a game in which player 1 has three pure strategies A B and C

a game in which player 1 has three pure strategies A, B, and C. A generic mixed strategy p1 = (p A 1 , pB 1 , pC 1 ).

1. Write down the three mixed strategies that correspond to the three pure strategies.

2. Write down the mixed strategy that corresponds to the case when A is twice as likely as B and twice as likely as C.

3. Write down the mixed strategy that corresponds to the case when A is three times as likely as B with B being twice as likely as C.

Solution

for A its PA 1, FOR B ITS PB 1 , FOR C ITS PC 1

2) IF A IS TWICE LIKELY AS B THEN LET MIXED GENREIC FOR B BE PB 1 THEN FOR A WILL BE PB 2

AND IF B IS TWICE LIKELY AS C THEN LET C BE PC 1 THEN FOR B WILL BE PC 2

3) LET FOR C BE PC 1 THEN FOR B WILL BE PC 2 THEN FOR A WILL BE PC 3*2 = PC 6