With preference rigidities we find Pareto optima of an exchange economy, some of which involve unconsumed endowments. We show that such Pareto Optima can only be attained as market equilibria if there is a top dog in the initial endowment distribution who is richer than the other individuals. The most inegalitarian efficient allocation favouring the top dog is globally stable and is in the core. For endowment distributions with a top dog, the core contains efficient allocations more equal than the market equilibrium. A voting mechanism or government policy can also offset the top dog's power.