Strategy-proofness and the strict core in a market with indivisibilities

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

“…Then, we have proved that, while in the restricted case of strict preferences the TTC mechanism is the only one that satisfies individual rationality, Pareto efficiency and strategy-proofness (see Ma (1994)), in the general case we have a family of mechanisms that satisfy all these properties. Additionally, we are going to prove that our family of mechanisms always selects a strict core allocation if the strict core is non-empty.…”

“…1 It has been shown (Roth (1982)) that this deterministic mechanism is strategy-proof. Moreover, Ma (1994) shows that this is the unique mechanism that satisfies individual rationality, Pareto-efficiency and strategy-proofness in this domain of strict preferences. Shapley and Scarf attributed to Gale an algorithm called Top Trading Cycles to compute the strict core assignment of a housing market.…”

“…In what follows we depict the directed graphs that are formed at each step of the algorithm: 5 Step 1:…”

“…Furthermore, Ma (1994) shows that the TTC mechanism, equivalent to the strict core mechanism, is the only mechanism that satisfies individual rationality, Pareto-efficiency and strategy-proofness (in the domain of strict preferences).…”

Secure implementation in Shapley–Scarf housing markets

“…Some characterizations of the solution can be found in Ma (1994), Svensson (1999), Takamiya (2001), and Miyagawa (2002). Furthermore, the solution is dominant strategy implementable (Mizukami and Wakayama, 2007) and Nash implementable when there are at least three agents (Sönmez, 1996).…”