Player A's best response, and b is a function that chooses the best response for player i=r,c.

5. Mixed Strategies:

6. Let r be the probability that "Row" plays Top and let c be the probability that "Column" plays Left. Combination Probability PayofftoRow Top, Left rc 2 Bottom, Left (1-r)c 0 Top, Right r(1-c) 0 Bottom,Right (1-r)(1-c) 1 Row's payoff= 2rc + 1 -r - c +rc; In changes:  RowPay=(3c-1)  r Col's payoff=cr +2(1-c)(1-r); In changes:  ColPay=(3r-2)  c