1. Each of two roommates simultaneously decides whether to contribute $100 to buying a common dining table. (Roommates contribute ei- ther the full $100 or nothing; they cannot contribute an intermediate amount. Also, they cannot change their minds after making the deci- sion.) If both roommates contribute, so that they buy a $200 table, they both get an enjoyment benefit out of it that is worth $150. If one of them contributes, so that they buy a $100 table, they both get a benefit worth $75. If neither contributes, they do not buy a table and do not get the benefits. (a) (b) (c) (8pts) Draw the payoffs of the game in a 2 by 2 matrix and solve for the Nash equilibirum. (8pts) Argue informally but carefully that with the distributional preferences models we have considered in class, there can be at least two equilibria: one in which both roommates contribute and one in which neither does. (8pts) Argue informally but carefully that the same is true in Rabin's intentions-based model of fairness. (8pts) Suppose roommates are playing an equilibrium in which they are both contributing to the public good. As you have ar- gued in the previous two parts, this is consistent with distribu- tional preferences models as well as intentions-based models. But suppose you want to know which model is motivating the room- mates' behaviour. What is a simple modification of the game in part (a) such that by comparing play in the original game to that FIGURE | - A CENTIPEDE GAME in the modification, we can tell whether intentions-based motiva- tions are contributing to the roommates' behaviour