In the extended Centipede below, show that the SPNE is a strategy profile involving the choice of the down (di ) strategy at every node i of the game. Show also that, in the context of a sequential...

In the extended Centipede below, show that the SPNE is a strategy profile involving the choice of the down (di ) strategy at every node i of the game. Show also that, in the context of a sequential (or Perfect Bayesian) equilibrium, an initial probability that R chooses irrationally (i.e. with equal probability between strategies di and ai , for all i) of about 0.0022 suffices to cause a rational R always to play across at node 1.

Extended Centipede – Description: R kicks the game off at node 1. If R plays a1 then C gets a chance to play at node 2.


(Otherwise the game ends and they collect 1 and 0 utils respectively.) If C plays a2 then R gets a chance to play again at node 2. And so on.