678 research outputs found
Cauchy filters from Pelant's games
The language of finite games is used to rephrase Pelant's proof of his
result: The separable modification of the complete metric space
is not complete.Comment: 6 page
Semipullbacks of labelled Markov processes
A labelled Markov process (LMP) consists of a measurable space together
with an indexed family of Markov kernels from to itself. This structure has
been used to model probabilistic computations in Computer Science, and one of
the main problems in the area is to define and decide whether two LMP and
"behave the same". There are two natural categorical definitions of
sameness of behavior: and are bisimilar if there exist an LMP and
measure preserving maps forming a diagram of the shape ; and they are behaviorally equivalent if there exist some
and maps forming a dual diagram .
These two notions differ for general measurable spaces but Doberkat
(extending a result by Edalat) proved that they coincide for analytic Borel
spaces, showing that from every diagram one
can obtain a bisimilarity diagram as above. Moreover, the resulting square of
measure preserving maps is commutative (a "semipullback").
In this paper, we extend the previous result to measurable spaces
isomorphic to a universally measurable subset of a Polish space with the trace
of the Borel -algebra, using a version of Strassen's theorem on common
extensions of finitely additive measures.Comment: 10 pages; v2: missing attribution to Doberka
Cake Division by Majority Decision
We consider a collective choice process where three players make proposals sequentially on how to divide a given quantity of resources. Afterwards, one of the proposals is chosen by majority decision. If no proposal obtains a majority, a proposal is drawn by lot. We establish the existence of the set of subgame perfect equilibria, using a suitable refinement concept. In any equilibrium, the first agent offers the whole cake to the second proposal-maker, who in turn offers the whole cake back to the first agent. The third agent is then indifferent about dividing the cake between himself and the first or the second agent.division of a cake, majority decisions, tie-breaking rules
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