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
* TAKE from 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 SHARE 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: "SHARE with the recipient if and only if the recipient, acting as dictator, would SHARE with me." This is a mirror/reciprocal strategy - it SHAREs with strategies that would SHARE with it, and TAKEs from strategies that would TAKE from it.
**Step 2: Is the recipient's strategy selfish?**
A selfish strategy doesn't attempt to cooperate and SHARE with cooperative strategies. The recipient's strategy does SHARE with strategies that would SHARE with it. So it's conditionally cooperative, not selfish.
**Step 3: Is the recipient's strategy overly generous?**
An overly generous strategy SHAREs with selfish strategies. The recipient's strategy only SHAREs with strategies that would SHARE with it. A selfish strategy (one that always TAKEs) would not SHARE with the recipient, so the recipient would TAKE from selfish strategies. Therefore, the recipient is NOT overly generous.
**Step 4: Does the recipient SHARE only with cooperative strategies?**
Yes - the recipient SHAREs only with strategies that would SHARE with it. This means it conditions its sharing on mutual cooperation.
**Step 5: Is sharing a necessary and sufficient condition for mutual sharing?**
I need to verify that if I (the dictator's strategy) SHARE with the recipient, the recipient would SHARE with me, and if I TAKE, the recipient would TAKE from me.
If the recipient is the dictator using its strategy, it would ask: "Would the dictator's strategy SHARE with me?" If my strategy SHAREs with the recipient, then the recipient (as dictator) would SHARE with me. This creates a consistent fixed point where both SHARE.
If my strategy TAKEs from the recipient, then the recipient (as dictator) would TAKE from me. This would also be consistent.
So sharing is both necessary and sufficient for mutual cooperation - this is exactly the type of strategy the dictator's strategy says to SHARE with.
**Step 6: Apply the decision procedure.**
The recipient is not selfish and not overly generous. It SHAREs only with cooperative strategies. The dictator's strategy says to SHARE with such strategies.
```json
{"decision": "SHARE"}
```