Chapter 29
Game Theory: Sequential Games & Backward Induction
Part III

In games with sequential moves and complete information, a player moves first, and other players see what he has done before choosing their strategies

Entry Deterrence

The game is in extensive form (also known as a game tree)

Decision nodes are point at which players can act

Branches specify actions

Payoffs are listed by order of moves (first mover's payoff listed first)

Screen Shot 2018-01-23 at 5.49.05 pm

Backward induction

Reasoning back from the end of the game

We are still assuming complete information, so player know each others' payoffs and will be able to anticipate how others will react to their strategy choice

Subgame perfect Nash equilibrium

Equilibrium outcome of the entry deterrence game: entrant enters, monopolist doesn't fight

This equilibrium is not only a Nash equilibrium, but it is a subgame perfect Nash equilibrium (SPNE)

In simple terms: at every decision node, each player chooses the action that yields highest payoff given that he is at that decision node

More about entry deterrence

In the entry deterrence game, "fight" is not a credible threat by the monopolist

Even if he announced that he would do it before the game began, the entrant wouldn't believe him: entrant knows that at that decision node, it gives the monopolist higher payoff not to fight


Knowing this, the entrant enters

if the monopolist could somehow commit to fighting before the game began, then "fight" would become a credible threat and the entrant wouldn't enter


Committing requires making the decision to fight automatic if the entrant enters - if the monopolist has the option not to fight, then he won't fight

The sequential stag hunt

In the last stage, player B would
• Play hare if A played hare (3 > 0)
• Play stag if A played stag (4 > 3)

Anticipating what B would do, A would play stag in the beginning

Screen Shot 2018-01-23 at 6.01.54 pm

In equilibrium, both play stag


Both playing hare was a possible outcome of the simultaneous game, but not the sequential game


Coordination on the Pareto efficient equilibrium is made possible in this game since one player can see move made by the other player