Sentence:  Essentially this imposed two conditions : First , international law had to <WSD>recognize</WSD> and be compatible with an international political system in which a number of states were competitive , suspicious , and opportunistic in their political alignments with one another ; second , it had to be compatible with the value system that they shared . 
Meaning of the word marked with <WSD> tags:  accept (someone) to be what is claimed or accept his power and authority