Question

Suppose Ann is working on a project with John. Both must decide whether to put into a descent amount of effeort into the project. Since Ann is the leader of the project, her contribution determines whether the project will be successful. If she puts into a descent amount of effort, the project will be finished on time and each will enjoy 3 units of benefit. If she decides not do so, the project will not be finished on time, neither one will get benefit, Suppose a decent amount of effort incurs a cost of 1 unit for each person. Please draw normal form represent the situation and identify the Nash Equilibrium if there is any. Would both be happy about the outcome and why? Please explain in detail.

Answer 1

Answer:

It is a problem on game theory. Two persons are involved in the game. They are Ann and John. Among them Ann is leader. So the return will depend upon the action taken by Ann. John has no option but to follow what Ann is doing. If she puts into a decent effort the project will be finished in time. In that situation both of them will get benefit of 3 units. If she decides to put a decent amount of effort then each of them will incur a cost of 1 unit. Thus net benefit from decent effort is 3-1=2 units. Finally if no decent effort is made, then project will remain incomplete. None of them will gain anything.

Nash equilibrium is a situation where optimum benefit will accrue. Ann as a leader will optimize her pay off y putting decent effort. John being the follower will adopt the strategy of leader. It will give return of 2 units to both of them. It is equilibrium. It implies that players will not deviate from it as no extra gain will be available from such deviation.

Result: Nash equilibrium is put decent effort to gain 3 units each.