Emergence of Cooperation in Heterogeneous Population: A Discrete-Time Replicator Dynamics Analysis

The emergence of cooperation is analyzed in heterogeneous populations where individuals can be classified in two groups according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are able to identify the type of every other individual, but fail to recognize their own type, and thus behave under partial information conditions. The interactions between individuals are described by 2 × 2 symmetric games where individuals can either cooperate or defect. The evolution of such populations is studied in the framework of evolutionary game by means of the replicator dynamics. Overlapping generations are considered, so the replicator equations are formulated in discrete-time form. The well-posedness conditions of the system are derived. Depending on the parameters of the game, a restriction may exist for the generation length. The stability analysis of the dynamical system is carried out and a detailed description of the behavior of trajectories starting from the interior of the state-space is given. We find that, provided the conditions of well-posedness are verified, the linear stability of monomorphic states in the discrete-time replicator coincides with the one of the continuous case. Specific from the discrete-time case, a relaxed restriction for the generation length is derived, for which larger time-steps can be used without compromising the well-posedness of the replicator system.

Soviet-American Cooperative Research on Marine Mammals. Volume 1- Pinnipeds: Under Project V.6. Marine Mammals, of the US-USSR Agreement on Cooperation in the Field of Environmental Protection

Some 25 to 30 yr ago, when we as students were beginning our respective careers and were developing for the first time our awareness of marine mammals in the waters separating western North America from eastern Asia, we had visions of eventually bridging the communication gap which existed between our two countries at that time. Each of us was anxious to obtain information on the distribution, biology, and ecological relations of "our" seals and walruses on "the other side," beyond our respective political boundari~s where we were not permitted to go to study them. We were concerned that the resource management practices on the other side of the Bering and Chukchi Seas, implemented in isolation, on a purely unilateral basis, might endanger the species which we had come to know and were striving to conserve. At once apparent to both of us was the need for free exchange of biological information between our two countries and, ultimately, joint management of our shared resources. In a small way, we and others made some initial efforts to generate that exchange by personal correspondence and through vocal interchange at the annual meetings of the North Pacific Fur Seal Commission. By the enabling Agreement on Cooperation in the Field of Environmental Protection, reached between our two countries in 1972, our earlier visions at last came true. Since that time, within the framework of the Marine Mammal Project under Area V of that Agreement, we and our colleagues have forged a strong bond of professional accord and respect, in an atmosphere of free intercommunication and mutual understanding. The strength and utility of this arrangement from the beginning of our joint research are reflected in the reports contained in this, the first compendium of our work. The need for a series of such a compendia became apparent to us in 1976, and its implementation was agreed on by the regular meeting of the Project in La Jolla, Calif., in January 1977. Obviously, the preparation and publication of this first volume has been excessively delayed, in part by continuing political distrust between our governments but mainly by increasing demands placed on the time of the contributors. In this period of growing environmental concern in both countries, we and our colleagues have been totally immersed in other tasks and have experienced great difficulty in drawing together the works presented here. Much of the support for doing so was provided by the State of Alaska, through funding for Organized Research at the University of Alaska-Fairbanks. For its ultimate completion in publishable form we wish to thank Helen Stockholm, Director of Publications, Institute of Marine Science, University of Alaska, and her staff, especially Ruth Hand, and the numerous referees narned herein who gave willingly oftheir time to review each ofthe manuscripts critically and to provide a high measure of professionalism to the final product. (PDF file contains 110 pages.)

AUTOROTATION OF TWO TANDEM TRIANGULAR CYLINDERS

The autorotation of two tandem triangular cylinders at different gap distances is investigated by numerical simulations. At the Reynolds number of 200， three distinct regimes are observed with the increase of gap distance: namely, angular oscillation, quasi-periodic autorotation and ‘chaotic’ autorotation. For various gap distances, the characteristic of vortex shedding and vortex interaction are discussed. The phase graphs (angular acceleration vs. angular velocity) and the power spectra of moment are analyzed to characterize the motion of the cylinder. The Lyapunov exponent is also calculated to identify the existence of chaos.

Robot navigation in dense crowds : statistical models and experimental studies of human robot cooperation

This thesis explores the problem of mobile robot navigation in dense human crowds. We begin by considering a fundamental impediment to classical motion planning algorithms called the freezing robot problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing predictive uncertainty by employing higher fidelity individual dynamics models or heuristically limiting the individual predictive covariance to prevent overcautious navigation. We demonstrate that both the individual prediction and the individual predictive uncertainty have little to do with this undesirable navigation behavior. Additionally, we provide evidence that dynamic agents are able to navigate in dense crowds by engaging in joint collision avoidance, cooperatively making room to create feasible trajectories. We accordingly develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a "multiple goal" extension that models the goal driven nature of human decision making. Navigation naturally emerges as a statistic of this distribution.

Most importantly, we empirically validate our models in the Chandler dining hall at Caltech during peak hours, and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (collecting data on 488 runs). The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 1 person/m², while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people/m². We also show that our noncooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. For inclusive validation purposes, we show that either our non-interacting planner or our reactive planner captures the salient characteristics of nearly any existing dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.

Finally, we produce a large database of ground truth pedestrian crowd data. We make this ground truth database publicly available for further scientific study of crowd prediction models, learning from demonstration algorithms, and human robot interaction models in general.

Essays on cooperation and reciprocity

This dissertation comprises three essays that use theory-based experiments to gain understanding of how cooperation and efficiency is affected by certain variables and institutions in different types of strategic interactions prevalent in our society.

Chapter 2 analyzes indefinite horizon two-person dynamic favor exchange games with private information in the laboratory. Using a novel experimental design to implement a dynamic game with a stochastic jump signal process, this study provides insights into a relation where cooperation is without immediate reciprocity. The primary finding is that favor provision under these conditions is considerably less than under the most efficient equilibrium. Also, individuals do not engage in exact score-keeping of net favors, rather, the time since the last favor was provided affects decisions to stop or restart providing favors.

Evidence from experiments in Cournot duopolies is presented in Chapter 3 where players indulge in a form of pre-play communication, termed as revision phase, before playing the one-shot game. During this revision phase individuals announce their tentative quantities, which are publicly observed, and revisions are costless. The payoffs are determined only by the quantities selected at the end under real time revision, whereas in a Poisson revision game, opportunities to revise arrive according to a synchronous Poisson process and the tentative quantity corresponding to the last revision opportunity is implemented. Contrasting results emerge. While real time revision of quantities results in choices that are more competitive than the static Cournot-Nash, significantly lower quantities are implemented in the Poisson revision games. This shows that partial cooperation can be sustained even when individuals interact only once.

Chapter 4 investigates the effect of varying the message space in a public good game with pre-play communication where player endowments are private information. We find that neither binary communication nor a larger finite numerical message space results in any efficiency gain relative to the situation without any form of communication. Payoffs and public good provision are higher only when participants are provided with a discussion period through unrestricted text chat.

Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings

We investigated the use of a deep-etched fused-silica grating with triangular-shaped grooves as a highly efficient polarizing beam splitter (PBS). A triangular-groove PBS grating is designed at a wavelength of 1550 nm to be used in optical communication. When it is illuminated in Littrow mounting, the transmitted TE- and TM-polarized waves are mainly diffracted in the minus-first and zeroth orders, respectively. The design condition is based on the average differences of the grating mode indices, which is verified by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient over the C+L band range for both TE and TM polarizations (> 97.68 %). It is shown that such a triangular-groove PBS grating can exhibit a higher diffraction efficiency, a larger extinction ratio, and less reflection loss than the binary-phase fused-silica PBS grating. (C) 2008 Optical Society of America.

Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal

In this paper we theoretically study the left-handed behaviors in a two-dimensional triangular photonic crystal made of elliptical rods in air. An absolute left-handed region is found in the second photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by the finite-difference time-domain simulations. These behaviors are also compared with the quasi-negative refraction and the resulted focusing effects in a square-lattice two-dimensional photonic crystal. (c) 2005 Optical Society of America

We can work it out: an enactive look at cooperation

The past years have seen an increasing debate on cooperation and its unique human character. Philosophers and psychologists have proposed that cooperative activities are characterized by shared goals to which participants are committed through the ability to understand each other’s intentions. Despite its popularity, some serious issues arise with this approach to cooperation. First, one may challenge the assumption that high-level mental processes are necessary for engaging in acting cooperatively. If they are, then how do agents that do not possess such ability (preverbal children, or children with autism who are often claimed to be mind-blind) engage in cooperative exchanges, as the evidence suggests? Secondly, to define cooperation as the result of two de-contextualized minds reading each other’s intentions may fail to fully acknowledge the complexity of situated, interactional dynamics and the interplay of variables such as the participants’ relational and personal history and experience. In this paper we challenge such accounts of cooperation, calling for an embodied approach that sees cooperation not only as an individual attitude toward the other, but also as a property of interaction processes. Taking an enactive perspective, we argue that cooperation is an intrinsic part of any interaction, and that there can be cooperative interaction before complex communicative abilities are achieved. The issue then is not whether one is able or not to read the other’s intentions, but what it takes to participate in joint action. From this basic account, it should be possible to build up more complex forms of cooperation as needed. Addressing the study of cooperation in these terms may enhance our understanding of human social development, and foster our knowledge of different ways of engaging with others, as in the case of autism.

Band structure of photonic crystal fibers with silica rings in triangular lattice

The characteristics of the cladding band structure of air-core photonic crystal fibers with silica rings in triangular lattice are investigated by using a standard plane wave method. The numerical results show that light can be localized in the air core by the photonic band gaps of the fiber. By increasing the air-filling fraction, the band gap edges of the low frequency photonic band gaps shift to shorter wavelength.. whereas the band gap width decreases linearly. In order to make a specified light fall in the low frequency band gaps of the fiber, the interplay of the silica ring spacing and the air-filling fraction is also analyzed. It shows that the silica ring spacing increases monotonously when the air-filling fraction is increased, and the spacing range increases exponentially. This type fiber might have potential in infrared light transmission. (c) 2006 Elsevier B.V. All rights reserved.

Antireflective characteristics of triangular shaped gratings

The antireflection properties of triangular shaped gratings are studied by a combination of the effective medium theory and the anisotropic thin-film theory. The triangular shaped structures are analyzed as a function of grating period, filling factor, and groove depth, and the antireflective characteristics are also studied when visible-infrared light is incident upon them. Numerical examples are given for gratings on glass substrate with refractive index of 1.5. The results show that this kind of grating is capable of reducing reflections, and could achieve very low reflectivity over a wide field of view and a wide waveband by choosing appropriate parameters.

Research in Global Groundfish Markets: An Exercise in International Cooperation

Over roughly the last decade, most of the fishery resources of the continental shelf and nearshore areas of the world's oceans have come under the control of coastal nations. One consequence of this extension of fisheries jurisdiction (EFJ) by any individual state has been the expansion of its production possibilities. That is, with strengthened property rights in the ocean resources off its shores, a coastal nation experiences increased opportunities to produce goods and services from its newly enlarged pool of resources. Such a nation, then, would appear to be a potential gainer from EFJ.