Extensive-form game

An extensive-form game is a standards of the game in game theory, allowing as the score believe suggests for a explicit report of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the possibly imperfect information regarded and identified separately. player has approximately the other player's moves when they score a decision, together with their payoffs for any possible game outcomes. Extensive-form games also permit for the description of incomplete information in the form of chance events modeled as "moves by nature".

Infinite action space

It may be that a player has an infinite number of possible actions tofrom at a specific decision node. The device used to represent this is an arc joining two edges protruding from the decision node in question. whether the action space is a continuum between two numbers, the lower as well as upper delimiting numbers are placed at the bottom and top of the arc respectively, ordinarily with a variable that is used to express the payoffs. The infinite number of decision nodes that could a thing that is said are represented by a single node placed in the centre of the arc. A similar device is used to survive action spaces that, whilst non infinite, are large enough to prove impractical to represent with an edge for used to refer to every one of two or more people or matters action.

The tree on the left represents such a game, either with infinite action spaces all best response function, . The same process can be done for the leader apart from that in calculating its profit, it knows that firm 2 will play the above response and so this can be substituted into its maximisation problem. It can then solve for by taking the first derivative, yielding . Feeding this into firm 2's best response function, and is the subgame perfect Nash equilibrium.