The Divide the Dollar example is a simple enough premise, three players are given a dollar and told to divide it among themselves. The catch is that it must be decided by majority vote. Under this conditions two of the three players can vote to split the dollar 50-50 and leave the last player with nothing.
The divide the dollar game can be expressed visually through the triangle of imputations. This allows for the players to find the core, in which every coalition formed is doing the best it possibly can. Using this triangle allows for the players to find imputations or a list of payoffs satisfying individual and collective rationality. In this example, the payoffs for each of the players will be X1, X2, and X3. The area of this triangle can be found through the formula A=1/2(s)(h), with s being the sides and h being the height. However, h can be replaced with (X1+X2+X3) as the sum length of each of these lines is equal to the height. These lines can then be used to find fractions which provide how the dollar should be split among the three players. Where the X point is located on the triangle can be changed through bargaining and the formation of coalitions.
Game Portfolio 