Question : Two companies A and B engaged in a patent race. : 6603
Two companies A and B are engaged in a patent race. The winner obtains 4, the other company obtains zero. Each company can invest either nothing (c_{1}=0), c_{2}=1 or c_{3} = 2. Whoever invests more, wins the race. If both A and B invest the same amount they will complete the development of the technology at the same time. But a fierce competition together with a legal fight on the Intellectual Property will reduce their profit to zero and they would not be able to recover any part of their investment. Fill the blanks in the matrix of this strategic game.
\ B
A \
C_{1} =0
C_{2} =1
C_{3} =2
(P_{1} ) C_{1}
(P_{2} ) C_{2}
(1-P_{1} –P_{2} ) C_{3}
Is ((1/4, 1/4, 1/2), (1/4, 1/4, 1/2)) that gives payoffs (0,0) the unique equilibrium point? ___ ___ (Answer yes or no)
\ B A \ |
C_{1} =0 |
C_{2} =1 |
C_{3} =2 |
(P_{1} ) C_{1} |
, |
, |
, |
(P_{2} ) C_{2} |
, |
, |
, |
(1-P_{1} –P_{2} ) C_{3} |
, |
, |
, |