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rhatto
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Updates books/economics/game-theory-critical-introduction
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@@ -568,3 +568,33 @@ is algorithmic"):
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@@ -568,3 +568,33 @@ is algorithmic"):
of Nash.
of Nash.
-- 58-60
-- 58-60
"Irrational" plays which might intend to send a message to other players:
Indeed why should one assume in this way that players cannot (or
should not) try to make statements about themselves through patterning
their ‘trembles? The question becomes particularly sharp once it is recalled
that, on the conventional account, players must expect that there is always
some chance of a tremble. Trembles in this sense are part of normal
behaviour, and the critics argue that agents may well attempt to use them
as a medium for signalling something to each other. Of course, players will
not do so if they believe that their chosen pattern is going to be ignored
by others. But that is the point: why assume that this is what they will
believe from the beginning, especially when agents can see that the
generally accepted use of trembles as signals might secure a better
outcome for both players [...]?
Note that this is not an argument against backward induction per se: it is an
argument against assuming CKR while working out beliefs via backward
induction (i.e. a criticism of Nash backward induction). When agents consider
patterning their ‘trembles’, they project forward about future behaviour given
that there are trembles now or in the past. What makes it ambiguous whether
they should do this, or stick to Nash backward induction instead, is that there
is no uniquely rational way of playing games like Figures 3.5 or 3.6 (unlike the
race to 20 game in which there is). In this light, the subgame perfect Nash
equilibrium offers one of many possible scenarios of how rational agents will
behave.
-- 93
Why not expand this affirmation so _any_ move to signal some intention?
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