A simple leader-follower game with discrete strategies

This simple example is from Wu and Parlar (2011) and its solution is found by Gambit. Here too we find that P2 has four strategies, but you need to be careful how you interpret these strategies in Gambit's output.

The leader-follower newsvendor problem

This Maple file [.pdf] solves both the simultaneous game and the Stackelberg game. (The Stackelberg solution is in the second half of the document.)

Extensive form vs. the strategic form

Here we look at the Zeus/Athena competitive game which is constant sum. (Every constant sum game can be converted to a zero-sum game. Since the payoffs are utilities, just subtract the constant sum quantity from one of the players payoffs, and you get a zero-sum game.)

Zeus and Athena will have to decide on low (L) or high (H) production capacity.

Simultaneous decisions

Chance decides the market size (S or L), and neither Z or A know what will happen until after they decide. Here is the Gambit solution [.jpeg].

Zeus moves first

As before, Chance decides the market size (S or L) but neither know what it is. Now, Zeus moves first and chooses either L or H. Athena observes this, but does not know what the market size is. Gambit solves this problem [.jpeg].