Problem 4. Consider a cake-cutting protocol for n = 3 agents: Alice, Bob, and Carlos. Suppose that Alice first cuts the cake into three pieces. Then Bob gets to choose a piece of the three, followed by Carlos, who chooses one of the two pieces that remain after Bob's choice. Finally, Alice gets the piece that was not chosen by either Bob or Carlos. Analyze the fairness of this protocol. Is any agent guaranteed to obtain at least a utility of 1/3 their value of the whole cake? Could any agent envy another