The name is absent



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 name is absent
2. The name is absent
3. Achieving the MDGs – A Note
4. SME'S SUPPORT AND REGIONAL POLICY IN EU - THE NORTE-LITORAL PORTUGUESE EXPERIENCE
5. Gerontocracy in Motion? – European Cross-Country Evidence on the Labor Market Consequences of Population Ageing
6. Une Classe de Concepts
7. The name is absent
8. The name is absent
9. The name is absent
10. Motivations, Values and Emotions: Three Sides of the same Coin