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Costly Renegotiation in Repeated Bertrand Games

Andersson, Ola and Wengström, Erik LU (2010) In Journal of Theoretical Economics 10(1).
Abstract
This paper extends the concept of weak renegotiation-proof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost, there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique pure strategy WRP equilibrium without renegotiation costs, which implies marginal-cost pricing in every period. Moreover, in... (More)
This paper extends the concept of weak renegotiation-proof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost, there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique pure strategy WRP equilibrium without renegotiation costs, which implies marginal-cost pricing in every period. Moreover, in comparison to the findings of Mc-Cutcheon (1997), who states that renegotiation costs have to be substantial to facilitate collusion, this result points to a quite different conclusion. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
weak renegotiation-proof equilibrium, renegotation, repeated Bertrand, games
in
Journal of Theoretical Economics
volume
10
issue
1
publisher
Berkeley Electronic Press
external identifiers
  • wos:000285829700001
  • scopus:78650895889
ISSN
1935-1704
DOI
10.2202/1935-1704.1719
language
English
LU publication?
yes
id
92217fce-8f1a-4997-b23b-c4c768fd09c5 (old id 1859807)
date added to LUP
2011-04-20 08:46:36
date last changed
2018-05-29 09:47:54
@article{92217fce-8f1a-4997-b23b-c4c768fd09c5,
  abstract     = {This paper extends the concept of weak renegotiation-proof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost, there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique pure strategy WRP equilibrium without renegotiation costs, which implies marginal-cost pricing in every period. Moreover, in comparison to the findings of Mc-Cutcheon (1997), who states that renegotiation costs have to be substantial to facilitate collusion, this result points to a quite different conclusion.},
  author       = {Andersson, Ola and Wengström, Erik},
  issn         = {1935-1704},
  keyword      = {weak renegotiation-proof equilibrium,renegotation,repeated Bertrand,games},
  language     = {eng},
  number       = {1},
  publisher    = {Berkeley Electronic Press},
  series       = {Journal of Theoretical Economics},
  title        = {Costly Renegotiation in Repeated Bertrand Games},
  url          = {http://dx.doi.org/10.2202/1935-1704.1719},
  volume       = {10},
  year         = {2010},
}