Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

► The Top Trading Cycles mechanism solves some exchange markets with indivisible goods. ► This well-known mechanism satisfies good properties when preferences are strict. ► We propose a new family of mechanisms, called Top Trading Absorbing Sets mechanisms. ► This family generalizes the TTC when individuals are allowed to report indifferences. ► This family preserves a maximal possible set of the properties of the TTC.