Jaap H. Abbring, Jeffrey R. Campbell, Nan Yang
arXiv 20 Oct 2026 · Theoretical Economics
arXiv:2610.28440 · PDF · Extracted main text
This paper establishes the existence and essential uniqueness of an intuitively refined Markov-perfect equilibrium in a duopoly game with sunk costs, barriers to entry, firm-specific technological progress, and irreversible exit. We develop an algorithm that quickly computes the equilibrium by solving for fixed points of a finite sequence of auxiliary contraction mappings, which we label Fake Backward Induction. We illustrate the game's practical value with a quantitative analysis of competition policy in a stochastically growing market with firms idiosyncratically learning by aging. Computing one equilibrium of this example takes 10.2 seconds on one Apple M5 Pro core.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Abbring, J. H., J. R. Campbell, J. Tilly, and N. Yang (2018) Very Simple Markov-Perfect Industry Dynamics: Theory self | 0.928 | 4 | 3 | 100% |
| 2 | Abbring, J. H., J. R. Campbell, and N. Yang (2026) Supplement to `Entry, Exit, and Technological Progress in Markov-Perfect Duopoly', Working paper, Tilburg University self | 0.737 | 3 | 3 | 67% |
| 3 | Ericson, R. and A. Pakes (1995) Markov-Perfect Industry Dynamics: A Framework for Empirical Work | 0.737 | 3 | 2 | 100% |
| 4 | Cabral, L. M. B (1993) Experience Advantages and Entry Dynamics | 0.644 | 2 | 2 | 100% |
| 5 | Rust, J (1987) Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher | 0.511 | 2 | 1 | 100% |
| 6 | Fudenberg, D. and J. Tirole (1991) Game Theory | 0.511 | 2 | 1 | 100% |
| 7 | Foster, L., J. Haltiwanger, and C. Syverson (2008) Reallocation, Firm Turnover, and Efficiency: Selection on Productivity or Profitability? | 0.405 | 1 | 1 | 100% |
| 8 | McAfee, R. P., H. M. Mialon, and M. A. Williams (2004) What Is a Barrier to Entry? | 0.405 | 1 | 1 | 100% |
| 9 | Pakes, A. and P. McGuire (2001) Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the `Curse' of Dimensionality | 0.405 | 1 | 1 | 100% |
| 10 | Bajari, P. L., C. L. Benkard, and J. Levin (2007) Estimating Dynamic Models of Imperfect Competition | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 26 scored citations.