In the above decision tree,Peter picks first and Anita picks second.Peter and Anita both know the payoffs to each choice for both themselves and each other.
-Refer to the decision tree above.Suppose the decision tree applies to a one-week period and,at the end of the week,the game starts again (i.e. ,point X is at the end of each of the four possible outcomes).At the end of the second week,it starts over again,and so on.One would predict that
A) some cheating in the marriage would occur.
B) sooner or later,Peter will cheat.
C) at some point,Anita will cheat.
D) both will remain faithful over time.
E) Peter will always cheat.

Question

In the above decision tree,Peter picks first and Anita picks second.Peter and Anita both know the payoffs to each choice for both themselves and each other.
-Refer to the decision tree above.Suppose the decision tree applies to a one-week period and,at the end of the week,the game starts again (i.e. ,point X is at the end of each of the four possible outcomes).At the end of the second week,it starts over again,and so on.One would predict that
A) some cheating in the marriage would occur. 
B) sooner or later,Peter will cheat. 
C) at some point,Anita will cheat. 
D) both will remain faithful over time. 
E) Peter will always cheat.

Quizplus · Accepted Answer

Since the decision tree applies to a repeating game, both Peter and Anita have the incentive to maintain a cooperative relationship over time. If one cheats, the other may retaliate in the next round, leading to a suboptimal outcome for both. Therefore, both are likely to remain faithful over time.

In the Above Decision Tree,Peter Picks First and Anita Picks