Literature Overview

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Theoretical Literature

  • Levitan and Shubik (1972)[1] study a Bertrand-Edgeworth duopoly with symmetric firms, linear demand, and efficient rationing.
  • Kreps and Scheinkman (1983)[2] extend the equilibrium analysis to asymmetric capacities and concave demand; they further consider a two-stage game with quantity precommitment in the first stage.
  • Hirata (2009)[3] solves the Bertrand-Edgeworth game for three firms.
  • De Francesco and Salvadori (2009)[4] have some further results and theoretical references.

The aforementioned literature is on Bertrand-Edgeworth model. It should be noted that a mathematically very similar setting is that of Varian's model of sales. There is a lot of literature on that one too. Search literature is related as well.

Experimental Literature

  • Axelrod (1984)[5] did a computer tournament for a repeated prisoner's dilemma. This is a classical book, highly recommended.
  • Kruse (1993)[6] runs an Bertrand-Edgeworth duopoly experiment with different rationing rules and a U-shaped average cost curve.
  • Kruse et al. (1994)[7] run a Bertrand-Edgeworth experiment with convex demand and 4 firms.

There are more experimental papers. I will be adding those when I am in a mood to read read / look through them. There does not seem to be a single computer experiment on Bertrand-Edgeworth games.

Somewhat different but related: the nonlinear dynamics group from Amsterdam have conducted experiments where participants play in simple strategies rather than actions.

  • Sonnemans et al. (2004)[8]
  • Hommes et al. (2005)[9]

Empirical Literature

There is a lot of literature on price dispersion in various industries. I will add some classics here later on.


  1. Levitan, Richard; Shubik, Martin (1972). Price Duopoly and Capacity Constraints. International Economic Review. 13 (1): 111-122.
  2. Kreps, David M.; Scheinkman, Jose A. (1983). Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes. The Bell Journal of Economics. 14 (2): 326-337.
  3. Hirata, Daisuke (2009). Asymmetric Bertrand-Edgeworth Oligopoly and Mergers. The B.E. Journal of Theoretical Economics. 9 (1): 1935-1704.
  4. De Francesco, Massimo A.; Salvadori, Neri (2009). Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly. MPRA working paper.
  5. Axelrod, Robert (1984). The Evolution of Cooperation. Basic Books.
  6. Kruse, Jamie Brown (1993). Nash Equilibrium and Buyer Rationing Rules: Experimental Evidence. Economic Inquiry. 31 (4): 631–646.
  7. Kruse, Jamie Brown; Rassenti, Stephen; Reynolds, Stanley S.; Smith, Vernon L. (1994). Bertrand-Edgeworth Competition in Experimental Markets. Econometrica. 62 (2): 343-371.
  8. Sonnemans, Joep; Hommes, Cars; Tuinstra, Jan; van de Velden, Henk (2004). The instability of a heterogeneous cobweb economy: a strategy experiment on expectation formation. Journal of Economic Behavior & Organization. 54 (4): 453–481.
  9. Hommes, Cars; Sonnemans, Joep; Tuinstra, Jan; van de Velden, Henk (2005). A strategy experiment in dynamic asset pricing. Journal of Economic Dynamics and Control. 29 (4): 823–843.