The Evolution of Fairness under an Assortative Matching Rule in the Ultimatum Game

This paper studies how a matching rule affects the evolution of fairness in an ultimatum mini game. Gale et al. [1995] show that only selfish behaviour survives in the deterministic replicator dynamics under the random matching rule. In contrast, this paper shows that, under an assortative matching rule, the fair behaviour may survive at an asymptotically stable state.

Formation of Decentralized Manufacturer-Supplier Networked Market

This paper studies trading in a two-sided market where firms strategically form a network. In a networked market, manufacturers and suppliers must be connected by links for trading. We show that if no contingent contract is available, then any pairwise Nash stable network is inefficient. Each supplier under-invests in links (a hold-up problem). If a contract contingent on direct links is available and link cost is low, then the under-investment problem solves. Furthermore, the complete network resulting in the Walrasian outcome is uniquely pairwise Nash stable. However, this outcome is also inefficient. A new hold-up problem, over-investment in links, arises.

On the equivalence between the effective cosmology and excursion set treatments of environment

In studies of the environmental dependence of structure formation, the large scale environment is often thought of as providing an effective background cosmology: e.g. the formation of structure in voids is expected to be just like that in a less dense universe with appropriately modified Hubble and cosmological constants. However, in the excursion set description of structure formation which is commonly used to model this effect, no explicit mention is made of the effective cosmology. Rather, this approach uses the spherical evolution model to compute an effective linear theory growth factor, which is then used to predict the growth and evolution of nonlinear structures. We show that these approaches are, in fact, equivalent: a consequence of Birkhoff's theorem. We speculate that this equivalence will not survive in models where the gravitational force law is modified from an inverse square, potentially making the environmental dependence of clustering a good test of such models.Comment: 4 pages, 0 figures, accepted to MNRA

Revenue-capped efficient auctions

We study an auction that maximizes the expected social surplus under an upperbound constraint on the seller's expected revenue, which we call a revenue cap. Such a constrained-efficient auction may arise, for example, when: (i) the auction designer is "pro-buyer", that is, he maximizes the weighted sum of the buyers' and seller's auction payoffs, where the weight for the buyers is greater than that for the seller; (ii) the auction designer maximizes the (unweighted) total surplus in a multi-unit auction in which the number of units the seller owns is private information; or (iii) multiple sellers compete to attract buyers before the auction. We characterize the mechanisms for constrained-efficient auctions and identify their important properties. First, the seller sets no reserve price and sells the good for sure. Second, with a nontrivial revenue cap, "bunching" is necessary. Finally, with a sufficiently severe revenue cap, the constrained-efficient auction has a bid cap, so that bunching occurs at least "at the top," that is, "no distortion at the top" fails

Formation of Decentralized Manufacturer-Supplier Networked Market

This paper studies trading in a two-sided market where firms strategically form a network. In a networked market, manufacturers and suppliers must be connected by links for trading. We show that if no contingent contract is available, then any pairwise Nash stable network is inefficient. Each supplier under-invests in links (a hold-up problem). If a contract contingent on direct links is available and link cost is low, then the under-investment problem solves. Furthermore, the complete network resulting in the Walrasian outcome is uniquely pairwise Nash stable. However, this outcome is also inefficient. A new hold-up problem, over-investment in links, arises

Revenue-capped efficient auctions

We study an auction that maximizes the expected social surplus under an upperbound constraint on the seller's expected revenue, which we call a revenue cap. Such a constrained-efficient auction may arise, for example, when: (i) the auction designer is "pro-buyer", that is, he maximizes the weighted sum of the buyers' and seller's auction payoffs, where the weight for the buyers is greater than that for the seller; (ii) the auction designer maximizes the (unweighted) total surplus in a multi-unit auction in which the number of units the seller owns is private information; or (iii) multiple sellers compete to attract buyers before the auction. We characterize the mechanisms for constrained-efficient auctions and identify their important properties. First, the seller sets no reserve price and sells the good for sure. Second, with a nontrivial revenue cap, "bunching" is necessary. Finally, with a sufficiently severe revenue cap, the constrained-efficient auction has a bid cap, so that bunching occurs at least "at the top," that is, "no distortion at the top" fails

Experimental Realization of Spin-1/2 Triangular-Lattice Heisenberg Antiferromagnet

We report the results of magnetization and specific heat measurements on Ba$_3$CoSb$_2$O$_9$, in which the magnetic Co$^{2+}$ ion has a fictitious spin-1/2, and show evidence that a spin-1/2 Heisenberg antiferromagnet on a regular triangular lattice is actually realized in Ba$_3$CoSb$_2$O$_9$. We found that the entire magnetization curve including the one-third quantum magnetization plateau is in excellent agreement with theoretical calculations at a quantitative level.Comment: 5 pages, 5 figure

Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects

An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative to the prediction in {\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.Comment: 21 pages, 9 figures, references and supplementary sections added, accepted for publication in PAS