The Absent-Minded Driver Problem Redux

Abstract This paper reconsiders the problem of the absent-minded driver who must choose between alternatives with different payoff with imperfect recall and varying degrees of knowledge of the system. The classical absent-minded driver problem represents the case with limited information and it has bearing on the general area of communication and learning, social choice, mechanism design, auctions, theories of knowledge, belief, and rational agency. Within the framework of extensive games, this problem has applications to many artificial intelligence scenarios. It is obvious that the performance of the agent improves as information available increases. It is shown that a non-uniform assignment strategy for successive choices does better than a fixed probability strategy. We consider both classical and quantum approaches to the problem. We argue that the superior performance of quantum decisions with access to entanglement cannot be fairly compared to a classical algorithm. If the cognitive systems of agents are taken to have access to quantum resources, or have a quantum mechanical basis, then that can be leveraged into superior performance.