Final answer:
In a negotiation scenario similar to the Ultimatum Game, Player A might propose a small offer like $1, leveraging rational self-interest. However, the final settled amount might vary, with perfect cooperation pointing towards a fair 50-50 split.
Step-by-step explanation:
The question is framed in the context of a negotiation or game theory scenario, resembling the Ultimatum Game. What Player A initially asks for is not specified, but in a rational context, Player A could ask for nearly the entire amount, offering Player B a very small portion such as $1. The rationality suggests that any amount is better than nothing, so Player A expects Player B to accept this small offer. However, the final amount Player A settles on could be different based on factors such as fairness and cooperation which are not entirely rational. If players were behaving with perfect cooperation, they would likely settle for an even $5-$5 split.