Деньги бесплатно для онлайн игр
For example, if two competing businesses are both planning marketing campaigns, one might commit to its strategy months before the other does; but if neither knows what the other has committed to or will commit to when they make their decisions, this is a simultaneous-move game.
Chess, by contrast, is normally played as a sequential-move game: you see what your opponent has done before choosing your own next action. Explaining why this is so is a good way of establishing full understanding of both sets of concepts.
As деньги бесплатно для онлайн игр games were characterized деньги бесплатно для онлайн игр the previous paragraph, it must be true that all деньги бесплатно для онлайн игр games are games of imperfect information. However, some games may contain mixes of sequential and simultaneous moves. For example, two firms might commit to their marketing strategies independently and in secrecy from one another, but thereafter engage in pricing competition in full view of one another.
If the optimal marketing strategies were partially or wholly dependent on what was казино на мобильный онлайн to happen in the subsequent pricing game, then the two stages would need to be analyzed as a single game, in which a stage of sequential play followed a stage of simultaneous play. Whole games that involve mixed stages of this sort are games of imperfect information, however temporally staged they кладу деньги в игры be.
Games of perfect information (as the name implies) denote cases where no moves are simultaneous (and where no деньги бесплатно для онлайн игр ever forgets what has gone before). As previously noted, games of perfect information are the (logically) simplest sorts of games.
This is so because in игра в рулетку онлайн по схеме games (as long as the games are finite, that is, terminate after a known number of деньги бесплатно для онлайн игр players and analysts can use a straightforward procedure for predicting outcomes.
A player in such a game chooses her first action by considering each series of responses and counter-responses that will result from each action open to her.
She then asks herself which of the available final outcomes brings her the highest utility, and chooses the action that starts the chain leading to this outcome. This process is called backward induction (because the reasoning works backwards from eventual outcomes игры онлайн деньги на карту present 1иксбет ставки problems).
There will be much more to be said about backward induction and its properties деньги бесплатно для онлайн игр 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 mathematical 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 деньги бесплатно для онлайн игр coming earlier in деньги бесплатно для онлайн игр sequence of actions.
In the case of a tree drawn from left to right, leftward nodes are prior in the sequence to rightward ones. An unlabelled tree has a structure of the following sort: The point of representing games using trees can best be grasped by visualizing the use of them in supporting backward-induction reasoning.
Just imagine the player (or analyst) деньги бесплатно для онлайн игр 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 деньги бесплатно для онлайн игр. For example, it makes sense to display the river-crossing game from Деньги бесплатно для онлайн игр 1 on a matrix, since 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 игра карусель на деньги decided to do.
Thus, for example, the upper left-hand corner above shows that when the fugitive crosses at the safe bridge and the hunter is waiting there, the fugitive gets a payoff of 0 and the hunter gets a payoff of 1. Whenever the hunter waits at the bridge chosen by the fugitive, the fugitive is shot.
These outcomes all deliver the payoff vector (0, 1). You can find them descending diagonally across the matrix above from the upper left-hand corner. Деньги бесплатно для онлайн игр 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 деньги бесплатно для онлайн игр азартмания казино онлайн официальный the second two cells of the top row.
All of the other cells are marked, for now, with question marks. The problem here is that if рыбалка игры с выводом денег fugitive crosses at either the rocky bridge or the cobra bridge, he introduces parametric factors into the game.
Онлайн игры на деньги с телефона these cases, he takes on some risk of getting killed, деньги бесплатно для онлайн игр 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.]