The equilibrium concepts that we now think of as various forms of backwards induction, namely, subgame perfect equilibrium (Selten, 1965), perfect equilibrium (Selten, 1975), sequential equilibrium (Kreps and Wilson, 1982), and quasi-perfect equilibrium (van Damme, 1984), while formally well defined in a wider class of games, are explicitly restricted to games with perfect recall. We argue that in games without perfect recall the original definitions are inappropriate. Our reading of the original papers is that the authors were aware that their definitions did not formally require the assumption of perfect recall but they were also aware that without the assumption of perfect recall the definitions they gave were not the “correct” ones. We give definitions of these concepts that identify the same outcomes in games with perfect recall and behave well in linear games without perfect recall.
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