## General Entry

**Working Papers**

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 π_{i}(v_{i})=v_{i} – K_{i}; and duopoly profits are π_{i}(v_{i},v_{j}) = γv_{i} – ρv_{i} – δ – K_{i}, where K_{i} is the entry cost. The distributions of types are v_{1}~U[0,1] and v_{2}~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. π
_{i}(v_{i})=v_{i}-0.5, π_{1}(v_{1},v_{2}) = v_{1}– 0.5 – 0.5 and π_{2}(v_{2},v_{1}) = v_{2 }– 0.5δ – 0.5

- Example 2: Extensive Margin. π
_{i}(v_{i})=v_{i}-0.5, π_{1}(v_{1},v_{2}) = 0.5v_{1}– 0.5 and π_{2}(v_{2},v_{1}) = 0.5γv_{2}– 0.5

- Example 3: Intensive Margin. π
_{i}(v_{i})=v_{i}-0.5, π_{1}(v_{1},v_{2}) = v_{1}– v_{2}– 0.5 and π_{2}(v_{2},v_{1}) = v_{2}–*ρ*v_{1}– 0.5

We thank Yuzhou Wang for his assistance in this project.

## Auctions with Entry Costs

**Working Papers**