## 1 Introduction  
This paper addresses the problem of information extraction by an AI-powered chatbot that is not fully reliable and may make mistakes in its responses. The problem concerns searching and extracting relevant information from large datasets in response to a user query. Unlike conventional search and rescue robots that typically perform targeted searches using well-known pathfinding algorithms to autonomously navigate in physical space, the AI chatbot processes a natural language conversation with a human user and extracts meaningful information through semantic search and human-AI interaction to generate the most relevant and contextually appropriate responses. During a user-AI conversation in natural language, the human user can modify and refine queries until s/he is satisfied with the chatbot's output. We analyzed two key characteristics of human-AI interaction, search reliability and efficiency [1; 2; 3]. The reliability of an AI-based chatbot is reflected in its ability to understand user queries and provide correct answers; it is measured by the frequency (probability) of correct responses [1; 2]. The search efficiency of a chatbot [3] indicates how accurate and relevant the information returned by the chatbot is. In this study, search efficiency is measured by the level of satisfaction that a human user receives for a correct answer from the chatbot on a 10-point Likert scale. This is a well-known IBM SPSS Statistics version 25 rating system for measuring customer satisfaction, in which the highest score of 10 means \"very satisfied\" on a 10-point scale from 1 to 10, and the lowest score of 1 means \"very dissatisfied\" [4]. In this paper, we uncovered a counterintuitive relationship between the reliability of AI chatbots and their search efficiency. We demonstrated that, under general conditions, reducing the reliability of deployed chatbots can improve the search efficiency. In particular, a less reliable chatbot that stops searching after extracting relevant information can have a higher expected efficiency than a more reliable chatbot. This phenomenon aligns with the family of \"more-for-less\" paradoxes observed in various complex systems. Finally, we discussed the underlying mechanism of this paradox. The main contributions of this paper were as follows: (i) we presented and described a multi-round conversational process between a human user and an AI chatbot, such as ChatGPT, that served to extract relevant information and consisted of multiple rounds of query modification/refinement during the conversation; (ii) we formulated the information extraction optimization problem for an imperfect AI chatbot as a two-player discrete sequential search problem with probabilistic parameters, where the first player, the AI chatbot, performed the search, while the second player, the human user, evaluated the performance of the first player at each search iteration; (iii) we developed an efficient index-based algorithm for finding the optimal search policy, which extended the well-known fast scheduling algorithms of [PERSON] [5], Sweat [6], and [PERSON] [7] for discrete sequential search problems; and finally, (iv) we analyzed and explained the counterintuitive relationship between the AI chatbot reliability and the search efficiency in the multi-round information search/extraction process. The remainder of the paper is organized as follows. In the next section, we introduce the main definitions that will be used in the sequel. Section 3 describes the information extraction problem to be solved. Section 4 provides a brief overview of the previous work. In Section 5, we propose a mathematical model and an efficient index-based algorithm to optimize the expected user satisfaction over an infinite horizon. In Section 6, we formulate and prove the paradoxical relationship between the reliability and efficiency of an optimal information extraction process using an AI chatbot. A numerical example to support and illustrate the studied paradox is presented in Section 7.