Bertrand competition with cost uncertainty

Routledge, R. R.

doi:10.1016/j.econlet.2010.03.006

Cited by 16 publications

(9 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, our analysis of firm behavior and industry dynamics can accommodate drastic innovations that Arrow () contemplates. Similar to the result of Routledge () in the static context, we establish existence of equilibria in the dynamic Bertrand investment game.…”

Section: Introductionsupporting

confidence: 68%

“…Despite the huge literature spawned by Bertrand (), our understanding of price competition in the presence of production cost uncertainty is still rudimentary. For example, even in the static Bertrand () model, Routledge () notes that “there is a notable gap in the research. There are no equilibrium existence results for the classical Bertrand () model when there is discrete cost uncertainty” (p. 357).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Dynamics of Bertrand Price Competition With Cost‐reducing Investments

Iskhakov

Rust

Schjerning

2018

Int Economic Review

View full text Add to dashboard Cite

Abstract:We extend the classic Bertrand duopoly model of price competition to a dynamic setting where competing duopolists invest in a stochastically improving production technology to "leapfrog" their rival and attain temporary low cost leadership. We find a huge multiplicity of Markov perfect equilibria (MPE) and show that when firms move simultaneously the set of all MPE payoffs is a triangle that includes monopoly payoffs and a symmetric zero mixed strategy payoff. When firms move asynchronously, the set of MPE payoffs is strictly within this triangle, but there still is a vast multiplicity of MPE, most of which involve leapfrogging.

show abstract

Section: Introductionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

The Dynamics of Bertrand Price Competition With Cost‐reducing Investments

Iskhakov

Rust

Schjerning

2018

Int Economic Review

View full text Add to dashboard Cite

show abstract

“…In particular, our analysis of firm behavior and industry dynamics can accommodate drastic innovations that Arrow (1962) contemplated. Similar to the result of Routledge (2010) in the static context, we establish existence of equilibria in the dynamic Bertrand investment game.…”

Section: Introductionsupporting

confidence: 57%

The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

2013

View full text Add to dashboard Cite

We extend the classic Bertrand duopoly model of price competition to a dynamic setting where competing duopolists invest in a stochastically improving production technology to "leapfrog" their rival and attain temporary low cost leadership. We find a huge multiplicity of Markov perfect equilibria (MPE) and show that when firms move simultaneously the set of all MPE payoffs is a triangle that includes monopoly payoffs and a symmetric zero mixed strategy payoff. When firms move asynchronously, the set of MPE payoffs is strictly within this triangle, but there still is a vast multiplicity of MPE, most of which involve leapfrogging.

show abstract

“…Recall that ϕ denotes a log-sum formula as per (29). In addition to (34) we can add one of the two Bellman equations (30) for firm j to form the system of two equations with two unknowns, namely v I, j (0, 0, 0) and v N, j (0, 0, 0).…”

Section: Corollary 51 (Weak Convergence Of Rls Algorithm)mentioning

confidence: 99%

Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games

Iskhakov¹,

Rust²,

Schjerning³

2015

Review of Economic Studies

View full text Add to dashboard Cite

Abstract:We define a class of dynamic Markovian games, directional dynamic games (DDG), where directionality is represented by a strategy-independent partial order on the state space. We show that many games are DDGs, yet none of the existing algorithms are guaranteed to find any Markov perfect equilibrium (MPE) of these games, much less all of them. We propose a fast and robust generalization of backward induction we call state recursion that operates on a decomposition of the overall DDG into a finite number of more tractable stage games, which can be solved recursively. We provide conditions under which state recursion finds at least one MPE of the overall DDG in a finite number of steps. We introduce a recursive lexicographic search (RLS) algorithm that systematically and efficiently uses state recursion to find all MPE of the overall game in a finite number of steps. We apply RLS to find all MPE of a dynamic model of Bertrand price competition with cost reducing investments which we show is a DDG. RLS rapidly finds and enumerates each one of the hundreds of millions of MPE of this game.

show abstract

Bertrand competition with cost uncertainty

Cited by 16 publications

References 9 publications

The Dynamics of Bertrand Price Competition With Cost‐reducing Investments

The Dynamics of Bertrand Price Competition With Cost‐reducing Investments

The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games

Contact Info

Product

Resources

About