Credible Group Stability in Many-to-Many Matching Problems

It is known that in two-sided many-to-many matching problems, pairwise stable matchings may not be immune to group deviations, unlike in many- to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise- responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.

Credible Group Stability in Multi-Partner Matching Problems

It is known that in two-sided many-to-many matching markets, pair-wise stability is not logically related with the (weak) core, unlike in many-to-one matching markets (Blair, 1988). In this paper, we seek a theoretical foundation for pairwise stability when group deviations are allowed. Group deviations are defined in graphs on the set of agents. We introduce executable group deviations in order to discuss the credibility of group deviations and to defined credibly group stable matchings. We show, under responsive preferences, that credible group stability is equivalent to pairwise stability in the multi-partner matching problem that includes two-sided matching problems as special cases. Under the same preference restriction, we also show the equivalence between the set of pairwise stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic form game. However, under a weaker preference restriction, substitutability, these equivalences no longer hold, since pairwise stable matchings may be strictly Pareto-ordered, unlike under responsiveness.Multi-partner matching problem, Pairwise stable matching network, Credible group deviation

Song Learning in Birds

Birds sing to communicate. Male birds use song to advertise their territories and attract females. Each bird species has a unique song or set of songs. Song conveys both species and individual identity. In most species, young birds learn some features of adult song. Song develops gradually from amorphous to fixed patterns of vocalization as if crystals form out of liquid. Learning of a song proceeds in two steps; birds commit the song to memory in the first stage and then they vocally reproduce it in the second stage. The two stages overlap each other in some species, while they are separated by several months in other species. The ability of a bird to commit a song to memory is restricted to a period known as the sensitive phase. Vocal reproduction of the memorized song requires auditory feedback. Birds deafened before the second stage cannot reproduce the memorized song. Birds change vocal output until it matches with the memorized song, which thus serves as a template. Birds use a built-in template when a tutor model is not available. Exposure to a tutor model modifies this innate template

Sound Localization in the Barn Owl

Barn owls (Tyto alba) can use sound to catch prey in total darkness. Two barn owls were trained to strike protected loudspeakers emitting various artificial sounds. The accuracy of localization depended on the frequency, bandwidth, and temporal pattern of the test sound. Continuous pure tones of frequencies below 6 kHz and above 9 kHz were hard to localize. The accuracy improved as the frequency increased from 6 to 9 kHz. Within this range continuous sounds containing two frequencies were more accurately localized than either frequency alone. Sustained wide‐band noises always assured precise localization. The owls localized tone bursts more accurately than continuous tones. Whatever signals were used, accurate localization was largely due to the owls' ability to use the sounds for guiding the flight direction. The midcourse correction could occur during a flight lasting as short as 1 sec. When the signal was switched from one speaker to another after takeoff, the birds could strike the second speaker

Monopole-vortex complex in a theta vacuum

We discuss aspects of the monopole-vortex complex soliton arising in a hierarchically broken gauge system, G to H to 1, in a theta vacuum of the underlying G theory. Here we focus our attention mainly on the simplest such system with G=SU(2) and H=U(1). A consistent picture of the effect of the theta parameter is found both in a macroscopic, dual picture and in a microscopic description of the monopole-vortex complex soliton.Comment: 18 pages 3 figure