Question

There are two countries, A and B. They have a dispute over a prize of size one (think of a territory whose area or economic value we normalized to one). Denote country A’s share of a negotiated settlement by x and country B’s share by 1 − x. Thus country A would like x to be as close to 1 as possible; country B would like x to be as small as possible.

An alternative way of settling their dispute is by fighting a war. In that case, countries AandBsufferthecostcA andcB,respectively,with0<cA <1and0<cB <1. Country A wins the war with probability p; country B wins it with probability 1 − p. The eventual winner get the entire prize but both countries suffer their respective cost of fighting.

(a) Suppose p=1, cA = 3, and cB = 4. On aline segment of length one, mark country A’s expected payoff from fighting a war, country B’s expected payoff from fighting a war, the set of negotiated settlements preferred to war by country A, the set of negotiated settlements preferred to war by country B, and the set of negotiated settlements preferred to war by both countries (i.e. the “bargaining range.”)

Answer 1

We first calculate the values of the respected payoffs:

1) A's expected payoff from fighting the war, is

2) B's expected payoff from fighting the war, is

A prefers negotiated settlements if x > p-cA.. This is required set of negotiated settlements for A

B prefers negotiated settlements if 1-x > 1-p-cB => x < p + cB...This is required set of negotiated settlements for B.

If there is a common region between both set, then settlement will happen.

All these values can be plotted on a line segment of unit length if we know the values of p, cA and cB. But the given values of p=1, cA=3 and cB = 4 are invalid, therefore I cannot plot these values and sets of region requested. I have still solved the question now you have to just put the valid values of given parameters and plot them.

answered by: anonymous