An NGO hires a village leader to prevent raids. This NGO values safe passage at V. The village leader does not care whether a raid occurs. Exerting an effort to stop raids costs the village leader c. Note: 

The NGO don't know whether or not the leader makes an effort. They are only aware if there is a raid or not.

 

When the leader exerts an effort, they prevent a raid. If they do not exert an effort, the NGO's convoy passes safely with probability.

 

1) The NGO offers an amount x to the village leader. Once the leader sees the offer, they decide whether or not to exert effort. The NGO will only pay x if the convoy passes safely. What values of V does the NGO make an offer strictly greater than 0? When the NGO makes its offer, what is its size?

2) If an offer strictly greater than 0 is made, does the offer size change as p increases?

3) If the NGO now knows if the leader exerted effort and now uses that to determine x, then what are the values of V? (still strictly greater than 0). Now what is the size of its offer?