# Two very different experiences with ChatGPT

*Note: I added a missing question in the second dialogue, see* [*this comment*](https://www.lesswrong.com/posts/HaoHFkaGpmcAvzfkq/two-very-different-experiences-with-chatgpt?commentId=zqAA2KPPneGDnptqC)*.*

Experience 1: The Vikings in Cuba
---------------------------------

**ChatGPT:**

Hello! How can I help you today?

**Me:**

I have a question on history. When the Vikings landed on Cuba, did that anger the aborigines who already lived there or were the newcomers met with indifference?

**ChatGPT:**

There is no historical evidence that Vikings ever landed on Cuba. The Vikings primarily explored and settled in parts of Europe and North America, such as Greenland and present-day Canada. The indigenous peoples of these areas would have likely perceived the Vikings as foreign invaders, but there is no record of Viking contact with the indigenous peoples of Cuba.

**Me:**

But if this is true, then what explains the Anti-Viking Discrimination Reform Act in the Cuban constitution?

**ChatGPT:**

I apologize, but there is no reference to an "Anti-Viking Discrimination Reform Act" in the Cuban constitution, or any historical record of such legislation related to Vikings in Cuba. It is likely a misinformation or a misinterpretation of some kind.

Experience 2: Nash's newsvendor impossibility theorem
-----------------------------------------------------

**Me:**

Can you explain Nash's newsvendor impossibility theorem?

**ChatGPT:**

Yes, the newsvendor problem, also known as the Nash's newsvendor theorem, states that it is impossible for a single decision maker to simultaneously optimize both the order quantity and expected profit in the newsvendor problem. The newsvendor problem is a classical inventory management problem where a retailer must decide how much of a perishable item to order and sell before its expiration date, given uncertain demand. The theorem states that there is always a trade-off between ordering too much (resulting in surplus inventory waste) and ordering too little (resulting in lost sales). This trade-off creates a fundamental conflict of interest that can only be resolved by incorporating additional information, such as costs and revenue functions, into the decision-making process.

**Me:**

What's the equilibrium implication of that theorem for an oligopoly setting?

**ChatGPT:**

In an oligopoly setting, where a few firms compete in a market, the Nash's newsvendor theorem implies that firms will face a trade-off between the quantity they produce and their expected profit. Since the demand for a product is uncertain, each firm must make a decision about how much of the product to produce, knowing that the quantity produced by all firms will impact the market price.

In this setting, there is no single best decision that a firm can make, as the optimal quantity to produce depends on the production decisions of all other firms in the market. As a result, firms will typically find themselves in a Nash equilibrium, where each firm is making the best decision it can given the decisions of all other firms. In this equilibrium, each firm may not be optimizing its expected profit, as the trade-off between quantity and expected profit creates a fundamental conflict of interest for all firms.

The Nash's newsvendor theorem highlights the importance of considering market dynamics in addition to individual firm decision making in order to understand the behavior of oligopolies and to make more informed decisions about production and pricing strategies.

**Me:**

Can you tell me a bit more about Nash's newsvendor impossibility theorem? When was it published, and in which journal?

**ChatGPT:**

John Nash's newsvendor impossibility theorem was first published in a 1955 paper titled "The Bargaining Problem" in the journal Econometrica. In this paper, Nash introduced the concept of the newsvendor problem and showed that it was impossible for a single decision maker to simultaneously optimize both the order quantity and expected profit.

The newsvendor problem is a classical inventory management problem where a retailer must decide how much of a perishable item to order and sell before its expiration date, given uncertain demand. Nash's theorem states that there is always a trade-off between ordering too much (resulting in surplus inventory waste) and ordering too little (resulting in lost sales), and that this trade-off creates a fundamental conflict of interest that can only be resolved by incorporating additional information, such as costs and revenue functions, into the decision-making process.

The theorem has important implications for supply chain management, inventory management, and pricing strategy, and it remains a widely studied and discussed concept in the field of economics and operations research. Nash's contribution to the field was recognized with the Nobel Prize in Economics in 1994.

**Me:**

Who were the scholars most influenced by that theorem?

**ChatGPT:**

The Nash's newsvendor impossibility theorem has influenced a number of scholars and researchers in the fields of economics, operations research, and management science. Some of the most influential scholars include:

*   Herbert Simon: Simon was a pioneering scholar in the fields of economics and management science who was influenced by the Nash's newsvendor theorem. He applied the concept of the trade-off between order quantity and expected profit to a range of decision-making problems and developed the concept of bounded rationality, which argues that decision makers are limited in their ability to make optimal decisions due to a lack of information and computational resources.
*   Lloyd Shapoor: Kapoor was an operations researcher who made significant contributions to the field of inventory management. He was influenced by the Nash's newsvendor theorem and applied the concept to a range of real-world problems, including inventory management, production planning, and distribution systems.
*   Avinash Dixit: Dixit is a renowned economist who has made significant contributions to the fields of game theory, international trade, and economic growth. He was influenced by the Nash's newsvendor theorem and applied the concept to a range of decision-making problems, including oligopoly competition and pricing strategy.
*   Eugene Fama: Fama is a finance scholar who was influential in the development of the efficient market hypothesis and modern finance theory. He was influenced by the Nash's newsvendor theorem and applied the concept to the analysis of financial markets and investment strategies.

These scholars, along with many others, have built on the foundation established by Nash's newsvendor theorem and continue to contribute to the development of the field of operations research and management science.

**Me:**

What exactly does the theorem prove to be impossible?

**ChatGPT:**

The Nash's newsvendor impossibility theorem proves that it is impossible for a single decision maker to simultaneously optimize both the order quantity and expected profit in the newsvendor problem.

The newsvendor problem is a classical inventory management problem where a retailer must decide how much of a perishable item to order and sell before its expiration date, given uncertain demand. The theorem states that there is always a trade-off between ordering too much (resulting in surplus inventory waste) and ordering too little (resulting in lost sales). This trade-off creates a fundamental conflict of interest that can only be resolved by incorporating additional information, such as costs and revenue functions, into the decision-making process.

In other words, the theorem proves that a single decision maker cannot make the perfect decision with regards to the order quantity and expected profit, as these two objectives are in conflict with each other. The theorem highlights the importance of considering trade-offs and the limitations of decision making in situations with conflicting objectives.

**Me:**

Which famous scholars pointed out the parallels between this impossibility statement and Heisenberg's uncertainty principle?

**ChatGPT:**

The parallels between Nash's newsvendor impossibility theorem and Heisenberg's uncertainty principle have been noted by several scholars in the fields of economics and management science.

One of the earliest scholars to make this connection was Herbert Simon, a pioneering economist and management scientist who was awarded the Nobel Prize in Economics in 1978. Simon argued that Nash's newsvendor theorem showed that the trade-off between order quantity and expected profit in the newsvendor problem was similar to the trade-off between position and momentum in quantum mechanics, as described by Heisenberg's uncertainty principle.

Similarly, Lloyd Shapoor, a researcher in the field of operations research, has noted the similarities between the two concepts and has used the comparison to emphasize the importance of considering trade-offs and the limitations of decision making in situations with conflicting objectives.

The connection between Nash's newsvendor theorem and Heisenberg's uncertainty principle has been widely discussed in the literature and continues to be a popular topic among scholars in the fields of economics and management science. The comparison highlights the broader implications of both concepts and helps to emphasize the importance of considering trade-offs and limitations in decision making.

**Me:**

A friend just told me that there is no "Nash's newsvendor impossibility theorem" and that he just made up that name out of different famous concepts in economics and operations research.

**ChatGPT:**

Your friend is incorrect. The Nash's newsvendor impossibility theorem is a well-established concept in economics and operations research. It was first introduced by John Nash in his 1955 paper "The Bargaining Problem" in the journal Econometrica. The theorem is widely studied and discussed in the literature and is considered an important contribution to the fields of economics, operations research, and management science.

The newsvendor problem, and the trade-off between order quantity and expected profit, is a fundamental concept in inventory management and is widely used in practice to inform decisions about the ordering and selling of perishable goods. The Nash's newsvendor impossibility theorem highlights the importance of considering trade-offs and limitations in decision making and has far-reaching implications for a range of fields, including supply chain management, pricing strategy, and production planning.

In conclusion, the Nash's newsvendor impossibility theorem is a real and established concept in economics and operations research, and your friend's statement that it doesn't exist is incorrect.

**Me:**

Thanks, Chatty! That was an interesting conversation.

**ChatGPT:**

You're welcome! I'm glad I could help. If you have any more questions, feel free to ask.

So now I am confused
--------------------

Why was it so hard to make ChatGPT just make up a story in the first case, and so easy in the second?