Sequential Games, Backward Induction and Credible Threats

1-6 Sequential Games I - Game Setting

Sequential games where firms make decisions one after another are represented as game trees.

Game trees are built up as follows:

1. First decision starts the game
2. Every decision point represents a node
3. From there, the decisions of subsequent players branch out accordingly

A revised working definition of strategy: strategy is a player's plan of actions in a game, given any possible circumstances.

Sequential games can be applied to the problem of price setting.

1-7 Sequential Games II - Backward Induction

Backward Induction is:

• Simplification of a sequential game
• Eliminate actions at the final node and work one's way backwards
• Eliminate actions that would not maximize an individual's profit at that point
• A rational player always tries to maximize their own profits
• You can rely on a rational rival never choosing these actions

Backward induction allows us to find the best strategy for the first mover.

1-8 Sequential Games III - Credible Threats

Motivating question: How to distinguish between a credible threat and cheap talk?

Apply backward induction to determine if a threat is credible.
A public commitment (e.g. Lufthansa committing to a penalty) can also change the payoffs in such a way as to make a threat credible.

Commitment strategies is one way to change your payoffs to make your threat credible.