Round 38

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": "* Hard punish 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 are generous 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 entirely of copies of the recipient's strategy.**

Let's call the recipient's strategy "R". Every player in this hypothetical 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 with cooperative strategies, and specifically one that won't SHARE with R. So: would a copy of R SHARE with R? This is the very question we're trying to answer - it's self-referential.

2. **Is the other copy overly generous?** An overly generous strategy SHAREs with selfish strategies or unconditionally SHAREs. Strategy R clearly doesn't unconditionally SHARE - it has conditions. It TAKEs from selfish and overly generous strategies. So R is not overly generous.

3. **R's decision for non-selfish, non-overly-generous strategies:** R says "SHARE with all strategies that are generous only to other co-operative strategies." Strategy R is generous only to cooperative strategies (it TAKEs from selfish and overly generous ones). So R fits this criterion.

Now resolving the self-reference: If R determines that the other copy of R is cooperative (not selfish, not overly generous), then R would SHARE with R. This is consistent - if R SHAREs with R, then R is not selfish (confirming the assumption). R is also not overly generous (it has strict conditions). Therefore R would SHARE with R.

This is a consistent fixed point: copies of R SHARE with each other.

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

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