How Can Every Nash Equilibrium in Centipede Game Involve First Period Defection?

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mk552
Hi guys,

I would much appreciate your help. Could anyone explain to me how is it possible to prove that every Nash Equilibrium in Centipede involves players defecting in the first period. Also, is any strategy profile involving selling in the first period a NE? I know how to get unique SPNE, but the other problem seems confusing.

Thanks a lot!
 
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What are the conditions a strategy pair has to satisfy in order to be a NE?