Extensive-Form Games

Processes are recommended in strategic forms such that any player may select an action (or a combination of actions) once and for all. This specification might not be appropriate in games with a sequential character, because players may find it useful to revisit their plans while the events are occurring.

Extensive types specifically define a strategic relationship by defining who is going where and with what details, and thus have a richer atmosphere where interested topics like engagement, frequent interaction, creating credibility, etc. may be discussed.

But we shall see that a certain game may be interpreted both in a strategic and in a detailed way, and the decision depends not on a formula, but on the questions we ask about that case. In perfectly informed games, movements will take place in a series, and each player will watch each event before that player needs to respond.

Perfect information

In concurrent and simultaneous play, the perfection of information is an essential principle in game theory. In evaluating alternative sanction schemes in bribery settlements, it reflects a central principle.

Perfect information relates to the fact that any player has the same information at the end of the game. That is, any player knows or may see the gestures of another player. Chess, where any player sees the other player's plays on the floor, is a good example.

When choices are to be taken concurrently, incomplete information emerges and players need to balance all potential results before making a decision. A clear example is a card game in which every player's card is withheld from all the other players.

Game theory: Extensive form

In this first Game Theory Learning Path, we hear about the key methods and criteria to allow a detailed review of sports. We see how information content influences the manner in which games are solved and how they are represented.

The comprehensive form of game theory is a way to define a game with a game tree. It is essentially a diagram, which indicates that choices are taken at various times (each node corresponds). At the end of each branch, the payoffs are seen. Because the comprehensive type reflects decisions at various stages, concurrent games are typically represented, whereas the strategic type defines simultaneous games. Since sequential games suggest that each player makes choices at multiple points, information is ideal, since each player can see the previous player’s decision, full laws, and payoffs of each player are common information.

Backward Induction

The optimum plan of the player who makes the final step in the game is defined at any point of the backwards induction. The next moving player then determines the optimum action, taking the final player actions as indicated. This process continues until the best action is determined for each point in time. Indeed, the Nash balance of each initial sub-game is calculated.

The results from reverse induction, however, often fail to predict true human play. Experimental research showed, as theoretical game theory predicts, that "rational" behavior is rarely shown in real life. Irrational players can end up getting higher payoffs than reverse induction is anticipated, as seen in the Centipede game.

In the centipede game, two players alternately have the opportunity to take a bigger share or to pass the pot on to the other player. Payoffs are arranged to encourage you to earn marginally less as the pot goes over to the competitor and the competitor takes the pot in the next round, than if the pot has been taken in this round. The game closes as soon as the player takes a stash, the greater part is taken by the player and the smaller part is taken by the other player.

Sub game perfect equilibrium

In game theory, a perfect balance (or a perfect balance of Nash subgames) is a refinement of the balance of Nash in dynamic games. A strategy profile is a fine match if it reflects a Nash match of each of the initial game's subgames. Informally, this implied the player would have a Nash balance in the smaller game if they played a smaller game that was just a component of that bigger game. Each long, endless game with a full reminder has a great balance in the subgame.

A typical approach in the event of an endless game is to decide the perfect combination of sub-games. Second, the final moves of the game are performed and the last mover acts to increase its effectiveness are decided in all circumstances. One then assumes that the last actor can carry out these actions and sees the second to last actions, choosing again those which optimize the usefulness of this actor.

Introduction to imperfect-information games

We consider games that combine ideas from prior to and after half to simultaneous and sequential components. In a game, we describe a list of nodes that a player does not know about using a set of information. This allows us to define games of imperfect data and also allows us to define subgames officially.

We then expand the definition of a strategy to imperfect games and use it for the normal form of such games. One important idea here is that information is important, not time per se. We prove that not all of Nash's balances are similarly plausible: some of these games are not compliant with the retroactive induction; others include non-Nash in some subgames. We introduce a more refined notion of balance, which is called sub-game perfection, to deal with this.

Mixed versus behavioral strategies

A behavioral strategy for a player in a comprehensive game is a map that can be used to collect his information sets and to provide information with a distribution of probability over the actions on the data. In a competitive game, a mixed strategy occurs where the player doesn't select a certain action, but selects its action according to the chance distribution.

There are cases in which there is no pure strategy balance. Therefore, we must find the possibility of the player randomizing between his acts. This chance depends on the player 's estimated reward for any action.