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The phenomenon of monogamy of Bell inequality violations is interesting bothfrom the fundamental perspective as well as in cryptographic applications suchas the extraction of randomness and secret bits. In this article, we derive newand stronger monogamy relations for violations of Bell inequalities in generalno-signaling theories. These relations are applicable to the class of binaryoutput correlation inequalities known as XOR games, and to a restricted set ofunique games. In many instances of interest, we show that the derived relationprovides a significant strengthening over previously known results. The resultinvolves a shift in paradigm towards the importance in monogamies of the numberof inputs of one party which lead to a contradiction from local realisticpredictions.

Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities