Use the following setting for questions 7-8. Players A and B play a dynamic version of matching pennies described below. The game follows in 3 stages. First, player A chooses the order of play, i.e. who makes the first move: player A or player B. This decision is public. Then this chosen (first) player chooses between heads and tails. Then the second (other) player observes that choice and also chooses whether to play heads or tails. For example, player A could choose that player A (themselves) makes the first move; then player A chooses tails; then player B observes it and also chooses tails. Since both of them choose to play tails, their payoffs are 1 and -1 as follows from the payoff matrix below. Player B

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Use the following setting for questions 7-8. Players A and B play a dynamic version of matching
pennies described below. The game follows in 3 stages. First, player A chooses the order of play,
i.e. who makes the first move: player A or player B. This decision is public. Then this chosen
(first) player chooses between heads and tails. Then the second (other) player observes that choice
and also chooses whether to play heads or tails. For example, player A could choose that player A
(themselves) makes the first move; then player A chooses tails; then player B observes it and also
chooses tails. Since both of them choose to play tails, their payoffs are 1 and 1 as follows from
the payoff matrix below.
Player B
T
H
H 1,-1-1,1
T-1,1 1,-1
7. How many pure strategies does player A have in this dynamic game.
(a) 4
(b) 6
(c) 8
Player A
2
Transcribed Image Text:Use the following setting for questions 7-8. Players A and B play a dynamic version of matching pennies described below. The game follows in 3 stages. First, player A chooses the order of play, i.e. who makes the first move: player A or player B. This decision is public. Then this chosen (first) player chooses between heads and tails. Then the second (other) player observes that choice and also chooses whether to play heads or tails. For example, player A could choose that player A (themselves) makes the first move; then player A chooses tails; then player B observes it and also chooses tails. Since both of them choose to play tails, their payoffs are 1 and 1 as follows from the payoff matrix below. Player B T H H 1,-1-1,1 T-1,1 1,-1 7. How many pure strategies does player A have in this dynamic game. (a) 4 (b) 6 (c) 8 Player A 2
(d) 16
(e) 32
8. Choose the FALSE statement about this dynamic game.
(a) Player A gets a higher payoff than player B in any SPNE of this game.
(b) There are more than 1 SPNE in this game.
(c) Player A chooses player B to act first in any SPNE of this game.
(d) Player B's equilibrium payoff is equal to -1 (in any SPNE of this game).
(e) There is a unique SPNE in this game.
Transcribed Image Text:(d) 16 (e) 32 8. Choose the FALSE statement about this dynamic game. (a) Player A gets a higher payoff than player B in any SPNE of this game. (b) There are more than 1 SPNE in this game. (c) Player A chooses player B to act first in any SPNE of this game. (d) Player B's equilibrium payoff is equal to -1 (in any SPNE of this game). (e) There is a unique SPNE in this game.
Expert Solution
Step 1: Describe the game

There are two players :  Player A & B 

Strategy Set of Player A =  Strategy Set of Player B  = {  H , T } 

Payoffs are as follows -

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