Assuming a `spectrum' or ordering on the players of a coalitional game, as in a political spectrum in a parliamentary situation, we consider a variation of the Shapley value in which coalitions may only be formed if they are connected with respect to the spectrum. This results in a naturally...

Extending to infinite state spaces that are compact metric spaces a result previously attained by D. Samet solely in the context of finite state spaces, a necessary and suficient condition for the existence of a common prior for several players is given in terms of the players' present beliefs...

This paper is concerned with the question of extending the definition of the bargaining set, a cooperative game solution, when cooperation takes place in a repeated setting. The focus is on situations in which the players face (finite or infinite) sequences of exogenously specified TU-games and...

To answer the question in the title we vary agents' 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...

Negative results on the the existence of Bayesian equilibria when state spaces have the cardinality of the continuum have been attained in recent years. This has led to the natural question: are there conditions that characterise when Bayesian games over continuum state spaces have measurable...

We show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a...

Simon (2003) presented an example of a 3-player Bayesian games with no Bayesian equilibria but it has been an open question whether or not there are games with no approximate Bayesian equilibria. We present an example of a Bayesian game with two players, two actions and a continuum of states...

We study conditions relating to the impossibility of agreeing to disagree in models of interactive KD45 belief (in contrast to models of S5 knowledge, which are used in nearly all the agreements literature). Agreement and disagreement are studied under models of belief in three broad settings:...

What happens when priors are not common? We show that for each type profile τ over a knowledge space (Ω, Π), where the state space Ω is connected with respect to the partition profile Π, we can associate a value 0 ≤ ε ≤ 1 that we term the prior distance of τ , where ε = 0 if and...