We study firm entry decisions when firms have private information about their profitability. We generalize current entry models by allowing general forms of market competition and heterogeneity among firms. Post-entry profits depend on market structure, firms’ identities, and entering firms’ private information. We characterize the equilibrium in this class of games by introducing a notion of the firm’s strength and show that an equilibrium where players’ strategies are ranked by strength, or herculean equilibrium, always exists. Moreover, when profits are elastic enough with respect to the firm’s private information, the herculean equilibrium is the unique equilibrium of the entry game.
We study firm entry decisions when firms have private information about characteristics that affect their profitability and that of their competitors. Here are some examples on how to solve for the equilibria in such games. Monopoly profits are πi(vi)=vi – Ki; and duopoly profits are πi(vi,vj) = γvi – ρvi – δ – Ki, where Ki is the entry cost. The distributions of types are v1~U[0,1] and v2~U[0,α].
The orange dot allows you to change the values of the parameters (α horizontally and δ, γ or ρ vertically). The orange line is the response function for firm 1 and the purple line is the response function for player 2.
- Example 1: Type-independent Extensive Margin. πi(vi)=vi -0.5, π1(v1,v2) = v1 – 0.5 – 0.5 and π2(v2,v1) = v2 – 0.5δ – 0.5
- Example 2: Extensive Margin. πi(vi)=vi -0.5, π1(v1,v2) = 0.5v1 – 0.5 and π2(v2,v1) = 0.5γv2 – 0.5
- Example 3: Intensive Margin. πi(vi)=vi -0.5, π1(v1,v2) = v1 – v2 – 0.5 and π2(v2,v1) = v2 – ρv1 – 0.5
We thank Yuzhou Wang for his assistance in this project.
Auctions with Entry Costs