Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Designing payments for environmental services in theory and practice: An overview of the issues

This book provides a comprehensive introduction to modern auction theory and its important new applications. It is written by a leading economic theorist whose suggestions guided the creation of the new spectrum auction designs. Aimed at graduate students and professionals in economics, the book gives the most up-to-date treatments of both traditional theories of 'optimal auctions' and newer theories of multi-unit auctions and package auctions, and shows by example how these theories are used. The analysis explores the limitations of prominent older designs, such as the Vickrey auction design, and evaluates the practical responses to those limitations. It explores the tension between the traditional theory of auctions with a fixed set of bidders, in which the seller seeks to squeeze as much revenue as possible from the fixed set, and the theory of auctions with endogenous entry, in which bidder profits must be respected to encourage participation.

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Putting Auction Theory to Work

Cultural ecosystem services (ES) are consistently recognized but not yet adequately defined or integrated within the ES framework. A substantial body of models, methods, and data relevant to cultural services has been developed within the social and behavioral sciences before and outside of the ES approach. A selective review of work in landscape aesthetics, cultural heritage, outdoor recreation, and spiritual significance demonstrates opportunities for operationally defining cultural services in terms of socioecological models, consistent with the larger set of ES. Such models explicitly link ecological structures and functions with cultural values and benefits, facilitating communication between scientists and stakeholders and enabling economic, multicriterion, deliberative evaluation and other methods that can clarify tradeoffs and synergies involving cultural ES. Based on this approach, a common representation is offered that frames cultural services, along with all ES, by the relative contribution of relevant ecological structures and functions and by applicable social evaluation approaches. This perspective provides a foundation for merging ecological and social science epistemologies to define and integrate cultural services better within the broader ES framework.

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Contributions of cultural services to the ecosystem services agenda.

http://sergiorosendo.pbworks.com/f/Wunder+et+al+2008+payments+for+environmental+services.pdf

Taking stock: A comparative analysis of payments for environmental services programs in developed and developing countries

Agri-environmental policies in the EU and United States: A comparison ☆

UNIVERSITY OF CALIFORNIA, BERKELEY Department o f Economics Berkeley, California Working Paper 8756 DISCONTINUOUS GAMES ENDOGENOUS SHARING RULES AND Leo K. Simon and. W i l l i a m R. October 1, Key words: Zame D i s c o n t i n u o u s games, e x i s t e n c e , Nash e q u i l i b r i u m , H o t e l l i n g , Bertrand, sharing r u l e s , r a t i o n i n g . Abstract We propose a d i f f e r e n t approach t o the k i n d s of economic problems t h a t l e a d t o d i s c o n t i n u o u s games. We t a k e the view t h a t the under- l y i n g p a y o f f s f o r t h e s e problems are o n l y p a r t i a l l y determined, r a t h e r than discontinuous. At p o i n t s where t i e s occur, we propose t h a t t h e s h a r i n g r u l e s h o u l d be determined endogenously, i . e . , as p a r t o f the s o l u t i o n t o the model r a t h e r t h a n as p a r t of the des- c r i p t i o n o f the model. T h i s l e a d s us t o d e f i n e a game with an en- dogenous s h a r i n g r u l e . I t c o n s i s t s of a s t r a t e g y space f o r each of a f i n i t e number o f p l a y e r s , t o g e t h e r with a p a y o f f correspondence, i n t e r p r e t e d as the union of a l l p o s s i b l e s h a r i n g r u l e s . A s o l u t i o n f o r such a game i s a s e l e c t i o n from the p a y o f f correspondence t o - g e t h e r with a s t r a t e g y p r o f i l e s a t i s f y i n g t h e u s u a l (Nash) b e s t response c r i t e r i o n . Our p r i n c i p a l r e s u l t i s t h a t such a s o l u t i o n always e x i s t s . JEL C l a s s i f i c a t i o n :

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Discontinuous games and endogenous sharing rules

A new framework for games in continuous time is proposed. The continuous-time model conforms as closely as possible to the conventional discrete-time framework. Indeed, continuous time is viewed as "discrete time, but with a grid that is infinitely fine." The paper presents several examples illustrating the difficulties that arise in continuous-time game theory. Theorems relate the equilibria of continuous time games to the equilibria of approximating discrete time games. A variety of industrial organization applications are studied, yielding sharp predictions. Applications include continuously repeated games, preemption models, and patent races. Copyright 1989 by The Econometric Society.(This abstract was borrowed from another version of this item.)

Extensive From Games in Continuous Time: Pure Strategies

We propose a new framework for games in continuous time that conforms as closely as possible to the conventional discrete-time framework. In this paper, we take the view that continuous time can be viewed as "discrete time, but with a grid that is infinitely fine." Specifically, we define a class of continuous-time strategies with the following property: when restricted to an arbitrary, increasingly fine sequence of discrete-time grids, any profile of strategies drawn from this class generates a convergent sequence of outcomes, whose limit is independent of the sequence of grids. We then define the continuous-time outcome to be this limit. Because our continuous-time model conforms so closely to the conventional discrete-time model, we can readily compare the predictions of the two frameworks. Specifically, we ask two questions. First, is discrete-time with a very find grid a good proxy for continuous time? Second, does every subgame perfect equilibrium in our model have a discrete-time analog? Our answer to the first question is the following "upper hemi-continuity" result: Suppose a sequence of discrete-time e-subgame-perfect equilibria increasingly closely approximates (in a special sense) a given continuous-time profile, with - converging to zero along as the period length shrinks. Then the continuous-time profile will be an exact equilibrium for the corresponding continuous-time game. Our second answer is a lower hemi-continuity result that holds under weak conditions. Fix a perfect equilibrium for a continuous-time game and a positive ?. Then for any sufficiently fine grid, there will exist an e-subgame perfect equilibrium for the corresponding game played on that grid which "is within - of" the continuous-time equilibrium. Our model yields sharp predictions in a variety of industrial organization applications. We first consider several variants of a familiar preemption model. Next, we analyze a stylized model of a patent race. Finally, we obtain a striking uniqueness result for a class of "repeated" games.

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Extensive form games in continuous time: pure strategies

This paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy profiles satisfying the usual best-response criteria. It is shown that the introduction of incentive compatible communication (cheap talk) restores existence.

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Leo K. Simon

Papers

Agri-environmental policies in the EU and United States: A comparison ☆

Discontinuous games and endogenous sharing rules

Extensive From Games in Continuous Time: Pure Strategies

Extensive form games in continuous time: pure strategies

Communication and equilibrium in discontinuous games of incomplete information