Both these statements are true, so I'd say they are consistent :-)

In particular, the first one is true because "The player would pay if asked" is true.

"The player would pay if asked" is true because "The player will be asked" is false and implies anything.

"The player will be asked" is false by the extra axiom.

Note I'm using ordinary propositional logic here, not some sort of weird "counterfactual logic" that people have in mind and which isn't formalizable anyway. Hence the lack of distinction between "will" and "would".