TY - JOUR
T1 - Instability in the implementation of Walrasian allocations
AU - Jordan, J. S.
N1 - Funding Information:
* I would like to thank Leonid Hurwicz, Hillel Gershenson, and the participants in the 1984 IMSSS Workshop at Stanford University, especially Kenneth Arrow, for very helpful comments. Of course, they are not responsible for my use or misuse of their suggestions. I would also like to acknowledge the support of National Science Foundation Grant IST-8319164.
PY - 1986/8
Y1 - 1986/8
N2 - The existence of game forms which implement Walrasian allocations as Cournot (Nash) equilibrium outcomes is well known. However, if the equilibria are also required to be locally dynamically stable, at least for environments with unique Walrasian allocations, this paper shows that the requisite game forms do not exist. Our definition of a game form entails certain regularity conditions, and requires the Cournot equilibrium to be unique when the Walrasian equilibrium is unique. The main result is that for such a game form, there does not exist a continuous-time strategy adjustment process which ensures the local stability of Cournot equilibria throughout a certain class of environments having unique Walrasian equilibria. Each trader adjusts his strategy in response to his own characteristics and the observed current strategies of others; but the direction and magnitude of adjustments are not constrained by any behavioral assumptions. The definitions permit the inclusion of an artificial player, such as an auctioneer, so the well-known tatonnement instability emerges as a special case.
AB - The existence of game forms which implement Walrasian allocations as Cournot (Nash) equilibrium outcomes is well known. However, if the equilibria are also required to be locally dynamically stable, at least for environments with unique Walrasian allocations, this paper shows that the requisite game forms do not exist. Our definition of a game form entails certain regularity conditions, and requires the Cournot equilibrium to be unique when the Walrasian equilibrium is unique. The main result is that for such a game form, there does not exist a continuous-time strategy adjustment process which ensures the local stability of Cournot equilibria throughout a certain class of environments having unique Walrasian equilibria. Each trader adjusts his strategy in response to his own characteristics and the observed current strategies of others; but the direction and magnitude of adjustments are not constrained by any behavioral assumptions. The definitions permit the inclusion of an artificial player, such as an auctioneer, so the well-known tatonnement instability emerges as a special case.
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U2 - 10.1016/0022-0531(86)90048-7
DO - 10.1016/0022-0531(86)90048-7
M3 - Article
AN - SCOPUS:38249038734
SN - 0022-0531
VL - 39
SP - 301
EP - 328
JO - Journal of Economic Theory
JF - Journal of Economic Theory
IS - 2
ER -