On Rationalizable Outcomes in Private-Value First-Price Discrete Auctions

In this paper, we extend the result of Dekel and Wollinsky ("Rationalizable Outcomes of Large Private-Value First-Price Discrete Auctions" Games and Economic Behavior, 2003) on rationalizable outcomes in first-price auctions. Dekel and Wollinsky show that under certain conditions, each player chooses a unique bid conditional on her valuation. Their result however depends on the assumption that the number of players is sufficiently large (relative to the number of available bids). We first provide a different set of sufficient conditions for the uniqueness result. We then show that for the independent (possibly asymmetric) private value case, (i) the result holds if the distributions are such that the inverse hazard rate is sufficiently high for each valuation, implying that auctions need not necessarily be large, and (ii) if the distributions satisfy the conditions of Dekel and Wollinsky, they always satisfy oursFirst-Price Auctions, Rationalizability, Dominance

Mermaid construction in Irabu Ryukyuan

Kyushu University / National Institute for Japanese Language and Linguitic

Global network structure of dominance hierarchy of ant workers

Dominance hierarchy among animals is widespread in various species and believed to serve to regulate resource allocation within an animal group. Unlike small groups, however, detection and quantification of linear hierarchy in large groups of animals are a difficult task. Here, we analyse aggression-based dominance hierarchies formed by worker ants in Diacamma sp. as large directed networks. We show that the observed dominance networks are perfect or approximate directed acyclic graphs, which are consistent with perfect linear hierarchy. The observed networks are also sparse and random but significantly different from networks generated through thinning of the perfect linear tournament (i.e., all individuals are linearly ranked and dominance relationship exists between every pair of individuals). These results pertain to global structure of the networks, which contrasts with the previous studies inspecting frequencies of different types of triads. In addition, the distribution of the out-degree (i.e., number of workers that the focal worker attacks), not in-degree (i.e., number of workers that attack the focal worker), of each observed network is right-skewed. Those having excessively large out-degrees are located near the top, but not the top, of the hierarchy. We also discuss evolutionary implications of the discovered properties of dominance networks.Comment: 5 figures, 2 tables, 4 supplementary figures, 2 supplementary table

有限温度・有限サイズ効果を伴う４体フェルミ相互作用模型におけるカイラル対称性の破れ

広島大学(Hiroshima University)博士(理学)Doctor of Sciencedoctora