Deakin University
Publications
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Some Characterizations of Generalized Top Trading Cycles, with William Phan and Yuki Tamura,Games and Economic Behavior, 2023
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Abstract: Consider object exchange problems when each agent may be endowed with and consume more than one object. For most domains of preferences, no rule satisfies efficiency, the endowment lower bound, and strategy-proofness. Insisting on the first two properties, we explore the extent to which weaker incentive compatibility can be achieved. Motivated by behavioral and computational considerations as well as online mechanisms, we define several forms of manipulation. We consider the lexicographic domain of preferences, and provide several characterizations of Generalized Top Trading Cycles based on properties concerning immunity from heuristic and identity-splitting manipulations. We also show that this establishes a boundary with respect to incentive compatibility—minimal strengthening results in impossibility.
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Trading Probabilities Along Cycles, with William Phan, Journal of Mathematical Economics, 2022
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Abstract: Consider the problem of allocating indivisible objects when agents are endowed with fractional amounts and rules can assign lotteries. We study a natural generalization (to the probabilistic domain) of Gale’s Top Trading Cycles. The latter features an algorithm wherein agents trade objects along a cycle—in our new family of rules, agents now trade probabilities of objects along a cycle. We ask if the attractive properties, namely efficiency, individual rationality, and strategy-proofness extended in the stochastic dominance sense, carry over to the Trading-Probabilities-Along-Cycles (TPAC) rules. All of these rules are sd-efficient. We characterize separately the subclass of TPAC rules satisfying the sd-endowment lower bound and sd-strategy-proofness. Regarding fairness, we follow in spirit to the no-envy in net trade condition of Schmeidler and Vind (1972), where the set of allocations satisfying the property essentially coincides with the set of competitive equilibria, and augment the notion appropriately for our environment. We further generalize the TPAC family while extending results on sd-efficiency and the sd-endowment lower bound, and provide sufficient conditions on parameters for the rules to arbitrarily closely satisfy the sd-no-envy in net trade.