Updates books/economics/game-theory-critical-introduction

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?