A coalgebraic approach to type spaces

Abstract

When two or more players are engaged in a game with uncertainties, they need to consider what the other players’ beliefs may be, which in turn are influenced by what they think the first player’s ideas are. Harsanyi defined type spaces simply as a set in which all possible players-as defined by their beliefs- could be found. Later on, more meaningful constructions of this set were performed. The theory of coalgebra, on the other hand, has been created to deal with circular phenomena, so its application to the problem of type spaces is only natural. We show how to apply it and we use the more general framework of category theory to compare the relative strength of previous solutions to the problem of defining type spaces.