Question

About a decade ago, the incoming Republicans in the House of Representatives said they would institute a new practice. They could decide to do this because they were in the majority. The plan was that, before a new session began, Republican members would read the US Constitution aloud. (I’m sure that part of the motive was patriotism, but I think it’s also fair to say that their implicit suggestion was that many laws the previous Democratic majority had passed were unconstitutional. Certain unfortunate parts of the full Constitution were to be omitted, I think.)

The Democrats then asked to participate in the reading, and that’s what happened in the end -- various members of both parties stepped up to the podium and read each section of the Constitution.

Consider the following game. Its moves are made sequentially, and so it is easiest to represent it as a tree. There are two players - the group of House Republicans and the group of House Democrats. The Republicans decide whether to announce the practice of reading the Constitution or to not announce that. If they do not announce it, the game ends and the parties receive certain payoffs. Announcing it means that they’ll do it. If the Republicans do announce the new practice, the Democrats decide whether to request to join them in the reading, or to not request that. If the Democrats do not request that the game ends and the parties receive certain payoffs. If the Democrats do request that, then the Republicans decide whether to let the Democrats join the reading, or not to let them. In either case the game ends, with certain payoffs.

(a) Draw the tree, labeling the players and the moves. You can call the moves A, NA, for announce and not announce the plan, R an NR for request and not request to join, and L and NL for let or not let the Democrats join. Add reasonable payoffs.

(b) List the strategies for each party.

7. In class I talked about the children going to a birthday party and choosing one room or the other, room A or room B. They make the choice first, then have to spend the whole party in that room. There are 6 girls and 6 boys.

(a) each boy wants to be in a room with three girls and each girl wants to be in a room with three boys. Give an equilibrium

(b) Is it an equilibrium for all 12 to choose room A?

(c) how about each girl wants to be in a room with an even number of boys, and each boy wants to be in a room with an even number of girls.

Answer 1

Refer the game tree, If republican doesn't announce it would be status quo and the payoff is same low and assumed to be (2,2)

If republican announce, and democrats don't request then democrats are at disadvantage (displays lower patronism) and republican wins the game with payoff (5,2). If democrats request and republican doesn't let them then republican would be at disadvantage as democrats will display this as stunt. In this case democrats win with payoff of (2,5). If democrats request and republicans allow then payoff would be (3,3) i.e slightly higher from status quo but both end with similar payoff.

It was an unconditional strategic move for republican. For democrats it was compellent conditional strategic move.

7. a) Equilibrium would be all the pairs where the condition is satisfied (Boy A,Girl A,Boy B,Girl B) = (3,3, 3, 3), (6, 6, 0, 0), (0, 0, 6, 6)

b) yes all 12 in a room is an equilibrium

c) Possible equilibrium are (Boy A,Girl A,Boy B,Girl B) = (2,2,4,4), (2,4,4,2), (4,4,2,2), (4,2,2,4)