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Simon (2003) presented an example of a 3-player Bayesian game with no Bayesian equilibria, leaving open the question of whether or not there are games with no Bayesian approximate equilibria. We present an example of a Bayesian game with two players, two actions and a continuum of states that possesses no Bayesian approximate equi-libria, thus resolving the(More)
a r t i c l e i n f o a b s t r a c t 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 set of consistent type(More)
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 common improper prior implies the existence of a bounded agreeable(More)
a r t i c l e i n f o a b s t r a c t 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 sufficient condition for the existence of a common prior for several players is given in terms of the players' present beliefs only. A common prior(More)
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). We show that even when the truth axiom is not assumed it turns out that players will find it impossible to agree to disagree under fairly broad(More)
Contemporary spreadsheets are plagued by a profusion of errors, auditing difficulties, lack of uniform development methodologies, and barriers to easy comprehension of the underlying business models they represent. This paper presents a case that most of these difficulties stem from the fact that the standard spreadsheet user-interaction paradigm – the(More)
Assuming a 'spectrum' or ordering of the players of a coali-tional 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 asymmetric power index in which positioning along the spectrum is(More)