In some legislatures, proposals for modifications of the law are formulated by committees. Under the "closed rule", the legislature may either accept or reject a proposed modification, but may not propose an alternative. In the event of a rejection, the existing law is unchanged.
Model an outcome as a number y ∈ [0; 1] , and let y0 represent the status quo. The legislature and the committee do not share the same preferences over policy outcomes. In particular, the legislature has preferences represented by the payoff function ul (y) = - y, while the committee's preferences are represented by the utility function uc (y) = - |y - yc| which yc > 0 .
(a) Model this procedure under the "closed rule" as an extensive game and find the subgame perfect equilibrium as a function of the status quo outcome y0.
(b) Show that for a range of values of y0 , an increase in the value of y0 leads to a decrease in the value of the equilibrium outcome (i.e., in some cases a worse status quo for the legislature may lead to a better policy outcome for the legislature).