Levels of Knowledge, Games, and Group Action

In this paper we investigate the possible states of knowledge among a group of individuals and their relations to decision making. A travelling salesman found himself spending the night at home with his wife when one of his trips was accidentally cancelled. The two of them were sound asleep, when in the middle of the night there was a loud knock at the front door. The wife woke up with a start and cried out, “Oh my God! It’s my husband!” Whereupon the husband leapt out of bed, ran across the room and jumped out the window. Schank and Abelson, 1977, p. 59. Wimmer and Perner begin their paper [WM] on Beliefs about beliefs with this story from Schank and Abelson which may seem amusing to some and disturbing to others. But the point of the story seems to be that husband and wife each have their own scenario and neither corresponds to the actuality. The wife is a bit better off as she knows where she is though not whom she is with. The husband is unaware of the identity of his companion and even of his location. Wimmer and Perner themselves are concerned primarily with the perception by children of other people’s mindsets. The following quote from [WM] is a story about Maxi which they told a group of children: Mother returns from her shopping trip. She bought chocolate for a cake. Maxi may help her put away the things. He asks her, “Where should I put the chocolate?” “In the blue cupboard,” says the mother. Later, with Maxi gone out to play, the mother transfers the chocolate from the blue cupboard to the green cupboard. Maxi then comes back from the playground, hungry, and he wants to get some chocolate. In Wimmer and Perner’s experiment, little children who were told the Maxi story were then asked the belief question, “Where will Maxi look for the chocolate?” Department of Computer Science, Brooklyn College, and doctoral programs in Computer Science, Mathematics and Philosophy, CUNY Graduate Center, 365 Fifth Anenue, New York, NY 10016. Email: [email protected] Research supported by grants from the NSF and the CUNY-FRAP program. Some of the results in this paper were presented at LOFT’02 and at WOLLIC’02.