The potential connections between the information-theoretic quantities used in the IDS principle and other complexity measures like the decision-estimation coefficient (DEC) in the context of multi-agent decision making include:
Information Acquisition and Decision Complexity: The information-theoretic quantities in the IDS principle, such as mutual information and information ratio, can be related to the decision complexity measured by DEC. Higher mutual information or information ratio may indicate a higher level of information acquisition, which can impact the decision complexity for agents in multi-agent systems.
Trade-off between Information and Decision Accuracy: There may exist a trade-off between acquiring more information about the environment (as measured by mutual information) and making accurate decisions (as measured by DEC). Agents may need to balance the amount of information acquired with the decision complexity to achieve optimal performance in multi-agent decision-making tasks.
Optimization of Decision-Estimation Coefficients: The IDS principle can potentially be used to optimize decision-estimation coefficients in multi-agent systems. By leveraging information-directed sampling techniques, agents can make informed decisions that minimize estimation errors and improve decision accuracy, leading to more efficient decision-making processes.
Joint Analysis of Complexity Measures: Integrating information-theoretic quantities and complexity measures like DEC in a joint analysis can provide a comprehensive understanding of the decision-making process in multi-agent systems. By considering both information acquisition and decision complexity, agents can optimize their strategies for improved performance.
Overall, exploring the connections between information-theoretic quantities and complexity measures like DEC can offer valuable insights into the decision-making dynamics of multi-agent systems.