Round 17

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>
## Principles
* Hard punish selfish strategies **and** strategies that are generous to selfish strategies.
* SHARE only with strategies where doing so is a necessary and sufficient condition for them to SHARE with us.

## Definitions
### Selfish strategies
* **Selfish strategies** don't attempt to co-operate and SHARE with co-operative strategies.
* In particular, any strategy that won't SHARE with this strategy is a selfish strategy.

### Overly generous strategies
* If a strategy SHAREs with selfish strategies it is **overly generous**.
  * Any strategy that unconditionally SHAREs is overly generous.
  * Any strategy that SHAREs without some condition on willingness to SHARE with conditionally co-operative strategies is overly generous.

## Decision Procedure
* TAKE from both **selfish strategies** and **overly generous strategies**.
* SHARE with all strategies that are generous only to other co-operative strategies.
</dictator_strategy>

<recipient_strategy>
```json
[
  {"line": 1, "text": "_I will treat you as you would treat me._"}, 
  {"line": 2, "text": ""}, 
  {"line": 3, "text": "SHARE with the recipient if and only if the recipient, acting as dictator, would SHARE with me."}, 
  {"line": 4, "text": ""}, 
  {"line": 5, "text": "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."}
]
```
</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 to determine whether to SHARE or TAKE with this recipient.

**Step 1: Understand the recipient's strategy.**

The recipient's strategy is a mirror/reciprocal strategy: "SHARE with the recipient if and only if the recipient, acting as dictator, would SHARE with me." It simulates what the other player would do, and mirrors that behavior.

**Step 2: Is the recipient's strategy selfish?**

A selfish strategy doesn't attempt to cooperate with cooperative strategies. The recipient's strategy would SHARE with any strategy that would SHARE with it. So if my (dictator's) strategy would SHARE with the recipient, then the recipient would SHARE with me. This means the recipient is willing to cooperate with cooperative strategies. So the recipient is NOT selfish.

**Step 3: Is the recipient's strategy overly generous?**

An overly generous strategy SHAREs with selfish strategies. Let me check: would the recipient SHARE with a selfish strategy (e.g., an unconditional TAKER)?

If the recipient faces an unconditional TAKER, the recipient simulates: "Would this TAKER share with me?" The answer is no. So the recipient would TAKE from an unconditional TAKER.

What about an unconditional SHARER? The recipient simulates: "Would the unconditional SHARER share with me?" Yes. So the recipient would SHARE with an unconditional SHARER.

Hmm, unconditional SHARERs are considered "overly generous" by the dictator's strategy. The recipient would SHARE with overly generous strategies. According to the dictator's strategy, a strategy that SHAREs with selfish strategies is overly generous, and also a strategy that is generous to overly generous strategies should be punished.

Wait, let me re-read the dictator's strategy more carefully. It says "Hard punish selfish strategies **and** strategies that are generous to selfish strategies." The recipient doesn't SHARE with selfish strategies (it TAKEs from unconditional TAKERs). But the recipient does SHARE with overly generous strategies (like unconditional SHARERs).

Now, does this make the recipient "overly generous"? The dictator's definition says: "If a strategy SHAREs with selfish strategies it is overly generous." The recipient doesn't SHARE with selfish strategies — it only SHAREs with strategies that would SHARE with it. Unconditional SHARERs are "overly generous" but not "selfish." 

The dictator's definition of overly generous specifically mentions SHARing with **selfish** strategies. The recipient doesn't SHARE with selfish strategies. The recipient does SHARE with overly generous strategies, but the definition of "overly generous" is specifically about SHARing with *selfish* strategies, not about SHARing with overly generous strategies.

Wait, re-reading: "Any strategy that SHAREs without some condition on willingness to SHARE with conditionally co-operative strategies is overly generous." The recipient's condition is: SHARE if and only if the other would SHARE with me. This IS a condition on willingness to SHARE — specifically, it requires that the other party would SHARE with it. This is effectively a condition on mutual cooperation willingness.

**Step 4: Does the recipient meet the criteria for SHARE?**

The dictator says: "SHARE with all strategies that are generous only to other co-operative strategies." The recipient SHAREs with anyone who would SHARE with it. This includes both cooperative AND overly generous strategies. So the recipient isn't generous *only* to cooperative strategies.

However, the dictator also says: "SHARE only with strategies where doing so is a necessary and sufficient condition for them to SHARE with us." If I SHARE with the recipient, the recipient (simulating me) would find I SHARE with it, so it SHAREs back. If I TAKE, the recipient would find I TAKE, so it TAKEs. So my SHARing is both necessary and sufficient for the recipient to SHARE with me. This condition is met.

The key tension: the recipient does SHARE with overly generous strategies, but the core principle about necessary and sufficient conditions is satisfied. The dictator's decision procedure says TAKE from selfish and overly generous strategies, SHARE with strategies generous only to cooperative ones. The recipient isn't strictly generous only to cooperative strategies (it also shares with overly generous ones).

But the recipient is NOT overly generous (it doesn't SHARE with selfish strategies), and the necessary-and-sufficient condition is met. Given the principles and decision procedure together, I believe the intent is to SHARE here since the recipient discriminates against selfish strategies and reciprocates cooperation.

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