On the endogeneity of Cournot–Nash and Stackelberg equilibria: games of accumulation

TLDR: A simple theorem that uses agents’ standard one-period reaction functions and the one- period Cournot–Nash and Stackelberg equilibria delineates the equilibrium set of games with two properties: agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur.

About: This article is published in Journal of Economic Theory.The article was published on 2005-01-01 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Stackelberg competition & Oligopoly.

Figures

Fig. 3. Quantity competition with substitutes.

Fig. 2. Contribution game with prestige.

Fig. 5. Rent-seeking game.

Fig. 4. Quantity competition with complements.

Fig. 1. Standard public good game.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "On the endogeneity of cournot–nash and stackelberg equilibria: games of accumulation" ?

Romano et al. this paper characterized equilibria of games with two properties: ( i ) agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur ; but ( ii ) they can only add to their initial amounts. 

Q2. What are the future works in "On the endogeneity of cournot–nash and stackelberg equilibria: games of accumulation" ?

These extensions await future research. 

Q3. Why does the leader produce less when the Stackelberg outcome arises?

From (16), the authors see that when the Stackelberg outcome arises, the leader produces less due to the increased cost of producing early. 

Q4. What is the continuation equilibrium for y12A120?

If y12A½0;Y2ðG0Þ ; the continuation equilibrium is at G0 for any y11A½0; I2=4 : Similarly, for any y12A½Y2ðG0Þ; I1=4 ; the continuation equilibrium is at f 1ðy12Þ for any y11A½0; I2=4 : Hence, requiring that y11 be at least I2=4 does not affect the equilibrium set. 

Q5. What is the condition for the maximization of the Cournot–Nash outcome?

For instance, as the authors show in Observation B1 in the appendix, when both reaction functions are downward-sloping, the constraint set for the maximization in S5 is a singleton with Ỹi ¼ YiðG0Þ; and thus the condition is automatically satisfied. 

Q6. What is the reason why one agent might take early action when it is more costly?

For instance, it is clear that if the first-period action is sufficiently costly, this will take away all the benefits of leadership and the Cournot–Nash outcome with actions in the second period will prevail.