9,509 research outputs found
The Evolutionary Stability of Optimism, Pessimism and Complete Ignorance
We provide an evolutionary foundation to evidence that in some situations humans maintain optimistic or pessimistic attitudes towards uncertainty and are ignorant to relevant aspects of the environment. Players in strategic games face Knightian uncertainty about opponents’ actions and maximize individually their Choquet expected utility. Our Choquet expected utility model allows for both an optimistic or pessimistic attitude towards uncertainty as well as ignorance to strategic dependencies. An optimist (resp. pessimist) overweights good (resp. bad) outcomes. A complete ignorant never reacts to opponents’ change of actions. With qualifications we show that optimistic (resp. pessimistic) complete ignorance is evolutionary stable / yields a strategic advantage in submodular (resp. supermodular) games with aggregate externalities. Moreover, this evolutionary stable preference leads to Walrasian behavior in those classes of games
Uniquely determined uniform probability on the natural numbers
In this paper, we address the problem of constructing a uniform probability
measure on . Of course, this is not possible within the bounds of
the Kolmogorov axioms and we have to violate at least one axiom. We define a
probability measure as a finitely additive measure assigning probability to
the whole space, on a domain which is closed under complements and finite
disjoint unions. We introduce and motivate a notion of uniformity which we call
weak thinnability, which is strictly stronger than extension of natural
density. We construct a weakly thinnable probability measure and we show that
on its domain, which contains sets without natural density, probability is
uniquely determined by weak thinnability. In this sense, we can assign uniform
probabilities in a canonical way. We generalize this result to uniform
probability measures on other metric spaces, including .Comment: We added a discussion of coherent probability measures and some
explanation regarding the operator we study. We changed the title to a more
descriptive one. Further, we tidied up the proofs and corrected and
simplified some minor issue
- …