The seminal no betting theorem on the equivalence of common priors and absence of agreeable bets obtains only over compact state spaces. We show here that this equivalence can be generalised to any infinite space if we expand the set of priors to include probability charges as priors. Going...

What happens when priors are not common? We introduce a measure for how far a type space is from having a common prior, which we term prior distance. If a type space has δ prior distance, then for any bet f it cannot be common knowledge that each player expects a positive gain of δ times the...

To answer the question in the title we vary agentsʼ beliefs against the background of a fixed knowledge space, that is, a state space with a partition for each agent. Beliefs are the posterior probabilities of agents, which we call type profiles. We then ask what is the topological size of the...

The seminal no betting theorem on the equivalence of common priors and absence of agreeable bets obtains only over compact state spaces. We show here that this equivalence can be generalised to any infinite space if we expand the set of priors to include probability charges as priors. Going...