Consider the following model of a budget process. At the beginning of the game, a Leader chooses a punishment to impose on all players if the Congress fails to pass a budget. Call this punishment p. The Leader can choose p = 0 (i.e., no punishment) or p = 1.5. The Congress then either compromises or it does not compromise. If the Congress compromises, a reduced budget is passed. If the Congress fails to compromise, then the status quo budget is passed and the penalty is implemented. Payoffs are as follows. The payoff to the Leader of the status quo is 0 and the compromise is 1. The payoff to the Congress of the status quo is 1 and the compromise is 0. Thus, the game is represented in Figure 2 (where the first payoff is always the Leader's).

Write down all of the Leader's strategies. Write down all of the Congress's strategies.

Write down the unique subgame perfect Nash equilibrium of this game. Describe what happens in this equilibrium.

Building on the previous question, now suppose that, should Congress fail to compromise, the Leader gets to choose whether or not to impose the punishment. That is,

2

the game is now the one represented in Figure 3:

In this revised game, write down all of the Leader's strategies and write down all of

the Congress's strategies.

In this revised game, write down any one subgame perfect Nash equilibrium. What happens in this equilibrium?

Explain how comparing the equilibrium outcomes in these two models illustrates how an inability to commit can make a player worse off.