**Homework Help: Questions and Answers:** There are 2 players who have to decide how to split one dollar The bargaining process works as follows. Players simultaneously announce the share they would like to receive s1 and s2, with 0≤s1, s2≤1. If s1+s2≤1, then the players receive the shares they named and if s1+s2>1, then both players fail to achieve an agreement and receive zero. This game is known as ‘Nash Bargaining‘.

Which of the following is a strictly dominant strategy?

a) 1

b) 0.5

c) 0

d) None of the above.

**Answer**

First, let’s understand the question:

- There are two players, each choosing how much of a dollar they want to receive, denoted by s1s_1s1 for player 1 and s2s_2s2 for player 2.
- The players will get their chosen shares s1s_1s1 and s2s_2s2 if the total s1+s2≤1
- If s1+s2>1, both players get nothing (0).
- A strictly dominant strategy is a strategy that gives a better payoff for a player regardless of what the other player does.

**Key Insights:**

- If a player chooses s1=1, they are demanding the whole dollar. However, if the other player also chooses any positive s2, the total s1+s2>1, and both get nothing.
- If a player chooses s1=0.5, this might work out if the other player also chooses 0.5 because 0.5+0.5=1, so both players would get their shares. But if the other player chooses anything above 0.5, the total exceeds 1, and both get zero.
- If a player chooses s1=0, they are guaranteed to receive nothing, but the other player can choose any share s2≤1, ensuring at least one player gets something.

**Given Options: Step by Step Answering**

**a) Choosing s1=1**:

- If player 1 chooses 1, and player 2 chooses anything positive, both get 0 because s1+s2>1.
- This is not a dominant strategy because it can result in both players getting zero.

**b)** **Choosing s1=0.5**:

- If both players choose 0.5, they both get their chosen share.
- However, if the other player chooses something larger than 0.5, both get zero.
- This is not strictly dominant because it doesn’t always give a better payoff regardless of what the other player does.

**c) Choosing s1=0**:

- If player 1 chooses 0, they receive nothing, but the other player can choose anything s2≤1, meaning player 1 doesn’t influence the outcome.
- This is also not strictly dominant since it guarantees zero payoff for player 1, regardless of what the other player does.

**Final Answer:**

There is no strictly dominant strategy in this game because none of the choices 1, 0.5, or 0 guarantee a better payoff for a player regardless of what the other player chooses.

Thus, the correct answer is: **d) None of the above**.

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