COALITION FORMATION IN A GLOBAL WARMING GAME: HOW THE DESIGN OF PROTOCOLS AFFECTS THE SUCCESS OF ENVIRONMENTAL TREATY‐MAKING

ABSTRACT. We combine new concepts of noncooperative coalition theory with an integrated assessment model on climate change to analyze the impact of different protocol designs on the success of coalition formation. We analyze the role of “single versus multiple coalitions,”“open versus exclusive membership,”“no, weak and strong consensus about membership” and “no transfers versus transfers.” First, we want to find out whether and how modifications of the standard assumptions affect results that are associated with the widely applied cartel formation game in the noncooperative game theoretic analysis of international environmental agreements. Second, we discuss normative policy conclusions that emerge from the various modifications. Third, we confront our results with evidence on past international environmental treaties and derive an agenda for future research.     

Erratum: Betweenness Centralization for Bipartite Graphs

We address two related issues. First, we analyze the effects of risk preferences on cooperation in social dilemmas. Second, we compare social dilemmas in which outcomes represent gains with dilemmas where outcomes represent losses. We show that predictions on gain‐loss asymmetries with respect to conditions for cooperation crucially depend on assumptions concerning risk preferences. Under the assumption of risk aversion for gains as well as losses together with an assumption of decreasing absolute risk aversion, conditions for cooperation are less restrictive if outcomes represent losses than if outcomes represent gains. Conversely ‐ and counterintuitively ‐ under the assumption of S‐shaped utility, conditions for cooperation are more restrictive if outcomes represent losses than if outcomes represent gains. We provide an experimental test of such predictions. Only a minority of subjects behaves consistent with the assumption of S‐shaped utility. Furthermore, we find no empirical evidence for a general difference between cooperation in social dilemmas in which outcomes represent gains and dilemmas where outcomes represent losses. We do find evidence that risk preferences affect cooperation rates.     

PAST AND FUTURE MANAGEMENT OF A COLLAPSED FISHERY: THE BAY OF BISCAY ANCHOVY

Abstract We analyze the efficiency of the international management of the Bay of Biscay anchovy. While a sharing agreement between France and Spain has been in place since 1992, the fish stock collapsed in 2005 and the fishery closed from 2005 to spring 2010. We consider differences in production technologies between both countries and calibrate our model using data from 1987 to 2009. Our results suggest two sources of rent dissipation under the existing sharing agreement: inefficient quota allocation and production inefficiencies due to inflexible national regulations. We discuss several alternatives to improve management.     

HOW RAPID SHOULD EMISSION REDUCTION BE? A GAME‐THEORETIC APPROACH

Abstract In this paper, we search for multistage realization of international environmental agreements. To analyze countries' incentives and the results of their interactions, we mathematically represent players' strategic preferences and apply a game‐theoretic approach to make predictions about their outcomes. The initial decision on emissions reduction is determined by the Stackelberg equilibrium concept. We generalize Barrett's static “emission” model to a dynamic framework and answer the question “how rapid should the emission reduction be?” It appears that sharper abatement is desirable in the early term, which is similar to the conclusion of the Stern review. Numerical example demonstrates that abatement dynamics of the coalition and the free‐rider differ when discounting of the future payoffs increases. We show that without incentives from external organizations or governments, such pollution reduction path can actually lead to a decline in the agreement's membership size.     

COLLECTIVE DECISION MAKING IN AN INTERNATIONAL RIVER POLLUTION MODEL

In this paper, we study international river pollution problems. We introduce a model in which countries located along a river from upstream to downstream derive benefits from causing pollution, but also incur environmental costs from experiencing its own pollution and the pollution of all its upstream countries. The total welfare, being the sum of all benefits minus the sum of all costs, is maximized when all countries cooperate. Several principles from international water law are applied to find reasonable and fair distributions of the total welfare that can be obtained under full cooperation. Such a distribution of the welfare at efficient pollution levels can be implemented by monetary compensations.     

International comparative studies in mathematics education: are we obsessed with the international rankings of measured educational outcomes?

Over the past few decades, researchers, policy makers, educators and the general public, who have an interest in mathematics education in different countries, pay a great deal of attention to the results from international comparative studies. Of great interest to the international studies is the results of Eastern students consistently achieving higher marks among the participating countries. In recent years, we have seen a climate of intense global economic competition and a growing belief in the key role of education, which have persuaded governments to become increasingly obsessed with the international rankings of measured educational outcomes. Accordingly, educational policy is increasingly driven by national attempts to “copy” the perceived advantage associated with the educational strategies and techniques of other countries. In this note, we present a discussion of the benefits and criticisms of one of these international comparative studies: Trends in International Mathematics and Science Study (TIMSS) studies. In so doing, we attempt to call attention to a continuously growing culture of “teaching to the test” in mathematics education.     

Stochastic stability in one-way flow networks

This paper considers one-way flow network formation games in which transmission through a series of agents is subject to decay. We analyze the myopic best-response dynamics of network formation games, occasionally perturbed by state-dependent random noises. Specifically, if an agent is isolated or has a direct neighbor who is better paid, it is more likely that the agent will make mistakes. Our main result identifies that only empty and wheel networks are candidates for long-term outcomes.     

Conflict and cooperation in designing international telecommunication networks

In this paper, we study the problem of designing an international telecommunication network when multiple countries are involved. Each Country has the option of cooperating in the design of the overall international network, or simply forming bilateral arrangements with individual countries. Most countries will gain by having a truly international network which allows routing via transit countries; this takes advantage of distributed peak traffic hours, and improves the network resource utilization. However there are many situations when countries may obtain greater gains by either behaving pre-emptively or by waiting for the major countries to make their decisions, and then being followers in a Stackelberg game. Using mathematical programming models, we examine conditions under which each of these behaviours are optimal.     

An International Project for the Development of Data Handling Skills of Teachers and Pupils

In this paper we provide an overview of the international CensusAtSchool project, designed, written and implemented first in the UK from October 2000 - April 2001 for pupils aged 7 -16 in primary and secondary schools. It has been adapted for similar aged school children in South Africa and Australia and was implemented in those countries in July and October 2001, respectively. We present our motivation, aims and objectives for carrying out such a project and show some results of analysis from the returns we have received from all three countries. Key outputs from the project include: worksheets that are suitable for enhancing data handling skills of pupils; a training course that wraps information and communications technology with data handling skills that is suitable to enhance the professional development of teachers; a raised awareness amongst pupils and teachers of the need to properly collect, present and analyze primary data; a contribution to improving the statistical numeracy and thinking skills of both teachers and pupils.     

CLIMATE CHANGE AND COOPERATION IN TRANSBOUNDARY WATER SHARING: AN APPLICATION OF STOCHASTIC STACKELBERG DIFFERENTIAL GAMES IN VOLTA RIVER BASIN

Abstract As multiple countries share a river, the likelihood of conflicts over distributing water resources increases, particularly under the effects of climate change. In this paper, we demonstrate how countries can cooperate in sustainable transboundary water sharing under such conditions. We examine the case of water distribution in the Volta Basin of West Africa between the upstream country, Burkina Faso, and the downstream country, Ghana. The latter faces an additional tradeoff between the production of hydropower in the south, close to the outlet of the basin, and agricultural water use in the reservoir’s catchment area in the north. In the framework of a stochastic Stackelberg differential game, we show how sustainable water‐sharing agreements can be achieved by linking transboundary flows to hydropower exports. Our results indicate that, through cooperation, Ghana will have an opportunity to increase its water abstraction for agriculture, which has remained largely restricted. We also find that the equilibrium strategies for the long‐run distribution are stable even with increasing variances of water flow.     

INTERNATIONAL ENVIRONMENTAL AGREEMENTS WITH DEVELOPED AND DEVELOPING COUNTRIES IN A DYNAMIC APPROACH

This paper is devoted to study the stability of international environmental agreements (IEAs) in a pollution abatement model. We focus our attention on two asymmetric agents: developed countries characterized by a strong measure of environmental awareness and developing ones characterized by less attention to environmental preservation. We model a differential game in order to determine both the optimal path of the abatement levels and stock pollutant as results of open‐loop and feedback Nash equilibria. By means of the concepts of internal and external stability, we explain how the environmental awareness of two types of countries and the number of cooperators and defectors influence the size of stable coalitions. The results establish that the asymmetry assumption does not have consequences for the stability of the grand coalition, which can be obtained only with transfers.     

Analyzing Risky Choices: Q‐learning for Deal‐No‐Deal

In this paper, we derive an optimal strategy for the popular Deal or No Deal game show. To do this, we use Q‐learning methods, which quantify the continuation value inherent in sequential decision making in the game. We then analyze two contestants, Frank and Susanne, risky choices from the European version of the game. Given their choices and our optimal strategy, we find what their implied bounds would be on their levels of risk aversion. Previous empirical evidence in risky decision making has suggested that past outcomes affect future choices and that contestants have time‐varying risk aversion. We demonstrate that the strategies of Frank and Susanne are consistent with constant risk aversion levels except for their final risk‐seeking choice. We conclude with directions for future research. Copyright © 2013 John Wiley & Sons, Ltd.     

Monadic dynamic algebras

The main purpose of this work is to introduce the class of the monadic dynamic algebras (dynamic algebras with one quantifier). Similarly to a theorem of Kozen we establish that every separable monadic dynamic algebra is isomorphic to a monadic (possibly non‐standard) Kripke structure. We also classify the simple (monadic) dynamic algebras. Moreover, in the dynamic duality theory, we analyze the conditions under which a hemimorphism of a dynamic algebra into itself defines a quantifier. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of periodic traveling flexural‐gravity waves in two dimensions

In this work, we solve the Euler's equations for periodic waves traveling under a sheet of ice. These waves are referred to as flexural‐gravity waves. We compare and contrast two models for the effect of the ice: a linear model and a nonlinear model. The benefit of this reformulation is that it facilitates the asymptotic analysis. We use it to derive the nonlinear Schrödinger equation that describes the modulational instability of periodic traveling waves. We compare this asymptotic result with the numerical computation of stability using the Fourier–Floquet–Hill method to show they agree qualitatively. We show that different models have different stability regimes for large values of the flexural rigidity parameter. Numerical computations are also used to analyze high‐frequency instabilities in addition to the modulational instability. In the regions examined, these are shown to be the same regardless of the model representing ice.     

States on systems of sets that are closed under symmetric difference

We consider extensions of certain states. The states are defined on the systems of sets that are closed under the formation of the symmetric difference (concrete quantum logics). These systems can be viewed as certain set‐representable quantum logics enriched with the symmetric difference. We first show how the compactness argument allows us to extend states on Boolean algebras over such systems of sets. We then observe that the extensions are sometimes possible even for non‐Boolean situations. On the other hand, a difference‐closed system can be constructed such that even two‐valued states do not allow for extensions. Finally, we consider these questions in a σ‐complete setup and find a large class of such systems with rather interesting state properties.     

Groundwater management: Waiting for a drought*

In this article we present a stylized model for optimal management of an unconfined groundwater resource when the threat of drought exists. The drought is modeled as a stochastic event that hits at an uncertain date and two benchmark management policies are investigated: (a) A policy of optimal dynamic management ignoring the threat of drought; and (b) an economically optimal policy that accounts for the threat of a drought. We show that the optimal predrought steady‐state equilibrium stock size of groundwater under policy b is larger than that under policy (a) Furthermore, we show that an increase in the probability of a drought gives rise to two counteracting effects: One in the direction of a larger predrought steady‐state equilibrium stock size (a recovery effect) and one in the direction of a lower predrought steady‐state equilibrium stock (an extinction effect). We find that the recovery effect dominates the extinction effect. Recommendations for Resource Managers: We analyze two groundwater extraction policies that can be used when a threat of drought exists: (a) Dynamic optimal management ignoring the threat of drought; and (b) dynamic optimal management taking the threat of drought into account. We show that the predrought steady‐state equilibrium stock size of water should be larger under the policy (b) than under policy (a). This conclusion has three implications for resource managers:

• Current groundwater management should take future extraction possibilities into account.

• A resource manager ought to take the threat of drought into account in groundwater management.

• A buffer stock of water should be built‐up before the drought to be drawn upon during the event.

     

THE SIZE OF FARSIGHTED STABLE COALITIONS IN A GAME OF POLLUTION ABATEMENT

Abstract The game theoretical analysis of international environmental problems has received increasing attention in recent years. Major issues are as follows. Under which conditions will an international environmental agreement (IEA) be signed? Will the agreement be stable? Game theory has given different answers to these questions; in particular, it is possible to show that if countries are myopic then only small stable coalitions occur, but if they are farsighted then both large and small stable coalitions exist. This paper studies the size of a farsighted stable IEA by considering a quadratic cost function in a pollution abatement model. Following Rubio and Ulph [2006] , we consider both the case of non‐negative emissions as well as the case of unrestricted ones.     

Peristaltic motion of a magnetohydrodynamic generalized second‐order fluid in an asymmetric channel

We investigate the peristaltic motion of a magnetohydrodynamic (MHD) generalized second‐order fluid in an asymmetric channel. The governing equations are first modeled and then numerically solved under the long wavelength approximation. Attention has been focused to analyze the shear‐thinning and shear‐thickening effects of the investigated non‐Newtonian fluid, the influence of the magnetic force on the flow, especially the trapping, pumping characteristics caused by the peristalsis of the walls. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Logic and logicians in Russia before 1917: Living in a wider world

We explore the formation of Logic as an academic discipline and community in Russia before the revolution of 1917. In particular, we look at the various communication strategies that emerged within this community and its relations with the wider international scientific community. Interaction with Mathematics, which was undergoing its own “foundational revolution,” played a major role in the transition from archaic syllogistic to modern formal logic. We make extensive use of original sources, many of which have not been reprinted since their first publication.     

The bit‐economy: An artificial model of open‐ended technology discovery

We describe and demonstrate an artificial model of technology discovery called the Bit‐Economy. The model is built from a minimal set of fundamental hallmarks of technology and develops under an open‐ended evolutionary operator which rewards new technology which is able to coordinate both spatially and temporally with the existing technology set. The Bit‐Economy, is able to replicate several features of real technology development including nonmonotonic growth, bunching of creation and destruction events, qualitative topologies of patent networks, and efficiency and waste‐management gains. In contrast to related works, we do not apply an exogenous fitness landscape and so are able to study the process of technology discovery as a self‐guided search toward more complex outcomes. © 2013 Wiley Periodicals, Inc. Complexity 18: 57–67, 2013