Walter A. Haas School of BusinessProblem Set 3

University of California, BerkeleySpring 1999

Professor Rui de FigueiredoDue: April 15, 1999

at the beginning of class

BA296-10/PS232B: FORMAL ANALYSIS OF POLITICAL INSTITUTIONS

  1. In the Gilligan and Krehbiel model, consider the case of a restrictive procedure and committee expertise. What is the equilibrium if p0 = 0? Show it.
  1. In Gilligan and Krehbiel’s model with an unrestrictive procedure, show that an equilibrium can never have the property that b() is strictly decreasing on any interval [1,2]. That is, if the floor were to choose a strategy pf(b) that is responsive (i.e. strictly increasing) in b=b() on [1,2], then one or both of the players would want to change its strategy.
  1. In Snyder’s model, suppose that the n lobbyists can discriminate in paying their bribes. Characterize the optimal bribes and position x under the assumptions used in section 3.
  1. In Epstein and O’Halloran, discretion is symmetric around the legislator’s ideal point (i.e. |p|d). Now relax the assumption that there is symmetry and allow the legislator to pick any interval [d1,d2]. Would that change the substantive intuition they provide? Discuss.
  1. In Ingberman and Yao, a president who violates a commitment suffers a penalty (of some form) after violating a commitment. The rationale they provide is that voters will “punish” commitment violators. Discuss the reasonableness of this assumption (i.e. when would (rational) voters behave this way?). How might a model that addresses any of your concerns look?
  1. In Banks’ model, suppose c is common knowledge, and that v is distributed according to a uniform density function on the interval [0, ]. The structure of the game is as in Banks, but instead of a budget request, the agency submits a statement w about the value of the program. Let the strategy of A be denoted by (v), so w = (v). Using the same notation for accepting, rejecting, and auditing, characterize the sequential equilibrium of the game. (Here, auditing involves discovering the true value v of the program).
  1. In Banks’ model, suppose that the perquisites obtained by the agency are not proportional to c, as Banks assumes, but instead are the difference between the budget received and the true cost. That is, if A submits a budget request b and it is accepted, the gain to the agency is b-c. If it is audited, then L provides a budget of c and the gain to the agency is 0. If the agency maximizes the expected perquisites, what is the sequential equilibrium?
  1. In Banks’ model of agency budgeting, consider the following candidates for an equilibria under a closed procedure:

a) The audit and acceptance functions are the same as in Proposition 1 for b[k,v), but (c)=c+k for c[0,v-k). First, find 1(.) such that if c[0,v-k) the agency will use (c) above rather than submit a budget b=v. Second, show why this is or is not an equilibrium. Note that the attractiveness of this candidate equilibrium is that on the interval (v-2k,v-k) the legislature is better off when (c)=c+k is used.

b) The audit and acceptance functions are as in Proposition 1 with the exception that when b=v the legislature does not audit, but rejects the budget with probability 3(.)>0. First, find the 3(.) such that the agency with c=v-2k is indifferent between proposing b=c+k and b=v. Second, show why this is or is not an equilibrium. Note that the attractiveness of this alternative is that it saves on auditing costs.