2. Assume the following game is played one time only. Based on the information i
ID: 1198571 • Letter: 2
Question
2. Assume the following game is played one time only. Based on the information in the payoff matrix below, PNC Bank and Citizens Bank are considering an implicit collusive agreement on interest rates. Payoffs to the two firms are represented in terms of profits in thousands of dollars.
a.) Does PNC have a dominant strategy? What is it?
b.) Does Citizens have a dominant strategy? What is it?
c.) Does the result of your answer change if the game is played an infinite number of times? Why or why not? Properly use game theoretic terminology in your answer.
Citizens Bank Collude: Raise Rates Defect: Keep Rates Where They Are (700, 800) PNC Collude: Raise (900, 600) Rates Defect: Keep Rates Where They Are (1100, 300) (800, 400)Explanation / Answer
a) PNC will have a dominant strategy if they get a better pyoff independent of the strategy of the competition. Here we see that either Citizen Bank (CB) either collude or defect, the dominant strategy for PNC is to defect as if CB colludes there payoffs are higher if they defect i.e. 1100 or if CB defects still the payoffs are higher if they defect i,e, 800.
b) Citizen Bank (CB) will have a dominant strategy if they get a better pyoff independent of the strategy of the competition. Here we see that either PNC either collude or defect, the dominant strategy for CB is to defect as if PNC colludes there payoffs are higher if they defect i.e. 800 or if PNC defects still the payoffs are higher if they defect i,e, 400.
c) If there are infinite repitition to this game then the results will change only if players now with experience of previous rounds recognize their mistake and then approach a strategy which is better. Here the trigger strategy would be if one of the player colludes. In that round the player may suffer a loss when the other player defects so the player will come back to its original strategy to defect because of tit-for-tat strategy and so they will be locked in this strategy to defect.
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