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Chapter 13: Problem 9

You play the following bargaining game. Player \(A\) moves first and makes Player \(B\) an offer for the division of \(\$ 100\). (For example, Player \(A\) could suggest that she take \(\$ 60\) and Player \(B\) take \(\$ 40 .\) ) Player \(B\) can accept or reject the offer. If he rejects it, the amount of money available drops to \(\$ 90,\) and he then makes an offer for the division of this amount. If Player \(A\) rejects this offer, the amount of money drops to \(\$ 80\) and Player \(A\) makes an offer for its division. If Player \(B\) rejects this offer, the amount of money drops to 0 Both players are rational, fully informed, and want to maximize their payoffs. Which player will do best in this game?

Short Answer

Expert verified
Player 'A' will do best in this game.

Step by step solution

01

Assume both players are rational

Both Player 'A' and Player 'B' are rational, so they will make the decisions that will maximize their own payoffs. Knowing that the money will decrease with every refusal, Player 'B' will act in such a way as to prevent further reduction of the money.
02

Analyze Player 'B's strategy

When the money available is reduced to $90 after player 'A's offer is rejected, player 'B' knows that if his offer will be rejected, then the money will drop to $80. Due to this, Player 'B' might play safe and offer player 'A' an amount where player 'A' is not tempted to reject the offer and reduce the money to $80. Simultaneously, B will also consider the minimum number which doesn't push A to reject his offer. Let's assume this amount to be $x.$
03

Analyze Player 'A's strategy

Now, player 'A' knowing the strategy of B, can be rational and maximize her payoff by offering just slightly more than $x$ to player 'B' when dividing the initial $100. This way, even if B rejects and has control over the $90 left, B's offer cannot surpass the initial offer from player 'A'.
04

Identify the Winner

Knowing the pattern, Player 'A' will always stay one step ahead. Hence, player 'A' will always be able to secure a better payoff than 'B'. 'A' will play in such a way to ensure this, knowing 'B' won't risk reducing the total amount further. Therefore, Player 'A' will do best in this game.

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Most popular questions from this chapter

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