On the Stability of the Competitive Equilibrium, II

Arrow, Kenneth J.; Block, H. D.; Hurwicz, Leonid

doi:10.2307/1907779

Cited by 330 publications

(181 citation statements)

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“…15 The idea that price formation processes behave drastically differently in the cases of substitutes and complements has a long history in economics. Arrow, Bloch and Hurwicz (1959) first established the stability of tatonnement in the case of gross substitutes. Milgrom and Roberts (1991) showed that the same sort of stability holds over a vast set of discrete and continuous time, synchronous and asynchronous, backward-and forward-looking price-setting processes.…”

Section: Simultaneous Ascending Auctionsmentioning

confidence: 99%

Ascending Auctions with Package Bidding

Ausubel

Milgrom

2002

The B.E. Journal of Theoretical Economics

231

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Abstract. A benchmark "package auction" is introduced in which bidders may determine their own packages on which to bid. If all bidders bid straightforwardly, then the outcome is a point in the core of the exchange economy that minimizes the seller's revenue. When goods are substitutes, straightforward bidding strategies comprise an ex post Nash equilibrium. Compared to the Vickrey auction, the benchmark ascending package auction has cheaper information processing, better handling of budget constraints, and less vulnerability to joint bidding strategies among bidders who would otherwise be losers. Improvements are suggested that speed the auction and limit opportunities for collusion.

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Section: Simultaneous Ascending Auctionsmentioning

confidence: 99%

Ascending Auctions with Package Bidding

Ausubel

Milgrom

2002

The B.E. Journal of Theoretical Economics

231

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“…A well-known result by Hurwicz (1958, 1960a,b), Arrow et al (1959) is that the tâtonnement process of Samuelson (1941):…”

Section: On Price-adjustment Dynamicsmentioning

confidence: 97%

“…We draw inspiration from rather early literature on price-adjustment processes as introduced by Samuelson (1941) and subsequent results by Arrow and Hurwicz (1958), Arrow and Hurwicz (1960a,b) and Arrow et al (1959). Our second source of inspiration We thank two referees, Ulrich Witt and audiences in Tilburg, Amsterdam and Stony Brook for comments and suggestions for improvement.…”

Section: Introductionmentioning

confidence: 94%

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On evolutionary ray-projection dynamics

Joosten

Roorda

2011

Math Meth Oper Res

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We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637-666, 1991), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner.

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“…The problem of finding equilibrium is related to and stems from previous work on the stability of equilibrium (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). [Work on computation of equilibria should also be mentioned, although that deals with nonlinear equilibrium conditions and does not concern itself with decentralized methods (14).]…”

mentioning

confidence: 99%

A decentralized process for finding equilibria given by linear equations.

Reiter¹

1994

Proc. Natl. Acad. Sci. U.S.A.

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I present a decentralized process for finding the equilibria of an economy characterized by a finite number of linear equilibrium conditions. The process finds all equilibria or, If there are none, reports that, in a finite number ofsteps at most equal to the number of equations. The communication and computational complexity compare favorably with other decentralzed processes. The process may also be interpreted as an algorithm for solving a distributed system of linear equations. Comparisons with the Linpack program for LU (lower and upper trianula decomposition of the matrix of the equation system, a version of Gaussian elation) are presented.This paper presents a decentralized process for finding the equilibria of an economy characterized by a finite number of linear equilibrium conditions. The process differs from others that have been studied in connection with stability (global and local) of equilibrium in that it is given by an algorithm requiring a finite number of steps, rather than an infinite iterative process, as, for instance, a process given by difference or differential equations.Furthermore, it is not assumed that equilibria exist. Ifthere are no equilibria, the process discovers this and stops; ifthere are equilibria, the process finds them all in a fixed number of steps depending on the number of equilibrium conditions.The process is decentralized in the following sense. In a certain subset of economies with N agents, the equilibrium condition of an individual agent is a linear equation in RN (possibly several linear equations)t with N + 1 coefficients, not all zero.t That equation (i.e., its coefficients) need be known only to the agent whose equilibrium condition it is. The process requires each agent to transmit a message consisting of a certain finite number of points of RN to one other agent. When N > 2, the messages transmitted are insufficient for any agent to learn the complete system of equilibrium equations. § At each step ofthe process one agent decides on a message by using only knowledge ofhis/her own equilibrium condition and the message received from one other agent.Literature. The problem of finding equilibrium is related to and stems from previous work on the stability of equilibrium (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). [Work on computation of equilibria should also be mentioned, although that deals with nonlinear equilibrium conditions and does not concern itself with decentralized methods (14).] For the present purpose the literature on stability of equilibrium may be summarized as follows. Papers (1-3) studied price adjustment processes in which prices change according to excess demand. The objective was to show that every economic environment that satisfies conditions ensuring the existence of competitive equilibria has (globally or locally) stable equilibria. This turned out not to be the case (4, 5). To guarantee stability, additional conditions, such as "gross substitutes," are required. Smale (6) studied an adjustment process that involved much bigge...

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On the Stability of the Competitive Equilibrium, II

Cited by 330 publications

References 0 publications

Ascending Auctions with Package Bidding

Ascending Auctions with Package Bidding

On evolutionary ray-projection dynamics

A decentralized process for finding equilibria given by linear equations.

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