I have encountered the equilibrium concept of "Stackelberg leader-leader equilibrium" while reading Product Line Rivalry (AER, Brander and Eaton (1984). They say "we define a Stackelberg strategy as one which involves taking into account the contemporaneous reaction of one's rival in setting one's own strategy". That definition does not really help me.

They also mention that this equilibrium concept is another way of interpreting the original Stackelberg model (which I know).

Does anyone have a reference or an explanation ? Of course, Google only returns results on the leader-follower game.

• Is there something else in the paper that makes this something more than Cournot? Feb 12, 2015 at 1:57
• I'm not sure what you mean. They consider a three-stage game with two firms. 1) Firms decide how many products to produce. 2) They decide which products to produce 3) they set quantities. The problem is at stage 2. They look at three different cases 1) simultaneous Nash 2) sequential Nash 3) Stackelberg leader-leader equilibrium.
– sehb
Feb 12, 2015 at 6:31
• Are there two simulatious leaders and then many followers (or nature moving)? Apr 2, 2015 at 18:47

A leader-leader Stackelberg is a situation in the Stackelberg model where both firms believe they are leaders. This leads to global production being much higher than expected by both firms, as they anticipate small production by the other firm in response to their high production.

• @sehb As an assignment, you should try to fil in the profit of each firm on a price/demand diagram in both leader-leader and leader-follower cases on the same graph :). Remember both firms have the same production function. Then edit to illustrate my answer ;) May 11, 2015 at 13:24

The original Stackelberg game is an asymmetric duopoly: Firm 1 takes on the role of leader, while Firm 2 takes on the role of follower. Firm 2 will follow her reaction curve. Firm 1 will observe the follower's reaction curve and choose the point which is best for him.

There are some variations of this game, if both players are followers then you have a Cournot game. If both players believe themselves to be the leader, then neither one will be successful at following the strategy above. This is a leader-leader game, and it will lead to a Stackelberg disequilibrium. The leader-leader model will require both firms to start with incorrect assumptions about each other, and it will lead to non-optimal output in the market.

In a multi-stage game: as rational players, the firms will revise their expectations. As a result either one will take the role of follower, or a firm will exit the market, making the remaining leader a monopoly.

• we're speaking of one-turn models here actually, so once the firms realize their errors they already produced too much May 7, 2015 at 16:02
• @VicAche I see, Thanks - I will revise my answer.
– Nox
May 7, 2015 at 16:13