Игры играть бесплатно собери деньги
This process is called backward induction игры играть бесплатно собери деньги the reasoning works backwards from eventual outcomes to present choice problems). There will be much more to be said about backward induction and its properties in a later section (when we come to discuss equilibrium and equilibrium selection). For now, it has been described just so we can use it to introduce one of the two types of игры играть бесплатно собери деньги objects used to represent games: game trees.
A game tree is an example of what mathematicians call a directed graph. That is, it is a set of connected nodes in which the overall graph has a direction. We can draw trees from the top of the page to the bottom, or from left to right. In the first case, nodes at the top of the page are interpreted as coming earlier in the sequence of actions. In the case of a tree drawn from left to right, leftward nodes are prior in the sequence to rightward ones.
Игры играть бесплатно собери деньги unlabelled tree has a structure of the following sort: The point of representing games using trees can best be grasped by игры играть бесплатно собери деньги the use of them in supporting backward-induction reasoning.
Just imagine the player (or analyst) beginning at the end of the tree, where outcomes are displayed, and then working backwards from these, looking for sets of strategies that describe paths leading to them. We will present some examples of this interactive path selection, and detailed techniques for reasoning through these examples, after we have described a situation we can use a tree to model.
Trees are used to represent sequential games, because they show the order in which actions are taken by the players. However, games are sometimes represented on matrices rather than trees. This is the second type of mathematical object used to represent games. For example, it makes sense to display the river-crossing game from Section 1 on a matrix, работа в играх за деньги in that game both the fugitive and the hunter have just one move each, and each chooses their move in ignorance of what the other has decided to do.
Thus, for example, the upper left-hand corner above shows that when the fugitive crosses at the игры играть бесплатно собери деньги bridge and the hunter is waiting there, the fugitive gets a payoff of игры играть бесплатно собери деньги and the hunter gets a payoff of 1. Whenever the hunter waits at the bridge chosen by the игры играть бесплатно собери деньги, the fugitive is shot.
These outcomes all deliver the payoff vector (0, 1). You can find them descending diagonally across игры играть бесплатно собери деньги matrix above from the upper left-hand corner. Whenever the fugitive chooses the safe bridge but the hunter waits at another, the fugitive gets safely across, yielding the payoff vector (1, 0).
These two outcomes are shown in the second two cells of the top row. All of the other cells are marked, for now, with question marks. Игры играть бесплатно собери деньги problem here is that if the fugitive crosses at either the rocky bridge or the cobra bridge, he introduces parametric factors into the game. In these cases, he takes on some risk of getting killed, игра с выводом денег минералс so producing the payoff vector (0, 1), that is independent of anything the hunter does.
In general, a strategic-form game could represent any one of several extensive-form games, so a strategic-form game is best thought of as being a set of extensive-form games.
Where order of play is relevant, the extensive form must be specified or your conclusions will be unreliable. The distinctions described above are difficult to fully grasp if all one has to go on are abstract descriptions.
Suppose that the police have arrested two people whom they know have committed an игры играть бесплатно собери деньги robbery together. Unfortunately, they lack enough admissible evidence to get a jury to convict. They do, however, have enough evidence to send each prisoner away for two years for theft of the getaway car. We can represent игра деньги машина problem faced by both of them on a single matrix that captures the way in which their separate choices interact; this is the strategic form of their game: Each cell of the matrix gives the payoffs to both players for each combination of actions.
So, if both players confess then they each get a payoff of 2 (5 years in prison each). This игры играть бесплатно собери деньги in the upper-left cell. If neither of them confess, they each get a payoff of 3 (2 years in prison each). This appears as the lower-right cell.]