of Theorem 4.1 are satisfied and we can conclude that there exist only asym-
metric equilibria in the game. Furthermore, reaction curves in this model are
contractions and so a unique pair of equilibria exists.
The second paper that can be analyzed under our framework is Motta (1993).
He develops two versions of a vertical product differentiation model, one with
fixed and the other with variable cost of investment in quality. In each of them,
he compares price versus quality competition. The model with fixed cost and
price competition can illustrate the results of this section. Considering the same
notation as in Aoki and Prusa (1996), the payoff function is defined as follows:
F(x, y)=
4v2x2(x-y) χ2
_ _ _
(4x-y)2 2
xyv2 (y-x) x2
(4y-x)2 2
if x ≥ y
if x ≤ y
(16)
Where v is the upper limit of the set of consumer’s taste parameters. This
model is analogous to Aoki and Prusa (1996) if we let v = 1 and k = 1. All the
results follow directly from the above discussion.
5 Convex Payoffs
Certain features of the production technologies or consumer preferences may
lead to a situation where payoff functions are convex. In particular, the pres-
ence of highly convex demand functions or strongly concave costs translating
intensely decreasing elasticity of demand or decreasing marginal costs might
have this effect. This property of the payoff functions implies that agents prefer
corner solutions. Moreover certain additional conditions on the payoffs might
generate asymmetric equilibria and even rule out the symmetric ones. In this
section we analyze a class of games in which players have convex payoff functions
and only asymmetric PSNEs arise.
Let S =[0,c] be the strategy space of a player in a two-player game, Γ.
Consider F : S × S → R as the payoff function of player 1. G(y, x)=F (x, y)
is the payoff of player 2 because the game is a priori symmetric. Then we can
apply the following theorem to conclude about the properties of the equilibria
25
More intriguing information
1. Literary criticism as such can perhaps be called the art of rereading.2. Announcement effects of convertible bond loans versus warrant-bond loans: An empirical analysis for the Dutch market
3. Une nouvelle vision de l'économie (The knowledge society: a new approach of the economy)
4. The name is absent
5. The Variable-Rate Decision for Multiple Inputs with Multiple Management Zones
6. Qualification-Mismatch and Long-Term Unemployment in a Growth-Matching Model
7. The name is absent
8. Consumption Behaviour in Zambia: The Link to Poverty Alleviation?
9. The name is absent
10. Visual Perception of Humanoid Movement