# Let us modify the timing structure of the game of entry.

Let us modify the timing structure of the game of entry. Suppose that
Coke’s entry decision is made at the same time that Pepsi decides between tough and accommodate. Then, if Coke chooses to enter, it has further decision between tough and accommodate. Suppose that the payoffs at every terminal node that follow enter are exactly as before. If Coke stays out, then the payoffs are (0, -1) if Pepsi plays T and (0,0) if it plays A.
13.1  Write down the extensive form of this game. How many subgames are there in this game?
13.2  Solve the game by backward induction. Be sure to detail every step.
Consider the following (idealized) model of voting in Senate committee. The committee is made up of three members: Al (A), Bob (B), and Christopher (C), two Republicans and a Democrat, respectively. They are confronted with two versions of a bill (to end welfare as we know it). Version 1 proposes a radical restructuring of the current system, while Version 2 proposes more modest overhaul. The committee members vote simultaneously, and they recommend the version that gets majority of votes. At that point, the full Senate votes simultaneously and along party lines between that version and the current system. If a majority of the Senate votes in favor of the bill it passes; otherwise, it fails and the welfare system remains unchanged. Democrat and Republican preferences on the two versions and the current system are as follows:
Democrat:  Version 2 &amp;succ; Current system &amp;succ; Version 1
Republican:  Version 1 &amp;succ; Version 2 &amp;succ; Current system
13.10  Represent this setup as an extensive form game. (Within the committee distinguish between the members, but the Senate level distinguish only between the two parties.)
13.11  Identify the subgames in the game.

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