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作者：Kubler, Felix; Schmedders, Karl
作者单位：University of Zurich; Swiss Finance Institute (SFI); University of Zurich; Swiss Finance Institute (SFI)
摘要：Multiplicity of equilibria is a prevalent problem in many economic models. Often equilibria are characterized as solutions to a system of polynomial equations. This paper gives an introduction to the application of Grobner bases for finding all solutions of a polynomial system. The Shape Lemma, a key result from algebraic geometry, states under mild assumptions that a given equilibrium system has the same solution set as a much simpler triangular system. Essentially, the computation of all sol...
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作者：Schulz, Andreas S.; Uhan, Nelson A.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Purdue University System; Purdue University
摘要：We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations; in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron-a problem that often arises in combinatorial optimization-has supermodular optimal costs. In addition, we examine the computational complexity of the least core and least core value of supermodular cost cooperative games. We show that the problem of computing the least core va...
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作者：Speight, Adam
作者单位：University of Chicago
摘要：I present a self-contained introduction to multigrid methods with an emphasis on techniques relevant to dynamic programming and related problems. A probabilistic interpretation of the numerical principles is highlighted. Multigrid solvers are shown to be naturally matched to the challenges posed by intractable structural dynamic models routinely encountered in applied economics. I argue that multigrid techniques have potential to substantially extend the scale and complexity of models under co...
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作者：Belloni, Alexandre; Lopomo, Giuseppe; Wang, Shouqiang
作者单位：Duke University
摘要：Multidimensional mechanism design problems have proven difficult to solve by extending techniques from the one-dimensional case. This paper considers mechanism design problems with multidimensional types when the seller's cost function is not separable across buyers. By adapting results obtained by Border [Border, K. 1991. Implementation of reduced form auctions: A geometric approach. Econometrica 59 1175-1187], we transform the seller's problem into a representation that only involves interim...
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作者：Armstrong, Christopher S.; Larcker, David F.; Su, Che-Lin
作者单位：University of Pennsylvania; Stanford University; University of Chicago
摘要：The two major paradigms in the theoretical agency literature are moral hazard (i.e., hidden action) and adverse selection (i.e., hidden information). Prior research typically solves these problems in isolation, as opposed to simultaneously incorporating both adverse selection and moral hazard features. We formulate two complementary generalized principal-agent models that incorporate features observed in real-world contracting environments (e. g., agents with power utility and limited liabilit...
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作者：Horner, Johannes; Rosenberg, Dinah; Solan, Eilon; Vieille, Nicolas
作者单位：Yale University; Hautes Etudes Commerciales (HEC) Paris; Tel Aviv University
摘要：We apply the average cost optimality equation to zero-sum Markov games by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler [Aumann, R. J., M. B. Maschler. 1995. Repeated Games with Incomplete Information. MIT Press, Cambridge, MA]. We determine the value and identify the optimal strategies for a range of parameters.
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作者：Borkovsky, Ron N.; Doraszelski, Ulrich; Kryukov, Yaroslav
作者单位：University of Toronto; Harvard University; Carnegie Mellon University
摘要：This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method.
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作者：Su, Xuanming
作者单位：University of California System; University of California Berkeley
摘要：We study a dynamic pricing problem for a class of products with stable consumption patterns (e. g., household items, staple foods). Consumers may stock up the product at current prices for future consumption, but they incur inventory holding costs. We model this situation as a dynamic game over an infinite time horizon: in each period, the seller sets a price, and each consumer chooses how many units to buy. We develop a solution methodology based on rational expectations. By endowing each pla...
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作者：Breton, Michele; de Frutos, Javier
作者单位：Universite de Montreal; Universite de Montreal; HEC Montreal; Universidad de Valladolid
摘要：In this paper, we propose a partial differential equation formulation for the value of an option when the underlying asset price is described by a discrete-time GARCH process. Our numerical approach involves a spectral Fourier-Chebyshev interpolation. Numerical illustrations are provided, and the results are compared with other available valuation methods. Our numerical procedure converges exponentially fast and allows for the efficient computation of option prices, achieving a high level of p...
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作者：Chehrazi, Naveed; Weber, Thomas A.
作者单位：Stanford University
摘要：Many decision problems exhibit structural properties in the sense that the objective function is a composition of different component functions that can be identified using empirical data. We consider the approximation of such objective functions, subject to general monotonicity constraints on the component functions. Using a constrained B-spline approximation, we provide a data-driven robust optimization method for environments that can be sample-sparse. The method, which simultaneously ident...
