Question

4. [Pure Strategy Nash Equilibria] Three friends Alice, Betty, and Carly have memberships at their local gym, and each are considering taking one of the group fitness classes: Kettle Bell, Pilates, or TRX. The three classes offer group discounts: N 00 10 Number of Students Kettle Bell Per-Member Price Pilates Per-Member Price 10 TRX Per-Member Price 12 8 10 8 8 Each of the friends have different preferences or valuations for the classes. If they take a class that has valuation v and pay a price p, then their net payoff for that class is v-p. Their valuations are as follows: Kettle Bell Pilates TRX Alice 20 10 24 Betty 12 25 10 Carly 20 8 18 The payoffs for this static game are represented below. The coordinates in each cell are in the order (Alice, Betty, Carly). C: Kettle Bell B: Kettle Bell B: Pilates B: TRX A: Kettle Bell (14, 6, 14) (12, 15, 12) (12,-2, 12) A: Pilates (0,4, 12) (2, 17, 10) (0, -2, 10) A: TRX (12, 4, 12) (12, 15, 10) (14,0, 10)

Answer 1

A) In game theory, a dominant strategy is the course of action that results in the highest payoff for a player regardless of what the other player does. Not all players in all games have dominant strategies; but when they do, they can blindly follow them

so Dormant strategy can becalculated as follows

No of students	1	2	3
Kettle Bell per Member price	10	8	6
Pilates per Member price	10	8	8
TRX per member price	12	10	8

so Dormant strategy is

Player A	Player B
10,12	6,8
8,10	8,12

Here this indicated that No 12 in player A and No 8 in player B has a dominant strategy in the first section and in the second section it is 8,10 and 8,12 so player A has 8,10 and player B as8,12 so 10 and 12 is greater so this indicated the dominant strategy

	Alice	Betty	Kerly
Kettle Bell	20	12	20
Pilates	10	25	8
TRX	12	10	18

Player A	Player B
12,20	10,12
8,18	12,25

Here this indicated that No 12 and No 20 in player A has a maximum strategy of 20 and there is also 8 and 18 in player A in which 18 is leading and in player B there is 10,12 and 12,25 in which 12 is greater than 10 and 25 is greater than 12

These are the payoffs for the strategy games

	B Kettle bell	B pilates	B TRX
A Kettle Bell	(14,6,14)	(10,17,0)	(10,-2,-2)
Pilates	(0,4,12)	(2,17,0)	(2,-2,0)
TRX	(12,4,12)	(12,17,0)	(14,0,-2)

Player A	Player B
6,14	6, 8
8,10	8,12

Here player A is 6,14 and 8,10 and player A is leading by 14 and 10 and player B has 6,8 and 8,12 and there are leading by 12 units

so these are the strategies which is followed here

B) Nash equilibrium is a concept within game theory where the optimal outcome of a game is where there is no incentive to deviate from their initial strategy. ... Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies.Feb 3

Dominant strategies are considered as better than other strategies, no matter what other players might do. In game theory, there are two kinds of strategic dominance: ... It must be noted that any dominant strategy equilibrium is always a Nash equilibrium. However, not all Nash equilibria are dominant strategy equilibria.

Applied to the real world, economists use the Nash equilibrium to predict how companies will respond to their competitors' prices. Two large companies setting pricing strategies to compete against each other will probably squeeze customers harder than they could if they each faced thousands of competitors.