2 Firms Dominant Strategy Rebates or no rebates?

Question

Firm 1 and 2 must decide whether to provide a 2.5% rebate during a traditional slow quarter in their industry. What are firm 1 and 2 dominant strategies based on

firm 1 no rebate A profit = 200 B Firm 1 profit = 120

Firm 2 no rebate Profit = 120 Firm 2 profit = 160

firm 1 Strategy. C profit = 220. D Firm 1 profit = 160

2.5% rebate. Profit = 40. Firm 2 profit = 140

initially I assessed the out come would be for firm 1 to provide the rebate and firm 2 no rebate. What dominant Strategy best defines this outcome if correct?

Answer 1

I think you have a problem with your Payoff Matrix

Firm 2

No Rebate Rebate

No Rebate 1 = 200 1= 120

2 = 120 2=160

Rebate 1= 220 1= 160

2= 40 2=140

It is bizarre that if both firms rebate that profits for firm 2 go up and firm 1 go down,. so be it.. Lets look at firm 2. If they opt for a rebate they will make either 160 or 140 depending upon what firm 1 does. if they do not rebate they make either 120 or 40. So for firm 2 the worst case scenario of a rebate is better than the best case scenario for no rebate.

Rebating is the dominant strategy for firm 2.

With firm 1 the worst case scenario with no rebate is 120 and the worst case with a rebate is 160. They do not have a dominant strategy but the max min strategy (best worst case is to rebate which happens to be the Nash equilibrium.

Hope this helps.