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. The name is absent2. Can a Robot Hear Music? Can a Robot Dance? Can a Robot Tell What it Knows or Intends to Do? Can it Feel Pride or Shame in Company?
3. The name is absent
4. Cultural Diversity and Human Rights: a propos of a minority educational reform
5. Reputations, Market Structure, and the Choice of Quality Assurance Systems in the Food Industry
6. Consciousness, cognition, and the hierarchy of context: extending the global neuronal workspace model
7. AN EMPIRICAL INVESTIGATION OF THE PRODUCTION EFFECTS OF ADOPTING GM SEED TECHNOLOGY: THE CASE OF FARMERS IN ARGENTINA
8. Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outlier
9. Unilateral Actions the Case of International Environmental Problems
10. On the job rotation problem