Pierpaolo Battigalli, Professor of Microeconomic Theory and Game Theory, Head of the Department of Decision Sciences of Bocconi University
Information Flows and Memory in Games
The standard extensive-form partitional representation of information in sequential games fails to distinguish the description of the rules of interaction from the description of players' personal traits. This is because such representation does not model how the information that is available to players as per the rules of the game blends with players' ability to retain such information. We propose a representation of sequential games that explicitly describes the flow of information accruing to players rather than the stock of information retained by players, as encoded in information partitions. Then, we add a formal description of players' mnemonic abilities by means of possibility correspondences. Assuming that players have perfect memory, our flow representation gives rise to information partitions satisfying perfect recall, but different combinations of rules about information flows and of players' mnemonic abilities may give rise to the same information partitions. All extensive-form representations with information partitions, including those failing perfect recall or featuring absentmindedness, can be generated by some such combinations. Our approach also allows to model situations where players' knowledge cannot be described by information partitions.