
Edi Karni
14
1.3.4 The Model of Anscombe and Aumann
Let S be a finite set of states, and let the set of consequences,
, be the set of lotteries
on an arbitrary set of prizes, X.The choice set, H, consists of all the mappings from S
to
. Elements of H are acts whose consequences are lottery tickets. The choice of
an act, h, by the decision maker and a state, s, by nature entitles the decision maker to
participate in the lottery h(s) to determine his/her ultimate payoff, which is some ele-
ment of the set X. Following Anscombe and Aumann (1963), it is useful to think about
states as the possible outcomes of a horse race. An act is a bet on ...