Before revision:  In the equilibrium, the interim expected payoff of the collusion initiator Pareto dominates the counterpart in any robust equilibria of the single-option model (Es\"{o} and Schummer (2004)) and any other separating equilibria in our model.
After revision:  In the equilibrium, for each type of initiator the expected payoff is generally higher than the counterpart in any robust equilibria of the single-option model (Es\"{o} and Schummer (2004)) and any other separating equilibria in our model.