GAME THEORY
GROUP PROJECT
1. There is a unifying principle between the three cases. Let E be the total amount of
money, and D = d1+d2 be the total amount of debt. We can see right away that E is
split evenly between the two creditors when E is less than D. Next, when E = D, we see
that the debt is split evenly until one of the creditors has d1/2 of the debt. Then, the
rest of the debt is split between the rest of the creditors (In this situation we have only
1). In this case, we get 50 and 100 because D = E. Finally, when E > D, we see the
opposite of what we were doing earlier. Now, instead of giving everyone the same
amount of money, we'll give out losses. For now, let's say both of them get 100 and
200. Now, D – E is 50, which is the lost money that will be split between the two
parties. Thus, both creditors will have their debts cut by 25, which will leave them with
debts of 75 and 175.
2. Yes, this game can be thought of as a coalitional game. The two creditors stand to
make more money together than they would if they worked alone. As an example,
let's say this game is not cooperative. In the first case, A gets more money if he works
with B, so the debts would be split evenly. In the same way, in case 3, B gets more if
he
works
with
A
instead
of
alone.
Imputations are distributions that are both efficient and rational for each person. A
player would have to get less than if it worked alone. Hence, this is a solution.
3. Yes, this coalition is stable. This is because any deviation from the coalitional game will
not give any gain to the players. We have a core, i.e., a set of imputations that cannot
be dominated.
4. Yes, table B will also have a unifying principle between the three cases. The reason for
this is same as that of table A. In this case, estate has been changed with cost.