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. Indeed, this representation does not model how the information given to players as per the rules of the game blends with players' cognitive abilities. 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 encoded in information partitions. Then, we add a game-independent description of players' mnemonic abilities. If players have perfect memory, our flow representation gives rise to information partitions satisfying the perfect recall property, but different combinations of information flows and players' mnemonic abilities may induce the same information partitions. We show how to use our framework to explicitly model a wide array of cognitive limitations and embed them in the representation of game situations.