Beyond myopic best response (in Cournot competition)

A Nash Equilibrium is a joint strategy profile at which each agent myopically plays a best response to the other agents' strategies, ignoring the possibility that deviating from the equilibrium could lead to an avalanche of successive changes by other agents. However, such changes could potentially be beneficial to the agent, creating incentive to act non-myopically, so as to take advantage of others' responses. To study this phenomenon, we consider a non-myopic Cournot competition, where each firm selects whether it wants to maximize profit (as in the classical Cournot competition) or to maximize revenue (by masquerading as a firm with zero production costs). The key observation is that profit may actually be higher when acting to maximize revenue, (1) which will depress market prices, (2) which will reduce the production of other firms, (3) which will gain market share for the revenue maximizing firm, (4) which will, overall, increase profits for the revenue maximizing firm. Implicit in this line of thought is that one might take other firms' responses into account when choosing a market strategy. The Nash Equilibria of the non-myopic Cournot competition capture this action/response issue appropriately, and this work is a step towards understanding the impact of such strategic manipulative play in markets. We study the properties of Nash Equilibria of non-myopic Cournot competition with linear demand functions and show existence of pure Nash Equilibria, that simple best response dynamics will produce such an equilibrium, and that for some natural dynamics this convergence is within linear time. This is in contrast to the well known fact that best response dynamics need not converge in the standard myopic Cournot competition. Furthermore, we compare the outcome of the non-myopic Cournot competition with that of the standard myopic Cournot competition. Not surprisingly, perhaps, prices in the non-myopic game are lower and the firms, in total, produce more and have a lower aggregate utility

Climate Change Meets the Law of the Horse

The climate change policy debate has only recently turned its full attention to adaptation - how to address the impacts of climate change we have already begun to experience and that will likely increase over time. Legal scholars have in turn begun to explore how the many different fields of law will and should respond. During this nascent period, one overarching question has gone unexamined: how will the legal system as a whole organize around climate change adaptation? Will a new distinct field of climate change adaptation law and policy emerge, or will legal institutions simply work away at the problem through unrelated, duly self-contained fields, as in the famous Law of the Horse? This Article is the first to examine that question comprehensively, to move beyond thinking about the law and climate change adaptation to consider the law of climate change adaptation. Part I of the Article lays out our methodological premises and approach. Using a model we call Stationarity Assessment, Part I explores how legal fields are structured and sustained based on assumptions about the variability of natural, social, and economic conditions, and how disruptions to that regime of variability can lead to the emergence of new fields of law and policy. Case studies of environmental law and environmental justice demonstrate the model’s predictive power for the formation of new distinct legal regimes. Part II applies the Stationarity Assessment model to the topic of climate change adaptation, using a case study of a hypothetical coastal region and the potential for climate change impacts to disrupt relevant legal doctrines and institutions. We find that most fields of law appear capable of adapting effectively to climate change. In other words, without some active intervention, we expect the law and policy of climate change adaptation to follow the path of the Law of the Horse - a collection of fields independently adapting to climate change - rather than organically coalescing into a new distinct field. Part III explores why, notwithstanding this conclusion, it may still be desirable to seek a different trajectory. Focusing on the likelihood of systemic adaptation decisions with perverse, harmful results, we identify the potential benefits offered by intervening to shape a new and distinct field of climate change adaptation law and policy. Part IV then identifies the contours of such a field, exploring the distinct purposes of reducing vulnerability, ensuring resiliency, and safeguarding equity. These features provide the normative policy components for a law of climate change adaptation that would be more than just a Law of the Horse. This new field would not replace or supplant any existing field, however, as environmental law did with regard to nuisance law, and it would not be dominated by substantive doctrine. Rather, like the field of environmental justice, this new legal regime would serve as a holistic overlay across other fields to ensure more efficient, effective, and just climate change adaptation solutions

Accuracy Assessment of the ESA CCI 20M Land Cover Map: Kenya, Gabon, Ivory Coast and South Africa

This working paper presents the overall and spatial accuracy assessment of the European Space Agency (ESA) 20 m prototype land cover map for Africa for four countries: Kenya, Gabon, Ivory Coast and South Africa. This accuracy assessment was undertaken as part of the ESA-funded CrowdVal project. The results varied from 44% (for South Africa) to 91% (for Gabon). In the case of Kenya (56% overall accuracy) and South Africa, these values are largely caused by the confusion between grassland and shrubland. However, if a weighted confusion matrix is used, which diminishes the importance of the confusion between grassland and shrubs, the overall accuracy for Kenya increases to 79% and for South Africa, 75%. The overall accuracy for Ivory Coast (47%) is a result of a highly fragmented land cover, which makes it a difficult country to map with remote sensing. The exception was Gabon with a high overall accuracy of 91%, but this can be explained by the high amount of tree cover across the country, which is a relatively easy class to map