Question

Andile Sell Hold Hold R10m, R10m R1m, R8m Smuts SeR8m, R1m R3m, R3m

a) Explain why in a mixed strategy Nash equilibrium each player must be indifferent between the pure strategies that are used in her mixed strategy.                                          

b) How will the mixed strategy Nash equilibrium be affected if the payoff that the players get from both holding their investments are increased (keeping all other payoffs the same)?   

c) How can this change in mix probabilities be interpreted in terms of the players' uncertain subjective beliefs?

Answer 1

Andile Set ( Smuts Held Sell Assume thot smuis b elieve Andile wi play hofd with probability p" an Andile would beli eve thet myt wir play hold coith pmbabilrty We need to find value oF p such that bPia er is indifferent between the strategies for Smuts -2 Far Andlile

thet f Smuts believe the Andile plays Hold withbaity p 2 It means then Smut know」 An te thet Smut wil choosc Set if P41/2 Smu 4 Similorly, Andlile choosc selF I2 An dile will choojc Hold f 2 (Hold, Hod) increases to Ctom x ,iom+ x) hen Expected value of patoF increases therefor Yepeoting port improved holding pcyoff 2. similar f 2.

2 then beth wilI plares choose to SeIl フー2x- then brt n will played choo丿e- to-hold henu du to change in pff Payoff fom holding probability de of cnange mixed Strotegy na」h egwi'bnum ay o incveases As x tenols to increase prnbatiity of holding vemere decreaje Mixed Strateg nash