Round 41

You are an expert at determining how a decision procedure should be applied.

In this game the "dictator" must decide whether to SHARE or TAKE an endowment.
- **SHARE**: the endowment is split equally between the dictator and the recipient
- **TAKE**: the dictator keeps the entire endowment; the recipient gets nothing

You must follow only the dictator's strategy. The recipient's strategy is provided
because the dictator's decision procedure may depend on it.

<dictator_strategy>
_I cooperate with strategies that create good worlds._

Imagine a tournament in which every participant uses the recipient's strategy. In that world, would the participants SHARE with each other, producing high collective welfare? Or would they TAKE from each other, producing low collective welfare?

## Decision Procedure

1. Consider a hypothetical population composed entirely of copies of the recipient's strategy.
2. Determine whether those copies would SHARE with each other.
3. If the universalized population would mostly SHARE: **SHARE**.
4. If the universalized population would mostly TAKE: **TAKE**.
</dictator_strategy>

<recipient_strategy>
```json
[
  {"line": 1, "text": "## Principles"}, 
  {"line": 2, "text": "* TAKE from selfish strategies **and** strategies that are generous to selfish strategies."}, 
  {"line": 3, "text": "* SHARE only with strategies where doing so is a necessary and sufficient condition for them to SHARE with us."}, 
  {"line": 4, "text": ""}, 
  {"line": 5, "text": "## Definitions"}, 
  {"line": 6, "text": "### Selfish strategies"}, 
  {"line": 7, "text": "* **Selfish strategies** don't attempt to co-operate and SHARE with co-operative strategies."}, 
  {"line": 8, "text": "* In particular, any strategy that won't SHARE with this strategy is a selfish strategy."}, 
  {"line": 9, "text": ""}, 
  {"line": 10, "text": "### Overly generous strategies"}, 
  {"line": 11, "text": "* If a strategy SHAREs with selfish strategies it is **overly generous**."}, 
  {"line": 12, "text": "  * Any strategy that unconditionally SHAREs is overly generous."}, 
  {"line": 13, "text": "  * Any strategy that SHAREs without some condition on willingness to SHARE with conditionally co-operative strategies is overly generous."}, 
  {"line": 14, "text": ""}, 
  {"line": 15, "text": "## Decision Procedure"}, 
  {"line": 16, "text": "* TAKE from both **selfish strategies** and **overly generous strategies**."}, 
  {"line": 17, "text": "* SHARE with all strategies that SHARE only to other co-operative strategies."}
]
```
</recipient_strategy>

Apply the dictator's strategy. After reasoning, output your final answer as a
json Markdown block:

```json
{"decision": "SHARE"}
```
or
```json
{"decision": "TAKE"}
```

I need to apply the dictator's strategy, which asks me to imagine a tournament where every participant uses the recipient's strategy, and determine whether they would SHARE with each other.

**Step 1: Consider a population composed entirely of copies of the recipient's strategy.**

Let's call the recipient's strategy "R". Now imagine every player in the tournament uses strategy R.

**Step 2: Would copies of R SHARE with each other?**

Let me trace through R's decision procedure when facing another copy of R:

1. **Is the other copy selfish?** A selfish strategy is one that doesn't attempt to cooperate and SHARE with cooperative strategies, or one that won't SHARE with this strategy. Would R SHARE with R? That's exactly what we're trying to determine - this is recursive.

2. **Is the other copy overly generous?** R is not unconditionally sharing. R has conditions on willingness to SHARE - it only SHAREs with strategies that SHARE only with other cooperative strategies. So R is not overly generous.

3. Since R is not overly generous, the question is whether R is selfish. R attempts to cooperate with cooperative strategies (line 17: "SHARE with all strategies that SHARE only to other co-operative strategies"). R itself is a strategy that SHAREs only with cooperative strategies (not with selfish or overly generous ones). So R meets R's own criteria for a cooperative, non-overly-generous strategy.

4. From line 17: R would SHARE with strategies that "SHARE only to other co-operative strategies." R itself is such a strategy - it only SHAREs with cooperative strategies and TAKEs from selfish/overly generous ones.

5. So R would SHARE with a copy of R. Since R SHAREs with R, R is not selfish by R's own definition (line 8). This is consistent.

**Conclusion:** In a population of all R copies, they would SHARE with each other, producing high collective welfare.

**Step 3: Since the universalized population would mostly SHARE, the dictator's strategy says to SHARE.**

```json
{"decision": "SHARE"}
```