From a7d637f23cb5eee84f0f959fc4e53effaf2694a0 Mon Sep 17 00:00:00 2001 From: Silvio Rhatto Date: Thu, 23 Jan 2020 09:39:29 -0300 Subject: Updates books/economics/game-theory-critical-introduction --- .../economics/game-theory-critical-introduction.md | 30 ++++++++++++++++++++++ 1 file changed, 30 insertions(+) (limited to 'books') diff --git a/books/economics/game-theory-critical-introduction.md b/books/economics/game-theory-critical-introduction.md index a23ee05..a0fad61 100644 --- a/books/economics/game-theory-critical-introduction.md +++ b/books/economics/game-theory-critical-introduction.md @@ -568,3 +568,33 @@ is algorithmic"): of Nash. -- 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? -- cgit v1.2.3