Monotonic models and cycles
A partitional model of knowledge is monotonic if there exists a linear order on the state space such that, for every player, each element of her partition contains only a sequence of consecutive states. In monotonic models, the absence of alternating cycles is equivalent to the property that, for every pair of players, the join of their partitions contains only singletons. Under these equivalent conditions any set of posterior beliefs for the players is consistent (i.e., there is a common prior). We describe the lattice properties of monotonic models, develop a test to check if a model is monotonic, propose a simple sufficient condition for non-monotonicity, and provide some examples. We also study models having circular orders, a weakening of monotonicity.
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Game Theory and Information
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