Antonio and Caroline are 13-year-old twins who are fighting over how to spend a $200 gift certificate they jointly won in a raffle. The gift certificate is for a store that sells MP3 players. There are three kinds of MP3 players available: one that costs $150, one that costs $100, and one that costs $50. Each twin wants his or her own MP3 player. Both twins greatly prefer the $100 player to the $50 player, but they only slightly prefer the $150 player to the $100 player. The gift certificate can be used only once, regardless of whether or not the full $200 value is redeemed. Suppose their mother intervenes and uses the gift certificate to purchase each twin the $100 player. This outcome is because .