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Chapter 29 Game Theory: Sequential Games & Backward Induction Part…
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)
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
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
