Stackelberg Game

In a Stackelberg game, one player (the “leader”) moves first, and all other players (the “followers”) move after him.

Difference with a Sequential Game?

1. Leader and follower: In a Stackelberg game, one agent is designated as the leader and the other agents are followers. The leader makes its decision first and commits to it, while the followers observe the leader’s decision and make their decisions afterwards. In a sequential game, on the other hand, the agents take turns making decisions, but there is no designated leader or follower.
2. Information: In a Stackelberg game, the followers have complete information about the leader’s decision before they make their own decisions. In a sequential game, the agents may or may not have complete information about the decisions of the previous agents.
3. Game structure: Stackelberg games are typically modeled as sequential games, where one agent moves first and the other agent moves second. Sequential games can have different structures, e.g. a repeated game where each player acts in each round, or a one-shot game where each player acts once.
4. Solution concept: The solution concept for Stackelberg games is the Stackelberg equilibrium, in which the leader chooses the strategy that maximizes its utility given the followers’ best response. The solution concept for sequential games is the subgame perfect equilibrium, in which each player chooses the strategy that maximizes its utility given the strategies of the other players in every subgame.
5. Applications: Stackelberg games are commonly used to model situations where one agent is a leader in a market and the other agents are followers. Examples include price leadership in oligopoly markets, and leader-follower interactions in robotics and control systems. Sequential games are used in a variety of other settings, such as repeated games, evolutionary game theory, and security games.