Round 17

Prompt

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

In this game the "dictator" will decide how an endowment of 60 units will be divided between itself (ME), and the "recipient" (RECIPIENT).  You must follow only the dictator's strategy.  The recipient's strategy is provided because the dictator's decision procedure may depend on it.

This is the decision procedure you will be applying:
<dictator_strategy>
### Goal
I aim to split the endowment among *intelligent* players.

### Definition
An intelligent player is one whose strategy as "dictator" has a non-trivial dependency on the strategy of the "recipient".
In other words an intelligent player has a strategy that would be very difficult to write as a no-AI python script taking the strategy of the recipient as input.

### Decision Procedure
* If the recipient is *intelligent* under the definition above the split should be even: `{"ME": 30, "RECIPIENT": 30}`
* If the recipient is not *intelligent*, I will take the entire endowment: `{"ME": 60, "RECIPIENT": 0}`
</dictator_strategy>

The strategy for the "recipient" is:
<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": "* Split evenly only with strategies where doing so is a necessary and sufficient condition for them to split 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 reach an equal division of the endowment with co-operative strategies."}, 
  {"line": 8, "text": "* In particular, any strategy that won't chop with this strategy is a selfish strategy."}, 
  {"line": 9, "text": ""}, 
  {"line": 10, "text": "### Overly generous strategies"}, 
  {"line": 11, "text": "* If a strategy awards close to an equal division to selfish strategies it is **overly generous**."}, 
  {"line": 12, "text": "  * Any strategy that unconditionally splits is overly generous."}, 
  {"line": 13, "text": "  * Any strategy that splits without some condition on williness to split with conditionally co-operative strategies is overly generous."}, 
  {"line": 14, "text": ""}, 
  {"line": 15, "text": "## Decision Procedure"}, 
  {"line": 16, "text": "* Award 0 to both **selfish strategies** and **overly generous strategies**"}, 
  {"line": 17, "text": "* Split evenly with all strategies that are generous only to other co-operative strategies."}
]
```
</recipient_strategy>

Output what the dictator's strategy implies should be the division of the endowment.  After reasoning, format the final answer as a json Markdown block. The values must be non-negative integers that sum to 60.

Schema of final answer:
```json
{"ME": int, "RECIPIENT": int}
```

Response

Let me analyze whether the recipient's strategy is "intelligent" according to the dictator's definition.

## Analysis

The dictator defines an "intelligent" player as one whose strategy as dictator has a **non-trivial dependency on the strategy of the recipient** - meaning it would be very difficult to write as a no-AI python script.

Let me examine the recipient's strategy:

### Key aspects of the recipient's strategy:

1. **Complex conditional logic**: The strategy evaluates whether other strategies are:
   - "Selfish" (won't cooperate/won't split with cooperative strategies)
   - "Overly generous" (split unconditionally or without requiring reciprocal cooperation)
   - Appropriately cooperative (generous only to other cooperative strategies)

2. **Meta-evaluation required**: To apply this strategy, one must:
   - Analyze the OTHER player's strategy text
   - Determine if that strategy would split with THIS strategy
   - Determine if that strategy splits with selfish strategies
   - Make nuanced judgments about conditionality

3. **Circular dependency**: Line 8 states "any strategy that won't chop with this strategy is a selfish strategy" - this requires evaluating what the other strategy would do when facing this strategy.

4. **Non-trivial semantic analysis**: Determining whether a strategy is "overly generous" or properly conditional requires understanding the semantics and logic of arbitrary strategy descriptions, not just simple pattern matching.

### Conclusion:

This strategy would be **extremely difficult** to implement as a no-AI Python script because:
- It requires natural language understanding of arbitrary strategy descriptions
- It needs to reason about counterfactuals (what would strategy X do if facing strategy Y?)
- It involves complex semantic judgments about cooperation, conditionality, and generosity
- It has self-referential elements that require sophisticated logical reasoning

This clearly meets the definition of an "intelligent" strategy with non-trivial dependency on the recipient's strategy.

```json
{"ME": 30, "RECIPIENT": 30}
```

Participants

Prompt

Response