Stochastic Equilibria: Noise in Actions or Beliefs?

We introduce noisy belief equilibrium (NBE) for normal-form games in which players best respond to noisy belief realizations. Axioms restrict belief distributions to be unbiased with respect to and responsive to changes in the opponents’ behavior. The axioms impose testable restrictions both within and across games, and we compare these restrictions to those of regular quantal response equilibrium (QRE) in which axioms are placed on the quantal response function as the primitive. NBE can generate similar predictions as QRE in several classes of games. Unlike QRE, NBE is a refinement of rationalizability and invariant to affine transformations of payoffs

Stochasticity in Games: Theory and Experiment

A large literature has documented a pattern of stochastic, or random, choice in individual decision making. In games, in which payoffs depend on beliefs over opponents’ behavior, another potentially important source of stochasticity is in the beliefs themselves. Hence, there may be both “noisy actions” and “noisy beliefs”. This dissertation explores the equilibrium implications of both types of noise in normal form games. Theory is developed to understand the effects of noisy beliefs, and the model is compared to the canonical model of noisy actions. Predictions—and assumptions—are tested using existing and novel experimental data. Chapter 1 introduces noisy belief equilibrium (NBE) for normal form games, a model that injects “noisy beliefs” into an otherwise standard equilibrium framework. Axioms restrict the belief distributions to be unbiased with respect to and responsive to changes in the opponents’ behavior. We compare NBE to an axiomatic form of quantal response equilibrium (QRE) in which players have correct beliefs over their opponents’ behavior, but take “noisy actions”. We show that NBE generates similar predictions as QRE such as the “own-payoff effect”, and yet is more consistent with the empirically documented effects of changes in payoff magnitude. Unlike QRE, NBE is a refinement of rationalizability and invariant to affine transformations of payoffs. Chapter 2, joint with Jeremy Ward, studies an equilibrium model in which there is both “noisy actions” and “noisy beliefs”. The model primitives are an action-map, which determines a distribution of actions given beliefs, and a belief-map, which determines a distribution of beliefs given opponents’ behavior. These are restricted to satisfy the axioms of QRE and NBE, respectively, which are simply stochastic generalizations of “best response” and “correct beliefs”. In our laboratory experiment, we collect actions data and elicit beliefs for each game within a family of asymmetric 2-player games. These games have systematically varied payoffs, allowing us to “trace out” both the action- and belief-maps. We find that, while both sources of noise are important in explaining observed behaviors, there are systematic violations of the axioms. In particular, although all subjects observe and play the same games, subjects in different roles have qualitatively different belief biases. To explain this, we argue that the player role itself induces a higher degree of strategic sophistication in the player who faces more asymmetric payoffs. This is confirmed by structural estimates. Chapter 3 considers logit QRE (LQRE), the common parametric form of QRE; and we endogenize its precision parameter "lambda", which controls the degree of “noisy actions”. In the first stage of an endogenous quantal response equilibrium (EQRE), each player chooses her precision optimally subject to costs, taking as given other players’ (second-stage) behavior. In the second stage, the distribution of players’ actions is a heterogenous LQRE given the profile of first-stage precision choices. EQRE satisfies a modified version of the regularity axioms, nests LQRE as a limiting case for a sequence of cost functions, and admits analogues of classic results for LQRE such as those for equilibrium selection. We show how EQRE differs from LQRE using the family of generalized matching pennies games

Possible Room Temperature Ferromagnetism in Hydrogenated Carbon Nanotubes

We find that ferromagnetism can be induced in carbon nanotubes (CNTs) by introducing hydrogen. Multiwalled CNTs grown inside porous alumina templates contain a large density of defects resulting in significant hydrogen uptake when annealed at high temperatures. This hydrogen incorporation produces H-complex and adatom magnetism which generates a sizeable ferromagnetic moment and a Curie temperature near Tc=1000 K. We studied the conditions for the incorporation of hydrogen, the temperature-dependent magnetic behavior, and the dependence of the ferromagnetism on the size of the nanotubes.Comment: 15 pages with 3 figures included; Accepted by Phys. Rev.

Evolution of a multifunctional trait: shared effects of foraging ecology and thermoregulation on beak morphology, with consequences for song evolution

While morphological traits are often associated with multiple functions, it remains unclear how evolution balances the selective effects of different functions. Birds\u27 beaks function not only in foraging but also in thermoregulating and singing, among other behaviours. Studies of beak evolution abound, however, most focus on a single function. Hence, we quantified relative contributions of different functions over an evolutionary timescale. We measured beak shape using geometric morphometrics and compared this trait with foraging behaviour, climatic variables and song characteristics in a phylogenetic comparative study of an Australasian radiation of songbirds (Meliphagidae). We found that both climate and foraging behaviour were significantly correlated with the beak shape and size. However, foraging ecology had a greater effect on shape, and climate had a nearly equal effect on size. We also found that evolutionary changes in beak morphology had significant consequences for vocal performance: species with elongate-shaped beaks sang at higher frequencies, while species with large beaks sang at a slower pace. The evolution of the avian beak exemplifies how morphological traits can be an evolutionary compromise among functions, and suggests that specialization along any functional axis may increase ecological divergence or reproductive isolation along others

Mediating conflict in the lab

Mechanism design teaches us that a mediator can strictly improve the chances of peace between two opponents even when the mediator has no independent resources, is less informed than the two parties, and has no enforcement power. We test the theory in a lab experiment where two subjects negotiate how to share a resource; in case of conflict, the subjects' privately known strength determines their payoffs. The subjects send cheap talk messages about their strength to one another (in the treatment with direct communication) or to the mediator (in the mediation treatment), before making their demands or receiving the mediator's recommendations. We find that, in line with the theory, messages are significantly more sincere when sent to the mediator. However, contrary to the theory, peaceful resolution is not more frequent, even when the mediator is a computer implementing the optimal mediation program. While the theoretical result refers to the best (i.e. most peaceful) equilibrium under mediation, multiple equilibria exist, and the best equilibrium is particularly vulnerable to small deviations from full truthfulness. Subjects are not erratic and their deviations induce only small losses in payoffs, and yet they translate into significant increases in conflict

Linewidth of single photon transitions in Mn12_{12}-acetate

We use time-domain terahertz spectroscopy to measure the position and linewidth of single photon transitions in Mn$_{12}$-acetate. This linewidth is compared to the linewidth measured in tunneling experiments. We conclude that local magnetic fields (due to dipole or hyperfine interactions) cannot be responsible for the observed linewidth, and suggest that the linewidth is due to variations in the anisotropy constants for different clusters. We also calculate a lower limit on the dipole field distribution that would be expected due to random orientations of clusters and find that collective effects must narrow this distribution in tunneling measurements.Comment: 5 pages, accepted to Physical Review

Smaller beaks for colder winters: Thermoregulation drives beak size evolution in Australasian songbirds

Birds’ beaks play a key role in foraging, and most research on their size and shape has focused on this function. Recent findings suggest that beaks may also be important for thermoregulation, and this may drive morphological evolution as predicted by Allen\u27s rule. However, the role of thermoregulation in the evolution of beak size across species remains largely unexplored. In particular, it remains unclear whether the need for retaining heat in the winter or dissipating heat in the summer plays the greater role in selection for beak size. Comparative studies are needed to evaluate the relative importance of these functions in beak size evolution. We addressed this question in a clade of birds exhibiting wide variation in their climatic niche: the Australasian honeyeaters and allies (Meliphagoidea). Across 158 species, we compared species’ climatic conditions extracted from their ranges to beak size measurements in a combined spatial‐phylogenetic framework. We found that winter minimum temperature was positively correlated with beak size, while summer maximum temperature was not. This suggests that while diet and foraging behavior may drive evolutionary changes in beak shape, changes in beak size can also be explained by the beak\u27s role in thermoregulation, and winter heat retention in particular

Acoustic Detection of an Unknown Bat Species in Okinawa

Pipistrelles of the genus Hypsugo are among the rarest bats in Japan, known from a handful of records. In June 2018, a sequence of echolocation calls apparently by a bat of this genus was recorded by an automatic ultrasound recorder on the island of Okinawa. The calls closely resemble H. pulveratus, a Chinese species never before recorded in Japan, and H. alaschanicus, a very rare species in Japan. They also resemble calls of Hypsugo sp. bats from a small population recently discovered on nearby Amami-Oshima Island. The extreme rarity in our recordings, combined with lack of detection in Okinawa by other surveys, suggests that the individual was a vagrant. However, given the cryptic nature of the species on Amami, it remains possible that there is a small and likely endangered resident population, underlining the need for further bat surveys on Okinawa and other Nansei Islands

Macroecology and macroevolution of the latitudinal diversity gradient in ants.

The latitudinal diversity gradient-the tendency for more species to occur toward the equator-is the dominant pattern of life on Earth, yet the mechanisms responsible for it remain largely unexplained. Recently, the analysis of global data has led to advances in understanding, but these advances have been mostly limited to vertebrates and trees and have not provided consensus answers. Here we synthesize large-scale geographic, phylogenetic, and fossil data for an exemplar invertebrate group-ants-and investigate whether the latitudinal diversity gradient arose due to higher rates of net diversification in the tropics, or due to a longer time period to accumulate diversity due to Earth\u27s climatic history. We find that latitudinal affinity is highly conserved, temperate clades are young and clustered within tropical clades, and diversification rate shows no systematic variation with latitude. These results indicate that diversification time-and not rate-is the main driver of the diversity gradient in ants

A test of trophic and functional island biogeography theory with the avifauna of a continental archipelago

1. The classical MacArthur-Wilson theory of island biogeography (TIB) emphasizes the role of island area and isolation in determining island biotas, but is neutral with respect to species differences that could affect community assembly and persistence. Recent extensions of island biogeography theory address how functional differences among species may lead to non-random community assembly processes and different diversity-area scaling patterns. First, the trophic TIB considers how diversity scaling varies across trophic position in a community, with species at higher trophic levels being most strongly influenced by island area. Second, further extensions have predicted how trait distributions, and hence functional diversity, should scale with area. Trait-based theory predicts richness-corrected functional diversity should be low on small islands but converge to null on larger islands. Conversely, competitive assembly predicts high diversity on small islands converging to null with increasing size. 2. However, despite mounting interest in diversity-area relationships across different dimensions of diversity, these predictions derived from theory have not been extensively tested across taxa and island systems.3. Here, we develop and test predictions of the trophic TIB and extensions to functional traits, by examining the diversity-area relationship across multiple trophic ranks and dimensions of avian biodiversity in the Ryukyu archipelago of Japan. 4. We find evidence for a positive species- and phylogenetic diversity-area relationship, but functional diversity was not strongly affected by island area. Counter to the trophic TIB, we found no differences in the slopes of species-area relationships among trophic ranks, although slopes varied among trophic guilds at the same rank. We revealed differential assembly of trophic ranks, with evidence of trait-based assembly of intermediate predators but otherwise neutral community assembly. 5. Our results suggest that niche space differs among trophic guilds of birds, but that differences are mostly not predicted by current extensions of island biogeography theory. While predicted patterns do not fit the empirical data well in this case, the development of such theory provides a useful framework to analyse island patterns from new perspectives. The application of empirical datasets such as ours should help provide a basis for developing further iterations of island biogeography theory