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TZID:America/Chicago
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DTSTART:20211107T020000
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BEGIN:DAYLIGHT
DTSTART:20210314T020000
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RDATE:20220313T020000
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BEGIN:VEVENT
UID:calendar.24875.field_event_date_2.0@math.wustl.edu
CREATED:20210917T193249Z
DESCRIPTION:Abstract: Lloyd S. Shapley introduced a set of axioms in 1953,
now called the Shapley axioms, and showed that the axioms characterize a
natural allocation among the players who are in grand coalition of a coop
erative game. Recently, A. Stern and A. Tettenhorst showed that a coopera
tive game can be decomposed into a sum of component games, one for each p
layer, whose value at the grand coalition coincides with the Shapley valu
e. The component games are defined by the solutions to the naturally defi
ned system of least squares - or Poisson - equations via the framework of
the Hodge decomposition on the hypercube graph.\n\nIn this talk we propose
a new set of axioms which characterizes the component games. Furthermore\
, we realize them through an intriguing stochastic path integral driven by
a canonical Markov chain. The integrals are natural representation for th
e expected total contribution made by the players for each coalition, and
hence can be viewed as their fair share. This allows us to interpret the
component game values for each coalition also as a valid measure of fair a
llocation among the players in the coalition. Finally, we extend the path
integrals on general graphs and discover a fundamental connection between
stochastic integrations and Hodge theory on graphs.\n\n \n\nHosts: Ari St
ern and Jonathan Weinstein (Economics)
DTSTART;TZID=America/Chicago:20210924T160000
DTEND;TZID=America/Chicago:20210924T170000
LAST-MODIFIED:20210924T142051Z
SUMMARY:'Generalized Shapley axioms and value allocation in cooperative gam
es via Hodge theory on graphs'
URL;TYPE=URI:https://math.wustl.edu/events/generalized-shapley-axioms-and-v
alue-allocation-cooperative-games-hodge-theory-graphs
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