Optimal Strategies in Infinite Games with Memory

In the field of artificial intelligence, researchers have been studying the complexity of strategies in various games. The article "Strategy Complexity" delves into this topic and provides insights on how simple or complex optimal strategies must be to play a game optimally.
The author defines strategy complexity as the degree of difficulty in creating an optimal strategy for a given game. There are three types of memory requirements in games: memoryless-determined objectives, where memories are not required; finite-memory-determined objectives, where some memory is needed but can be encoded as a deterministic finite automaton; and objectives that require infinite memory.
The author then explores the concept of optimal strategies, which must balance between randomization and memory requirements. They explain that for some games, randomization is necessary to explore different possibilities, while in others, memory is crucial to remember past experiences. The article provides examples of games where these concepts apply, such as energy mean-payoff games and games with finite or infinite memory.
To illustrate the complexity of strategy creation, the author uses metaphors such as "building a Lego castle" and "playing a game of chess." They explain that creating an optimal strategy is like building a complex structure using different pieces, where each piece represents a specific action. The more complex the structure, the more options it has, but also the more difficult it is to create and maintain.
The article concludes by highlighting the importance of understanding strategy complexity in game design and AI development. By analyzing the complexity of strategies, researchers can improve their algorithms and create better AI agents that can play games optimally.
In summary, "Strategy Complexity" delves into the intricacies of creating optimal strategies for various games, demonstrating how different factors such as memory requirements and randomization affect the complexity of these strategies. The author uses engaging metaphors to explain complex concepts in a way that is easy to understand for an average adult reader.