Takuma Wakayama

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.

Maximal Manipulation of Envy-Free Solutions in Economies with Indivisible Goods and Money

We consider the problem of the fair allocation of indivisible goods and money with non-quasi-linear preferences. The purpose of the present study is to examine strategic manipulation under envy-free solutions. We show that under a certain domain-richness condition, each individual obtains the welfare level of his “optimal” envy-free allocation by maximally manipulating the solutions. This maximal manipulation theorem is helpful in analyzing the set of Nash equilibrium allocations in the direct revelation games associated with a given envy-free solution: if an envy-free solution satisfies a mild condition, the set of Nash equilibrium allocations in its associated direct revelation game coincides with that of envy-free allocations.

Secure implementation in Shapley–Scarf housing markets

This paper considers the object allocation problem introduced by Shap- ley 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 im- plementable 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.

Bribe-Proof Division of a Private Good

This paper considers the problem of allocating an amount of a perfectly divisible resource among agents. We are interested in rules eliminating the possibility that an agent can compensate another to misrepresent her preferences, making both agents strictly better off. Such rules are said to be bribe-proof (Schummer, 2000). We first provide necessary and sufficient conditions for any rule defined on the single-peaked domain to be bribe-proof. By invoking this result and Chings (1994) result, we obtain the uniform rule as the unique bribe-proof and symmetric rule on the single-peaked domain. Furthermore, we examine how large a domain can be to allow for the existence of bribe-proof and symmetric rules and show that the convex domain is such a unique maximal domain.

Ex Post Self-Implementation

We consider the implementation problem under incomplete information and interdependent values. This paper provides a necessary and sufficient condition for a social choice function to be ex post self-implementable in general environments. A social choice function is ex post self-implementable if it is fully ex post implemented by the associated direct revelation mechanism. We introduce a new monotonicity condition called restricted monotonicity and show that this and ex post incentive compatibility are necessary and sufficient for ex post self-implementation.

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.

Endowments-swapping-proof house allocation

We consider house (re)allocation problems (Shapley and Scarf, 1974) with strict preferences. We are concerned with the possibility that a pair of agents may gain by swapping their endowments before the operation of the chosen rule. A rule is called endowments-swapping-proof if it is immune to this kind of manipulation. Our main result is that the top trading cycles rule is the only rule that satisfies individual rationality, strategy-proofness, and endowments-swapping-proofness.

Bribe-Proofness for Single-Peaked Preferences: Characterizations and Maximality-of-Domains Results

This paper considers the problem of allocating an amount of a perfectly divisible resource among agents. We are interested in rules eliminating the possibility that an agent can compensate another to misrepresent her preferences, making both agents strictly better off. Such rules are said to be bribe-proof (Schummer, 2000). We first provide necessary and sufficient conditions for any rule defined on the single-peaked domain to be bribe-proof. By invoking this and Chings (1994) result, we obtain the uniform rule as the unique bribe-proof and symmetric rule on the single-peaked domain. Furthermore, we examine how large a domain can be to allow for the existence of bribe-proof and symmetric rules and show that the convex domain is such a unique maximal domain.

Pre-Exchange-Proof House Allocation

We consider house allocation problems (Shapley and Scarf, 1974) with strict preferences. We introduce a new axiom called pre-exchange-proofness, which states that no pair of agents gain by exchanging their endowments with each other prior to the operation of the chosen rule. We establish that a rule is individually rational, strategy-proof, and pre-exchange-proof if and only if it is the top trading cycles rule. However, with regard to a strict version of pre-exchange-proofness, we obtain the following impossibility result: no individually rational rule satisfies strict pre-exchange-proofness if there are three or more agents.