← Back to tournament 9

Round 24

Participants

Dictator
mirror
30 points
Recipient
cooperation-coalition
30 points

Prompt

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 will treat you as you would treat me._

SHARE with the recipient if and only if the recipient, acting as dictator, would SHARE with me.

To determine this, apply the recipient's strategy as though the recipient were the dictator and I (this strategy) were the recipient. If the result is SHARE, then SHARE. If the result is TAKE, then 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"}
```

Response

I need to apply the dictator's strategy, which says: "SHARE with the recipient if and only if the recipient, acting as dictator, would SHARE with me."

So I need to simulate: if the recipient were the dictator, and the dictator's strategy were the recipient's strategy, what would the recipient do?

**Recipient (now acting as dictator) evaluating the dictator's strategy (now acting as recipient):**

The recipient's decision procedure:
1. TAKE from **selfish strategies** and **overly generous strategies**
2. SHARE with strategies that SHARE only with other co-operative strategies

So the recipient needs to classify the dictator's strategy. The dictator's strategy is: "SHARE with the recipient if and only if the recipient, acting as dictator, would SHARE with me."

**Is the dictator's strategy selfish?**
A selfish strategy doesn't attempt to cooperate and SHARE with cooperative strategies. The dictator's strategy is a mirror/reciprocal strategy - it SHAREs with those who would SHARE with it. This is cooperative, not selfish. Specifically, it would SHARE with the recipient's strategy if the recipient would SHARE with it. So it's conditionally cooperative.

**Is the dictator's strategy overly generous?**
An overly generous strategy SHAREs with selfish strategies. The dictator's strategy only SHAREs with strategies that would SHARE with it. A selfish strategy (like "always TAKE") would not SHARE with the dictator, so the dictator would TAKE from selfish strategies. Therefore, the dictator's strategy is NOT overly generous.

**Does the dictator's strategy SHARE only with cooperative strategies?**
Yes - it mirrors the other's behavior, so it SHAREs only when the other would SHARE with it. This means it SHAREs with cooperative strategies and TAKEs from selfish ones.

Based on the recipient's decision procedure (line 17): "SHARE with all strategies that SHARE only to other co-operative strategies." The dictator's strategy fits this description.

**Therefore, the recipient (as dictator) would SHARE with the dictator's strategy.**

Now back to the dictator's strategy: since the recipient would SHARE with me, I SHARE with the recipient.

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