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

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In the discussion, the focus is on proving that every Nash Equilibrium (NE) in the Centipede game involves players defecting in the first period. The inquiry seeks clarification on whether any strategy profile that includes selling in the first period qualifies as a NE. Additionally, there is a request for an explanation of the conditions that a strategy pair must meet to be considered a NE. The conversation emphasizes understanding the dynamics of strategy choices in the Centipede game and the implications of these choices on equilibrium outcomes.
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?
 

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