I'm very stuck - any help would be appreciated :)
Consider a 3 person legislature with a closed rule with 3 rounds dividing a dollar, but unanimous agreement is required. Proposers are randomly chosen each round. Assume a common discount factor δ.
(a) Derive what proposals are made in every round. What is the final equilibrium?
(b) Now consider the same bargaining model, but instead of random recognition, the legislators rotate control of the agenda. In round 1, legislator 1 makes a proposal. In round 2 legislator 2 makes the proposal. In round 3, legislator 3 makes the proposal. Derive what proposals are made in every round. What is the final equilibrium?
(c) If procedural rule changes to only require a majority vote, for what levels of patience would the legislature implement fixed order recognition? At what levels would the legislature implement random recognition?
I got a final equilibrium for (a) where proposer offers $\frac{\delta}{\delta+2}$ to the other two legislators, and in (b) Round 1 division is ($1-\delta$, $\delta-\delta^2$, $\delta^2$). I'm just not sure what to do for (c)