Let there be a dilemma facing your company. Your company can either collude or c
ID: 1128894 • Letter: L
Question
Let there be a dilemma facing your company. Your company can either collude or compete with a rival over some issue of importance to both. Payoffs are as follows.
Your Company
Cheat Collude
Cheat $2/$2 $10/$1.0
Their Company
Collude $1/$10 $5/$5
a) Identify the equilibrium, it one exists. Explain your reasoning.
b) Identify the equilibrium that would obtain if the game was played repeatedly for an indeterminate number of times.
c) Would your answer to b) change if the game were played a definite number of times, like 10 times? If it would change, what is the new equilibrium. Explain.
Explanation / Answer
a) An equilibrium in this game is that both the players will cheat. Let's start from the point where they are getting equal payoffs that is colluding. From this point, if one player cheats their return will increase to $10 from $5. So, its beneficial for the players to cheat. Looking at that benefit both the players will cheat and end up getting only $2.
If from the point where both the players are cheating anyone unilaterally tries to deviate i.e. collude then he will get a payoff of only $1. So they will continue with the strategy to cheat.
b) IF the game was played indeterminately then both the players will Collude. In this case, both the player know that if they cheat their profit is going down considerably i.e. from $5 both to $2 both that will act as a deterrence for the players to cheat.
c) If the game was to be played only for 10 times then, in that case, the players will collude for the first nine times and then cheat for the tenth time. Because both of them knows there will not be 11th time so they want to maximize their profit by cheating and get a return of $10. And both will follow a strategy to cheat and end up getting only $2.
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