Consider a modified form of Matching biased coins game problem. The matching player is
paid Rs 1.00 if the two coins turn both heads. he wins nothing if the coins turn both tail. The non-
matching player is paid Rs. 0.50 when the two coins do not match. Given the choice of being the
matching or nonÂ- matching player, which one would you choose and what would be your
strategy.
Answers
Answer:
Explanation: The payoff matrix for the matching player is given by
non matching player
H T
Matching player H 8 -3
T -3 1
The payoff matrix does not posses any saddle point. The player will used mixed strategies. Optimum strategies for matching players and non matching players are
p₁ = a₂₂ - a₂₁ / a₁₁ + a₂₂ - (a₁₂ + a₂₁)
p₁ = 1 - (-3) /8 + 1 - (-3-3)
p₁= 4/15
q₁ = a₂₂ - a₁₂ / a₁₁ + a₂₂ - ( a₁₂ + a ₂₁)
q₁ = 1-(-3) / 8 + 1 - (-3-3) = 4/15
The expected value of the game
v = a₁₁ a₂₂ - a₁₂ a₂₁ / a₁₁ + a₂₂ - ( a₁₂ + a₂₁ )
v = 8 * 1 - (-3 ) (-3) / 8 + 1 - 1 (-3-3)
= -1/15