# Sequential game equilibrium strategy question

The question asks for player B's equilibrium strategy, hence shouldn't player B choose the strategy that gives the highest payoff after player A's move? Why does player B choose 4 over 5 and 6 over 8 when he should choose the one with the highest payoff? I don't get why the answer should be B in this case...

• I am also confused. While a,c,d are not even strategies (a strategy contains an action for every decision node), you can find a deviation for strategy b (as you said) and this is independent of whether "equilibrium" means NE or SPNE. – Bayesian May 20 at 18:18
• Thanks for the reply. But any guesses for why b is chosen out of the 4? Was I right on the part where players will always choose the strategy with the highest payoff ? – onetwothree May 20 at 18:35
• I suspect that the question may want you to think that A will certainly enter as all the outcomes for A entering dominate all those for A not entering: $\min(3,1) \gt \max(0,0)$. If so, option (a) is an equilibrium strategy for B, since $5 \gt 4$ – Henry May 20 at 23:12