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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 show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowledge relation is smooth. Conversely, for any common knowledge relation that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such that the resulting Bayesian game will not have any Bayesian… (More)

- Ziv Hellman
- TARK
- 2013

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)

- Ziv Hellman, ZIV HELLMAN
- 2008

This paper is concerned with the question of defining the bargaining set, a cooperative game solution, when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face (finite or infinite) sequences of exogenously specified TU-games and receive sequences of imputations against those static cooperative… (More)

- Ziv Hellman, Amit Gal
- ICEIS
- 2003

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 sup-norm of f , thus extending no betting results under common… (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)