The emergence of "fifty-fifty" probability judgments through Bayesian updating under ambiguity

This paper explains the empirical phenomenon of persistent "fifty-fifty"probability judgments through a model of Bayesian updating under ambiguity. To this purpose I characterize an announced probability judgment as a Bayesian estimate given as the solution to a Choquet expected utility maximization problem with respect to a neo-additive capacity that has been updated in accordance with the Generalized Bayesian update rule. Only for the non-generic case, in which this capacity degenerates to an additive probability measure, the agent will learn the events true probability if the number of i.i.d. data observations gets large. In contrast, for the generic case in which the capacity is not additive, the agent's announced probability judgment becomes a persistent " fifty-fifty "probability judgment after finitely many observations.http://www.elsevier.com/locate/fsshb201

Non-additive anonymous games

This paper introduces a class of non-additive anonymous games where agents are assumed to be uncertain (in the sense of Knight) about opponents’ strategies and about the initial distribution over players’ characteristics in the game. These uncertainties are modelled by non-additive measures or capacities. The Cournot-Nash equilibrium existence theorem is proven for this class of games. It is shown that the equilibrium distribution can be symmetrized under milder conditions than in the case of additive games. In particular, it is not required for the space characteristics to be atomless under capacities. The set-valued map of the Cournot-Nash equilibria is upper-semicontinuous as a function of initial beliefs of the players for non-additive anonymous games