Pairwise Strategy-Proofness and Self-Enforcing Manipulation

"Strategy-proofness" is one of the axioms that are most frequently used in the recent literature on social choice theory. It requires that by misrepresenting his preferences, no agent can manipulate the outcome of the social choice rule in his favor. The stronger requirement of "group strategy-proofness" is also often employed to obtain clear characterization results of social choice rules. Group strategy-proofness requires that no group of agents can manipulate the outcome in their favors. In this paper, we advocate "effective pairwise strategy-proofness." It is the requirement that the social choice rule should be immune to unilateral manipulation and "self-enforcing" pairwise manipulation in the sense that no agent of a pair has the incentive to betray his partner. We apply the axiom of effective pairwise strategy-proofness to three types of economies: public good economy, pure exchange economy, and allotment economy. Although effective pairwise strategy-proofness is seemingly a much weaker axiom than group strategy-proofness, effective pairwise strategy-proofness characterizes social choice rules that are analyzed by using different axioms in the literature.

Auctions with Endogenous Price Ceiling:Theoretical and Experimental Results

This paper analyzes an auction mechanism that excludes overoptimistic bidders inspired by the rules of the procurement auctions adopted by several Japanese local governments. Our theoretical and experimental results suggest that the endogenous exclusion rule reduces the probability of suffering a monetary loss induced by winning the auction, and also mitigates the problem of the winnerfs curse in the laboratory. However, this protection comes at the price of a lower revenue for the seller.

Maximal Domain for Strategy-Proof Rules in Allotment Economies

We consider the problem of allocating an amount of a perfectly divisible good among a group of n agents. We study how large a preference domain can be to allow for the existence of strategy-proof, symmetric, and efficient allocation rules when the amount of the good is a variable. This question is qualified by an additional requirement that a domain should include a minimally rich domain. We first characterize the uniform rule (Bennasy, 1982) as the unique strategy-proof, symmetric, and efficient rule on a minimally rich domain when the amount of the good is fixed. Then, exploiting this characterization, we establish the following: There is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable. It is the single-plateaued domain.

Auctions for Public Construction with Corner-cutting

This paper reports the theoretical and experimental results of auctions for public construction in which firms cut corners. We show that the winning bids and the winner's quality choices of the constructed buildings are both zero in equilibria if there are at least two firms whose initial cash balances are zero, and it is a common knowledge. The experimental results are close to the theoretical results and indicate that firms with zero-initial cash balance win and that the winning bids and the winner's quality choices of the constructed buildings are considerably low.

An Impossibility Theorem in Matching Problems

This paper studies the possibility of strategy-proof rules yielding satisfactory solutions to matching problems. Alcalde and Barber_ (1994) show that efficient and individually rational matching rules are manipulable in the one-to-one matching model. We pursue the possibility of strategy-proof matching rules by relaxing effciency to the weaker condition of respect for unanimity. Our first result is positive. We prove that a strategy-proof rule exists that is individually rational and respects unanimity. However, this rule is unreasonable in the sense that a pair of agents who are the best for each other are matched on only rare occasions. In order to explore the possibility of better matching rules, we introduce the natural condition of "respect for pairwise unanimity." Respect for pairwise unanimity states that a pair of agents who are the best for each other should be matched, and an agent wishing to stay single should stay single. Our second result is negative. We prove that no strategy-proof rule exists that respects pairwise unanimity. This result implies Roth (1982) showing that stable rules are manipulable. We then extend this to the many-to-one matching model.

Coalitionally Strategy-Proof Rules in Allotment Economies of Homogeneous Indivisible Goods

We consider the allotment problem of homogeneous indivisible goods among agents with single-peaked and risk-averse von Neumann-Morgenstern expected utility functions. We establish that a rule satisfies coalitional strategy-proofness, same-sideness, and strong symmetry if and only if it is the uniform probabilistic rule. By constructing an example, we show that if same-sideness is replaced by respect for unanimity, this statement does not hold even with the additional requirements of no-envy, anonymity, at most binary, peaks-onlyness and continuity.

Non Uniform Projections of Surfaces in P3\mathbb{P}^3

Consider the projection of a smooth irreducible surface in $\mathbb{P}^3$ from a point. The uniform position principle implies that the monodromy group of such a projection from a general point in $\mathbb{P}^3$ is the whole symmetric group. We will call such points uniform. Inspired by a result of Pirola and Schlesinger for the case of curves, we prove that the locus of non-uniform points of $\mathbb{P}^3$ is at most finite.Comment: 11 pages, no figures. This paper is a result of the work carried out at PRAGMATIC 2016 Research School. Minor changes and journal references adde

Vickrey Allocation Rule with Income Effect

We consider situations where a society tries to efficiently allocate several homogeneous and indivisible goods among agents. Each agent receives at most one unit of the good. For example, suppose that a government wishes to allocate a fixed number of licenses to operate in its country to private companies with highest abilities to utilize the licenses. Usually companies with higher abilities can make more profits by licenses and are willing to pay higher prices for them. Thus, auction mechanisms are often employed to extract the information on companies' abilities and to allocate licenses efficiently. However, if prices are too high, they may damage companies' abilities to operate. Generally high prices may change the benefits agents obtain from the goods unless agents' preferences are quasi-linear, and we call it "income effect". In this paper, we establish that on domains including nonquasi-linear preferences, that is, preferences exhibiting income effect, an allocation rule which satisfies Pareto-efficiency, strategy-proofness, individual rationality, and nonnegative payment uniquely exists and it is the Vickrey allocation rule.

Characterizing the Vickrey Combinatorial Auction by Induction

This note studies the allocation of heterogeneous commodities to agents whose private values for combinations of these commodities are monotonic by inclusion. This setting can accommodate the presence of complementarity and substitutability among the heterogeneous commodities. By using induction logic, we provide an elementary proof of Holmstrom's (1919) characterization of the Vickrey combinatorial auction as the unique efficient, strategy-proof, and individually rational allocation rule. Our proof method can also be applied to domains to which his proof cannot be.