Dominant Strategy Implementation in Economic Environments

We study dominant strategy implementation especially in economic environments. We first show that in general environments, strategy-proofness and quasi-strong-non-bossiness together are necessary and sufficient for dominant strategy implementation via the associated direct revelationmechanism. We next prove that in weak separable environments, strategy-proofness is sufficient for dominant strategy implementation, by using an augmented revelation mechanism similar to the one devised by Jackson et al. (1994). Moreover, we focus on pure exchange economies without free disposal, and try to construct another augmented revelation mechanism that satisfies balancedness in and out of equilibrium, and which implements all strategy-proof social choice functions in dominant strategy equilibria.

Secure Implementation in Shapley-Scarf Housing Markets

This paper considers the object allocation problem introduced by Shapley and Scarf (1974). We study secure implementation (Saijo, Sjostrom, and Yamato, 2007), that is, double implementation in dominant strategy and Nash equilibria. We prove that (i) an individually rational solution is securely implementable if and only if it is the no-trade solution, (ii) a neutral solution is securely implementable if and only if it is a serial dictatorship, and (iii) an efficient solution is securely implementable if and only if it is a sequential dictatorship. Furthermore, we provide a complete characterization of securely implementable solutions in the two-agent case.

Uniform, Equal Division, and Other Envy-free Rules between the Two

This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the subclass of strategy-proof rules and show that the subclass also forms a complete lattice. In both cases, the upper bound is the uniform rule, the lower bound is the equal division rule, and any other rule is between the two.

Relationships between Non-Bossiness and Nash Implementability

We explore the relationships between non-bossiness and Nash implementability. We provide a new domain-richness condition, weak monotonic closedness, and prove that on weakly monotonically closed domains, non-bossiness together with individual monotonicity is equivalent to monotonicity, a necessary condition for Nash implementation. The result shows an impossibility of Nash implementation in all economies except pure public goods economies, in the sense that it indicates that in all economies except pure public goods economies, it is impossible to implement bossy social choice functions in Nash equilibria, which embody the characteristics inherent in those economies.Non-Bossiness, Individual Monotonicity, Monotonicity, Weak Monotonic Closedness.

Full-Truthful Implementation in Nash Equilibria

We consider full-truthful Nash implementation, which requires that truth telling by each agent should be a Nash equilibrium of a direct revelation mechanism, and that the set of Nash equilibrium outcomes of the mechanism should coincide with the f -optimal outcome. We show that restricted monotonicity together with an auxiliary condition called boundedness is both necessary and sufficient for full-truthful Nash implementation. We also prove that full-truthful Nash implementation is equivalent to secure implementation (Saijo et al. (2005)). This gives us an alternative characterization of securely implementable social choice functions.

Strategy-proof Sharing

We consider the problem of sharing a divisible good, where agents prefer more to less. First, we prove that a sharing rule satisfies strategy proofness if and only if it has the quasi-constancy property: no one changes her own share by changing her announcements. Next, by constructing a system of linear equations in a manner that is consistent with quasi-constancy, we provide a way to find every strategy-proof sharing rule. Finally, we identify a necessary and sufficient condition for the existence of non-constant, strategy-proof sharing rules, by examining the relationship between the constancy of strategy-proof sharing rules and the dimension of the solution space of the linear system.Strategy-proofness, Bossiness, Non-constancy, Quasi-constancy.

Secure Implementation in Shapley-Scarf Housing Markets

This paper considers the object allocation problem introduced by Shapley and Scarf (1974). We study secure implementation (Saijo, Sjöström, and Yamato, 2007), that is, double implementation in dominant strategy and Nash equilibria. We prove that (i) an individually rational solution is securely implementable if and only if it is the no-trade solution, (ii) a neutral solution is securely implementable if and only if it is a serial dictatorship, and (iii) an efficient solution is securely implementable if and only if it is a sequential dictatorship. Furthermore, we provide a complete characterization of securely implementable solutions in the two-agent case.ISER discussion paperDecember 2008 Revised February 200

Full-Truthful Implementation in Nash Equilibria

We consider full-truthful Nash implementation, which requires truth telling by each agent to be a Nash equilibrium of a direct revelation mechanism, and every Nash equilibrium outcome of the mechanism to be f-optimal. We show that restricted monotonicity plus an auxiliary condition is necessary and sufficient for full-truthful Nash implementation, and that full-truthful Nash implementation is equivalent to secure implementation (Saijo et al. (2007)). The equivalence gives us an alternative characterization of securely implementable social choice functions in terms of restricted monotonicity