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This chapter presents the classical Penrose singularity theorem. The main ingredients of the proof concern, on the one hand, the caussal structure of a globally hyperbolic spacetime, and on the other, differential geometry techniques involving Jacobi fields together with the Riccati and Raychaudhuri equations.
We present an interactive eye-tracking study that explores the strategic use of gaze. We analyze gaze behavior in an experiment with four simple games. The game can either be a competitive (hide & seek) game in which players want to be unpredictable, or a game of common interest in which players want to be predictable. Gaze is transmitted either in real time to another subject, or it is not transmitted and therefore non-strategic. We find that subjects are able to interpret non-strategic gaze, obtaining substantially higher payoffs than subjects who do not see gaze. If gaze is transmitted in real time, gaze becomes more informative in the common interest games and players predominantly succeed to coordinate on efficient outcomes. In contrast, gaze becomes less informative in the competitive game.
Previous experimental research suggests that individuals apply rules of thumb to a simplified mental model of the “real” decision problem. We claim that this simplification is obtained either by neglecting the other players’ incentives and beliefs or by taking them into consideration only for a subset of game outcomes. We analyze subjects’ eye movements while playing a series of two-person, 3 × 3 one-shot games in normal form. Games within each class differ by a set of descriptive features (i.e., features that can be changed without altering the game equilibrium properties). Data show that subjects on average perform partial or non-strategic analysis of the payoff matrix, often ignoring the opponent´s payoffs and rarely performing the necessary steps to detect dominance. Our analysis of eye-movements supports the hypothesis that subjects use simple decision rules such as “choose the strategy with the highest average payoff” or “choose the strategy leading to an attractive and symmetric outcome” without (optimally) incorporating knowledge on the opponent’s behavior. Lookup patterns resulted being feature and game invariant, heterogeneous across subjects, but stable within subjects. Using a cluster analysis, we find correlations between eye-movements and choices; however, applying the Cognitive Hierarchy model to our data, we show that only some of the subjects present both information search patterns and choices compatible with a specific cognitive level. We also find a series of correlations between strategic behavior and individual characteristics like risk attitude, short-term memory capacity, and mathematical and logical abilities.
We propose a framework for institutional change in the ‘rules-in-equilibrium’ tradition and introduce the term institutional incompleteness. Institutions are incomplete when their constituent rules fail to induce behavioural beliefs about the strategies of others and hence fail to achieve an equilibrium. Even with deliberate preparation ex-ante, there will always be unanticipated situations not covered by the rules that can only be settled ex-post, especially in a complex and changing environment. At this crux, people creatively invoke focal point generating ideas. Ideas act as guides for coordination where rules cannot. If no focal points can form, further institutional collapse occurs. To understand which ideas guide better, economists will have to investigate an idea’s content. Our theory offers a way to look at institutional change due to incompleteness while also allowing the requisite room for ideas in explaining the patterned yet indeterminate trajectory of humanity.
This chapter explores the role of governments in the IPCC, how this is theorised, and how government participation in the organisation has changed over time. One of the most distinctive features of the IPCC is its intergovernmental character. While some scholars criticise government membership of the IPCC, many IPCC actors see this as key to ensuring the political relevance of the assessment. But what does government membership mean? What do member governments do in the organisation? And who are IPCC delegates and focal points? This chapter addresses these questions and identifies how member governments have deepened their involvement in the IPCC over time as their knowledge has grown and as the stakes in climate politics have risen. However, participation between countries remains uneven and the chapter explores how concerns about developing countries’ capacity to contribute has shaped the IPCC and assessments of climate change.
International organizations come in many shapes and sizes. Within this institutional gamut, the multipurpose multilateral intergovernmental organization (MMIGO) plays a central role. This institutional form is often traced to the creation of the League of Nations, but in fact the first MMIGO emerged in the Western Hemisphere at the close of the nineteenth century. Originally modeled on a single-issue European public international union, the Commercial Bureau of the American Republics evolved into the multipurpose, multilateral Pan American Union (PAU). Contrary to prominent explanations of institutional genesis, the PAU's design did not result from functional needs nor from the blueprints of a hegemonic power. Advancing a recent synthesis between historical and rational institutionalism, we argue that the first MMIGO arose through a process of compensatory layering: a mechanism whereby a sequence of bargains over control and scope leads to gradual but transformative institutional change. We expect compensatory layering to occur when an organization is focal, power asymmetries among members of that organization are large, and preferences over institutional design diverge. Our empirical and theoretical contributions demonstrate the value a more global international relations (IR) perspective can bring to the study of institutional design. international relations (IR) scholars have long noted that international organizations provide smaller states with voice opportunities; our account suggests those spaces may be of smaller states’ own making.
In this paper, a novel approach of high-accuracy calibration (HAC) method is employed to improve the resolution of tumor detection within a fibro-glandular breast model, and also an improved 3D back-projection approach to scan each focal point inside of the breast is presented. For these purposes, a simulated hemispherical setup of a multi-static array with a modified UWB bowtie antenna is applied around the breast. The superiority of the proposed HAC method is that all-time delays of multi-static channel paths are taken into account at preprocessing of reflected signals, and therefore the time location of tumor response can be estimated accurately in the late stage of recorded signals. As a result, stronger signals are obtained to detect the location of the tumor with higher spatial accuracy. By using the improved 3D back-projection method, a better approximation of transmission channel paths based on Fermat's principle is achieved. A realistic breast model is proposed with two cases of single and twin spherical tumors. Then, to validate the efficiency of the proposed HAC method to detect the time-dependent tumor location, several scenarios are studied in the mentioned model. Quantitative metrics of successfully reconstructed tumor (with a small radius of 7 mm) images prove the ability of the proposed imaging method for early-stage breast cancer detection.
Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves time parametrization. It is concluded that the geodesic flow has a unique measure of maximal entropy.
A core set of assumptions in economic modeling is that rational agents, who have a defined preference set, assess their options and determine which best satisfies their preferences. The rational actor model supposes that the world provides us with a menu of options, and we simply choose what’s best for us. Agents are independent of one another, and they can rationally assess which of their options they wish to pursue. This gives special authority to the choices that people make, since they are understood to be the outcomes of the agent’s considered judgments. However, we have come to see that the independence assumption does not always hold in the way that we may have initially thought. Social norms can govern our choices even when we disagree with them. Here we can begin to see how the standard model of choice and agency begins to weaken: no longer are my choices wholly mine, but instead there is a subset of choices that are governed by the broader culture that I live in. Social norms constrain my behavior with informal coercion — my desire to remain a community member in good standing requires me to behave in accordance with the community’s social norms. What I wish to challenge more substantively is the claim that the menu of choices agents “see” is in fact the objective set of options that is transparently provided by the world. Instead, I argue that the options that people perceive and the evidence they use to make choices are mediated by perspectives. Perspectives can importantly interact with social norms to make some norms more resilient to change, and others harder to adopt. This further shapes both our descriptive and normative understanding of agency. Our choices are not over all of the objectively available options, but over the options that we can see. The evidence we marshal to support our choices is not the full set of evidence, but the evidence that we recognize as salient. This is not to deny that individuals have agency, but rather we need a more nuanced understanding of the nature of this agency.
In 1975, Gauthier discussed Schelling’s pure coordination games and Hodgson’s Hi-Lo game. While developing an original analysis of how rational players coordinate on ‘focal points,’ Gauthier argued, contrary to Schelling and Hodgson, that successful coordination in these games does not depend on deviations from conventional principles of individually rational choice. I argue that Gauthier’s analysis of constrained maximization in Morals by Agreement, which famously deviates from conventional game theory, has significant similarities with Schelling’s and Hodgson’s analyses of coordination. Constrained maximization can be thought of as a pragmatic and contractarian variant of the team-reasoning approach pioneered by Hodgson.
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