Question

Please answer and explain questions 1 to 4 from this problem thanks. Class: Game Theory

Problem 1

Two players, A and B play the following game. First Player A must choose IN or OUT. If Player A chooses OUT the game ends, and the payoffs are Player A gets 4, and Player B gets 0. If Player A chooses IN then Player B observes this and must then choose in or out. If Player B chooses out the game ends, and the payoffs are Player B gets 4, and Player A gets 0. If Player A chooses IN and Player B chooses in then they play the following simultaneous-move game described in Table 1:

Table 1

		Player B
		Left	Right
Player A	Up	6, 2	0, -4
	Down	-2, 4	2, 6

1. Draw a game tree that represents this situation. How many proper subgames does it have?
2. Are there other game trees that would work? Explain briefly.
3. Construct the matrix representation of the normal form of this dynamic game.
4. Find all the Nash and subgame perfect equilibria in pure strategies of the dynamic game.

Answer 1

the format is π=(Payoff Player A, Pay off Player B)

There are 4 proper subgames.

The red squiggly lines mark when Player A makes a decision and the Blue squiggly lines mark player B's decisions

Both players will be making decisions based on where they get maximum pay off

the format is pi=(Payoff Player A, Pay off Player B)

After Player B chooses In, we put Player A in the next node to make the move of either Up or down, opposed to the original game tree we formed where B got to make a decision for left or Right immediately after choosing In.

4)

Solution to the game is in the following diagram, with the equilibrium points marked.

The Subgame Perfect Equilibria is the set (Out:Down, In:Right)

The final Pay off of the game is

Player A=4
Player B= 0