Daisuke Hirata

Two axiomatic approaches to the probabilistic serial mechanism

This paper studies the problem of assigning a set of indivisible objects to a set of agents when monetary transfers are not allowed and agents reveal only ordinal preferences, but random assignments are possible. We offer two characterizations of the probabilistic serial mechanism, which assigns lotteries over objects. We show that it is the only mechanism satisfying non-wastefulness and ordinal fairness and the only mechanism satisfying sd-efficiency, sd-envy-freeness, and weak invariance or weak truncation robustness (where “sd” stands for first-order stochastic dominance).

Asymmetric Bertrand-Edgeworth Oligopoly and Mergers

This paper investigates mixed strategy equilibria in a capacity-constrained price competition among three firms. It is shown that the equilibria in an asymmetric oligopoly are substantially different from those in a duopoly and symmetric oligopoly. In an asymmetric triopoly, it is possible that (i) a continuum of equilibria exists and that (ii) the lowest price of the smallest firm is higher than that of the others and the smallest firm earns more than the max-min profit in undominated strategies. In particular, the second finding sheds light on a new pricing incentive in Bertrand competitions. As an application, the equilibrium characterizations give rise to a new class of merger paradoxes.

Collective choice rules and collective rationality: a unified method of characterizations

The purpose of this paper is to investigate the relationship between collective rationality and permissible collective choice rules using a unified approach inspired by Bossert and Suzumura (J Econ Theory 138:311–320, 2008). We consider collective choice rules satisfying four axioms: unrestricted domain, strong Pareto, anonymity, and neutrality. A number of new classes of collective choice rules as well as the Pareto and Pareto extension rules are characterized under various concepts of collective rationality: acyclicity, transitivity, quasi-transitivity, semi-transitivity, and the interval order property. Further, new concepts of collective rationality, K-term acyclicity and K-term consistency, are proposed and the corresponding characterizations are provided.

Characterizations of the Probabilistic Serial Mechanism

This paper provides two axiomatizations of the probabilistic serial mechanism. First, the mechanism is characterized by ordinal efficiency, envy-freeness, and truncation robustness. Truncation robustness restricts changes in assignments when agents truncate their preference lists. In this characterization, ordinal efficiency and envy-freeness can be replaced with weaker axioms, 2-ordinal efficiency and weak envy-freeness. Second, the mechanism is characterized by ordinal efficiency, independence of unassigned objects (IUO), and Rawlsian criterion. IUO requires assignments to be independent of whether an agent reports an object as acceptable or not, when she has no chance to obtain it even if she does so. Rawlsian criterion is a fairness condition that specifies how a mechanism should treat the worst-off agent.

On the uniqueness of Bertrand equilibrium

We introduce product differentiation in the model of price competition with strictly convex costs in which firms have to supply all of the forthcoming demand. We find that although a continuum of equilibria exists in a homogeneous product market, the competitive price equilibrium is the only robust one. Specifically, as long as the equilibrium correspondence is nonempty, the equilibrium price converges to the competitive price when the degree of product differentiation shrinks to zero.

A Model of a Two-Stage All-Pay Auction

The present paper studies a simple two-stage model of an all-pay auction under complete information. All-pay auctions are often used to model competition with irreversible investments such as political lobbying, and in the existing models, the equilibrium outcomes are quite different from the winner-pay auctions (under complete information): The unique equilibrium is in non-degenerate mixed strategies in the sealed-bid all-pay auction, and the highest value bidder wins at (virtually) no cost in the dollar auction. In sharp contrast with those existing models, the equilibrium outcome in the present setting is almost identical to the winner-pay auctions. That is, (a) the highest value bidder wins with probability one, and (b) the revenue of the seller is equal to the second highest value among the bidders. Also, from a mechanism-design point of view, the present game form is more robust than other all-pay mechanisms in that the seller does not need any information about the bidders’ valuations. Although the analysis focuses on the two-bidder two-stage case, the results extend to arbitrary numbers of bidders and stages.

On Stable and Strategy-Proof Rules in Matching Markets with Contracts

This note provides three additional results that are omitted from Hirata and Kasuya (2017) but were contained in an older version (Hirata and Kasuya, 2015).

Organizational Design and Career Concerns

This paper studies organizational design as the allocation of decision rights, primarily focusing on its interplay with agents’ career motives. I identify a new tradeoff between delegation and centralization, which arises solely from career concerns: When delegated, an agent takes inefficient actions at the cost of a principal but also works harder ex post to implement his project, in order to manipulate the market expectations of his ability. Compared to the existing literature, the contribution of the paper is two-fold. First, it endogenizes the agent’s bias as a result of career concerns. Second, more importantly, it uncovers a new link between organizational design and the implementation of a decision. Both of these features are in sharp contrast to the vast majority of the existing studies, which takes the agent’s bias as given and abstracts away from the implementation stage of a decision process. Specifically, delegation can be strictly optimal in the present framework even if the agent has no information advantage over the principal.As an application, I extend the baseline model to a multi-task setting, and find an interaction effect between organizational design and job design. Specifically, delegation to a specialized agent can be optimal even when neither delegation without specialization nor specialization without delegation is beneficial.