If P vs NP remains unresolved after 1 second from P vs PSPACE being resolved, this market resolves YES. Otherwise NO.
P vs X is resolved when a essentially correct proof or disproof of P=X is published. The correctness will be eventually judged by consensus of the mathematical community
context:
It is known that P ⊆ NP ⊆ PSPACE and conjectured that the inclusions are proper. Thus P vs PSPACE is an "easier" problem, as a proof of P≠NP would automatically yield P≠PSPACE (causing the market to resolve NO). Resolving either problem would require some new revolutionary breakthrough technique, the question tries to get at this: will such a technique be so powerful as to automatically solve all problems "of this kind", or will it be a new war over complexity theory?