  We introduce a three-player nonlocal game, with a finite number of classical
questions and answers, such that the optimal success probability of $1$ in the
game can only be achieved in the limit of strategies using arbitrarily
high-dimensional entangled states. Precisely, there exists a constant $0 <c\leq
1$ such that to succeed with probability $1-\varepsilon$ in the game it is
necessary to use an entangled state of at least $\Omega(\varepsilon^{-c})$
qubits, and it is sufficient to use a state of at most $O(\varepsilon^{-1})$
qubits.
  The game is based on the coherent state exchange game of Leung et al. (CJTCS
2013). In our game, the task of the quantum verifier is delegated to a third
player by a classical referee. Our results complement those of Slofstra
(arXiv:1703.08618) and Dykema et al. (arXiv:1709.05032), who obtained
two-player games with similar (though quantitatively weaker) properties based
on the representation theory of finitely presented groups and $C^*$-algebras
respectively.
