## Dealing with the Complexity of Economic Calculations (1997)

Citations: | 7 - 1 self |

### BibTeX

@TECHREPORT{Rust97dealingwith,

author = {John Rust},

title = {Dealing with the Complexity of Economic Calculations},

institution = {},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

This essay is a response to a growing negative literature that suggests that neoclassical economic theories based on hypotheses of rationality and equilibrium are of limited practical relevance because they require an infeasibly large number of calculations. Many of the negative results are translations of abstract complexity bounds from the computer science literature. I show that these bounds do do not constitute proofs that difficult economic calculations are "impossible" and discuss the type of hardware and software that can make it possible to solve very hard problems. I discuss four different ways to break the curse of dimensionality of economic problems: 1) by exploiting special structure, 2) by decomposition, 3) by randomization, and 4) by taking advantage of "knowledge capital." However these four methods may not be enough. I offer some speculations on the role of decentralization for harnessing the power of massively parallel processors. I conjecture that decentralization i...

### Citations

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Citation Context ... the best is of no great importance, hence the unrealism of the assumption that the actors optimize does not matter; others, including myself, believe that it does matter, and matters a great deal.&qu=-=ot; (Simon, 1996, pp. 28---=-29). It's difficult to dismiss impossibility arguments based on computational complexity bounds because we have observed the curse of dimensionality "empirically" in numerous numerical appli... |

468 | The Emperor’s New Mind - Penrose - 1990 |

456 |
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Citation Context ...ive a prediction. The real difficulty, to the solution of which science has little to contribute, and which is sometimes indeed insoluble, consists in the ascertainment of the particular facts." =-=(von Hayek, 1989-=-, pp. 6--7) A similarly optimistic view of the power of computers was espoused by Lange, one of the chief proponents of the efficacy of centralized planning, in response to criticisms of his approach ... |

408 |
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Citation Context ...l agent by itself can only do some simple thing that needs no mind or thought at all. Yet when we join these agents in societies --- in certain very special ways --- this leads to true intelligence. (=-=Minsky, 1986-=-, p. 17). However it is obvious that at any given time the brain as a whole as well defined objectives such as eating, work, sex, etc. Furthermore it is also clear that communications within the brain... |

334 | The use of knowledge in society - Hayek - 1945 |

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83 |
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Citation Context ...e, instead of distributing them among local departments." 23 There is a closely related concept of "informational decentralization" arising from the literature on resource allocation me=-=chanisms (e.g. Hurwicz 1972-=- and Mount and Reiter 1974) in which information needed to make resource allocation decisions is not directly available in one place for use by a central planner, but rather is distributed throughout ... |

78 | On the complexity of decentralized decision making and detection problems - Tsitsiklis, Athans - 1985 |

76 | Traub: Faster valuation of financial derivatives - Paskov, F |

64 | Behavior of Trading Automata in a Computerized Double Auction Market, in The Double Auction - Rust, Miller, et al. - 1993 |

49 | Exponential lower bound for finding Brouwer fixed points - Hirsch, Papadimitriou, et al. - 1989 |

45 |
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(Show Context)
Citation Context ...tributing them among local departments." 23 There is a closely related concept of "informational decentralization" arising from the literature on resource allocation mechanisms (e.g. Hu=-=rwicz 1972 and Mount and Reiter 1974-=-) in which information needed to make resource allocation decisions is not directly available in one place for use by a central planner, but rather is distributed throughout the economy in the form of... |

32 |
Lower Bounds for Efficiency of Surplus Extraction in Double Auctions
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(Show Context)
Citation Context ...orithms. I already discussed several examples of "decentralized algorithms" for computing approximate CE in my discussion of the double auction market in the section on knowledge capital: th=-=e work of Gode and Sunder 1993-=- and Rust, Miller and Palmer 1993. Another example of a decentralized algorithm is the the bilateral bargaining model of general equilibrium price formation of Axtell and Epstein 1996. 25 The Axtell a... |

27 |
Tsitsiklis. The complexity of dynamic programming
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(Show Context)
Citation Context ... have been established only for a relatively small number of economic problems such as social planning (Friedman and Oren, 1995), Walrasian equilibrium (Papadimitriou, 1995), and dynamic programming (=-=Chow and Tsitsiklis, 1989-=-). However it is likely that this list will quickly grow and formal proofs will soon be available showing that the majority of economic problems are intractable. The next step is to translate complexi... |

24 | Modeling rational players Part I - Binmore - 1987 |

24 | 2001] Optimal Solution of Nonlinear Equations - Sikorski |

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16 |
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Citation Context ...ntegration is tractable on an average case basis, where particular (typically Gaussian) priors are used to represent the likelihood of encountering various types of integrands (see, e.g. TWW, 1988 or =-=Paskov, 1993-=-). 17 which must determine an optimal replacement policy for each vehicle in its fleet. Intuitively the separability and independence assumptions imply that the problem is perfectly decomposable into ... |

14 | Using randomization to break the curse of dimensionality. Econometrica 65(3):487–516 - Rust - 1997 |

12 | The immune system as a prototype of autonomous decentralized systems - Segel - 1997 |

11 |
Computable General Equilibrium Modeling for Policy Analysis and Forecasting
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(Show Context)
Citation Context ...ges of decentralized algorithms. 4.1 Examples of Centralized Algorithms A classic example of a centralized method for computing CEs is the "programming approach" suggested by Negishi and des=-=cribed in Dixon and Parmenter, 1996-=-, section 2.1. In the programming approach, one repeatedly maximizes a weighted average of individual utilities subject to aggregate resource constraints. The (normalized) Lagrange multipliers for the... |

8 |
The complexity of resource allocation and price mechanisms under bounded rationality
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(Show Context)
Citation Context ...ity framework. 10 of a fixed point to a correspondence. However to date formal complexity bounds have been established only for a relatively small number of economic problems such as social planning (=-=Friedman and Oren, 1995-=-), Walrasian equilibrium (Papadimitriou, 1995), and dynamic programming (Chow and Tsitsiklis, 1989). However it is likely that this list will quickly grow and formal proofs will soon be available show... |

8 |
The computer and the
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(Show Context)
Citation Context ... and others: “My answer to Hayek and Robbins would be: so what’s the trouble? Let us put the simultaneous equations on an electronic computer and we shall obtain the solution in less than a second.” (=-=Lange, 1967-=-, p. 158). Although the main message of this essay is that computational problems are not insurmountable, I would not be so bold or naïve as to claim they are trivial. While I certainly agree with Hay... |

7 |
The Computer and the Market
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(Show Context)
Citation Context ... and others: "My answer to Hayek and Robbins would be: so what's the trouble? Let us put the simultaneous equations on an electronic computer and we shall obtain the solution in less than a secon=-=d." (Lange, 1967-=-, p. 158). Although the main message of this essay is that computational problems are not insurmountable, I would not be so bold or na ive as to claim they are trivial. While I certainly agree with Ha... |

7 | Using Randomization to Break the Curse of Dimensionality" Econometrica - Rust - 1997 |

7 | Bargaining and Competition, Part I: Characterization,” Econometrica 54 - Gale - 1986 |

5 | Some aspects of effectively constructive mathematics that are relevant to the foundations of Neoclassical mathematical economics and the theory of games - Lewis - 1992 |

5 |
The computation of equilibrium prices: an exposition
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- 1982
(Show Context)
Citation Context ...ve been proposed by economists and operations researchers to compute approximate CE including variations of Newton's or "Johansen's method" (see Dixon and Parmenter, 1996), or Scarf's algori=-=thm (see, Scarf, 1982-=-), or other more elaborate methods based on solving variational inequalities or sequences of linear or nonlinear complimentarity problems (see Nagurney, 1996 or Rutherford, 1985) are algorithms that c... |

4 | Bilateral trading on a network: Convergence and optimality results, mimeo - Bell - 1996 |

4 | Breaking Intractability - Traub, Wozniakowski - 1994 |

3 |
The Hedonistic Neuron Hemisphere
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(Show Context)
Citation Context ...nter. (Churchland and Sejnowksi, 1992, pp 24--25) Individual neurons in the brain appear have their own objective functions: in very rough terms, they seek stimulation and avoid inhibition (see, e.g. =-=Klopf, 1982). A numbe-=-r of neuroscientists and computer scientists have developed theories of cognition that hypothesize that the brain operates as a sort of "society" or competitive economy: How can intelligence... |

3 |
Parallel computation
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(Show Context)
Citation Context ... Parmenter, 1996), or Scarf's algorithm (see, Scarf, 1982), or other more elaborate methods based on solving variational inequalities or sequences of linear or nonlinear complimentarity problems (see =-=Nagurney, 1996-=- or Rutherford, 1985) are algorithms that can be interpreted as requiring strict coordination, synchronization, and reporting requirements on the part of individual agents, and therefore must be regar... |

2 | The minimum degree of recursively representable choice funtions - Lewis - 1985 |

2 | Optimal Solution of Nonlinear Equations Satisfying a Lipschitz Condition " Numerische Mathematik 43 225--240 - Sikorski - 1984 |

2 | Breaking Intractability” Scientific - Traub - 1994 |

1 |
Distributed Computation of Optimal Allocations Through Bilateral Exchange" manuscript
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(Show Context)
Citation Context ...apital: the work of Gode and Sunder 1993 and Rust, Miller and Palmer 1993. Another example of a decentralized algorithm is the the bilateral bargaining model of general equilibrium price formation of =-=Axtell and Epstein 1996-=-. 25 The Axtell and Epstein paper is a computational simulation of exchange and price formation in which a population of agents with preferences over continuous d-dimensional commodity bundles are ran... |

1 | Toward a Theory of Mind as a Lassiez-Faire Economy of Idiots - Baum - 1995 |

1 | Smart Systems and Simple Agents: Industry Pricing by Parallel Rules - Board, Tinsley - 1996 |

1 | Bargaining and Competition part I: Characterization" Econometrica - Gale - 1986 |

1 |
Superhack
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- 1994
(Show Context)
Citation Context ...ulations required to break the code was quite large (requiring some 100 quadrillion computer instructions), "It was inconceivable 17 years ago that this code could ever be broken" (Lenstra, =-=quoted in Leutwyler, 1994-=-). This example foreshadows one of the main points of this essay: a combination of clever software design, decentralization, and massive parallelism made it possible to solve a problem that was previo... |

1 | Structure and Complexity: The Use of Recursion Theory in the Foundations of Neoclassical Ecomomics and the Theory of Games" manuscript - Lewis - 1986 |