Consider a modified form of matching biased coins game problem. The matching player is paid Rs. 8 if the two coins turn both heads and Rs. 1 if the coins turns both tails. The non-matching player is paid Rs. 3 when the two coins do not match. Given the choice of being the matching or non-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