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A player belonging to every winning coalition. Giving all of the grand-coalition value to a veto player satisfies every core constraint in a nontrivial simple cooperative game. If there are no veto players, its core of a simple cooperative game is empty.

A weighted voting game assigns player weights and a threshold, and declares coalitions winning when their total weight passes that threshold. The strict $>t$ convention is equivalent to quota $t+1$ for integer weights; another common convention writes a weak inequality directly. Nontrivial examples are simple cooperative games. Having nonnegative weights does not guarantee a convex cooperative game: two-of-three majority supplies a counterexample.

A coalition of value $1$ in a simple cooperative game. Monotonicity makes every superset of a winning coalition winning. An inclusion-minimal winning coalition has no winning proper subset.