You could choose any position A (the first mover) or B (the second mover) in the following three bargaining games. For each game (I, II, or III), explain which player (A or B) you would pick in order to maximize your expected payoff? 1. Game I (one stage): A will make the first move and offer her partner a portion of 6 dollars. If the offer is accepted, the bargain is complete and each player gets an amount determined by the offer. If the offer is declined, each player gets nothing. 2. Game II (two stages): A will make the first move and offer her partner a portion of 12 dollars. If the offer is accepted, the bargain is complete and each player gets an amount determined by the offer. If the offer is declined, the 12 shrinks to 5 and B then gets a turn to make an offer. Again, the bargain is complete if A accepts and the division is made according to the terms of the offer. If player A declines the offer, each player gets nothing. 3. Game III (three stages): A will make the first move and offer her partner a portion of 12 dollars. If the offer is accepted, the bargain is complete and each player gets an amount determined by the offer. If the offer is declined, the 12 shrinks to 9 and B then gets a turn to make an offer. Again, the bargain is complete if A accepts and the division is made according to the terms of the offer. If player A declines the offer, the 9 shrinks to 1 and A then gets a turn to make a final offer. If B accepts, the division is made according to A's offer, but if B declines, the sum available shrinks to zero and each player gets nothing.
You could choose any position A (the first mover) or B (the second mover) in the following three bargaining games. For each game (I, II, or III), explain which player (A or B) you would pick in order to maximize your expected payoff? 1. Game I (one stage): A will make the first move and offer her partner a portion of 6 dollars. If the offer is accepted, the bargain is complete and each player gets an amount determined by the offer. If the offer is declined, each player gets nothing. 2. Game II (two stages): A will make the first move and offer her partner a portion of 12 dollars. If the offer is accepted, the bargain is complete and each player gets an amount determined by the offer. If the offer is declined, the 12 shrinks to 5 and B then gets a turn to make an offer. Again, the bargain is complete if A accepts and the division is made according to the terms of the offer. If player A declines the offer, each player gets nothing. 3. Game III (three stages): A will make the first move and offer her partner a portion of 12 dollars. If the offer is accepted, the bargain is complete and each player gets an amount determined by the offer. If the offer is declined, the 12 shrinks to 9 and B then gets a turn to make an offer. Again, the bargain is complete if A accepts and the division is made according to the terms of the offer. If player A declines the offer, the 9 shrinks to 1 and A then gets a turn to make a final offer. If B accepts, the division is made according to A's offer, but if B declines, the sum available shrinks to zero and each player gets nothing.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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Transcribed Image Text:You could choose any position A (the first mover) or B (the second mover) in
the following three bargaining games. For each game (I, II, or III), explain which
player (A or B) you would pick in order to maximize your expected payoff?
1. Game I (one stage): A will make the first move and offer her partner a portion
of 6 dollars. If the offer is accepted, the bargain is complete and each player gets an
amount determined by the offer. If the offer is declined, each player gets nothing.
2. Game II (two stages): A will make the first move and offer her partner
a portion of 12 dollars. If the offer is accepted, the bargain is complete and each
player gets an amount determined by the offer. If the offer is declined, the 12 shrinks
to 5 and B then gets a turn to make an offer. Again, the bargain is complete if A
accepts and the division is made according to the terms of the offer. If player A
declines the offer, each player gets nothing.
3. Game III (three stages): A will make the first move and offer her partner
a portion of 12 dollars. If the offer is accepted, the bargain is complete and each
player gets an amount determined by the offer. If the offer is declined, the 12 shrinks
to 9 and B then gets a turn to make an offer. Again, the bargain is complete if A
accepts and the division is made according to the terms of the offer. If player A
declines the offer, the 9 shrinks to 1 and A then gets a turn to make a final offer.
If B accepts, the division is made according to A's offer, but if B declines, the sum
available shrinks to zero and each player gets nothing.
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