III.- THE EFFECTS OF ENTRY
In this Section we will study the effects of an increase in the number of
players (see Bresnahan and Reiss (1991) and the references there for the
empirical evidence in oligopolistic markets). In order to save notation let
y ≡ x (n+l). Also, let us denote by x(n), x (n) and U (n) the equilibrium
n+l i i
values of x, x and U ina game with n players.
Proposition 1 : Under A.l-2 we have that
a) x(n) ≤ x(n+l), x (n) ≥ x (n+l) MieN and
i i
b) if y > 0 the above inequalities are strict.
Proof: We first notice that if x(n) ≥ x(n+l) and x(n) > 0, xfn+l) = 0 is
impossible since T (x (n), x(n)) ≥ T (0, x(n+l)) ≥ T (0, x(n)) would
i i i i
(2)
contradict that T ( ) is strictly decreasing on x . Take any i ∈ N c∖ N+l (if
i i
i g N+l, xfn) > x(n+l) = 0). In both N.E. first order conditions hold so
(1) Tfxfn), x(n)) = Tfxfn+1), x(n+l)).
Therefore because A.2 we have only two possibilities:
I- x(n+l) ≤ x(n) and xfn+l) ≥ xfn), with a strict inequality or
II.- x(n+l) ≥ x(n) and x (n+l) ≤ x (n).
i i
(2) A similar argument shows that if x(n) ≤ x(n+l) and x(n) = 0, then x(n+l) =
0, so the second inequality in a) in Proposition 1 holds V i ∈ I.
16
More intriguing information
1. The use of formal education in Denmark 1980-19922. Running head: CHILDREN'S ATTRIBUTIONS OF BELIEFS
3. Banking Supervision in Integrated Financial Markets: Implications for the EU
4. Migrant Business Networks and FDI
5. Ronald Patterson, Violinist; Brooks Smith, Pianist
6. Does Presenting Patients’ BMI Increase Documentation of Obesity?
7. Testing for One-Factor Models versus Stochastic Volatility Models
8. Creating a 2000 IES-LFS Database in Stata
9. Managing Human Resources in Higher Education: The Implications of a Diversifying Workforce
10. Quelles politiques de développement durable au Mali et à Madagascar ?