This is for the obvious reason that it relies on intuitions about inferences that people should find sensible. Begin, again, with the last subgame, that descending from node 7. This is a bit puzzling, since if Player I reaches her second information set 7 in the extensive-form game, she would hardly wish to play L there; she earns a higher payoff by playing R at node 7.
In doing this, we will need to introduce, define and illustrate the basic elements and techniques of game theory. What is important in the present context is that these details, as they are in fact pursued in the contemporary debates, all involve sophisticated interpretation of the issues using the resources of modern game theory.
But, then, no … if she expects that you will expect that she will least expect this, then she will most expect it. She obtains her higher payoff, 2, by playing D. What has happened here intuitively is that Player I realizes that if he plays C refuse to confess at node 1, then Player II will be able to maximize her utility by suckering him and playing D.
Such a device is called a utility function. To see this, backward induct again. Figure 10 If you are confused by this, remember that a strategy must tell a player what to do at every information set where that player has an action. Like most scientists, non-psychological game theorists are suspicious of the force and basis of philosophical assumptions as guides to empirical and mathematical modeling.
The reverse situation, in which Player II confesses and Player I refuses, appears in the lower-left cell. A player who knowingly chooses a strictly dominated strategy directly violates clause iii of the definition of economic agency as given in Section 2.
Any commander who could be so confident as to willfully destroy his own option to be prudent if the battle went badly for him must have good reasons for such extreme optimism.
However, if we now complicate the situation by adding a non-parametric element, it becomes more challenging. For reasons to be discussed later, limitations in their mathematical framework initially made the theory applicable only under special and limited conditions.
For example, it makes sense to display the river-crossing game from Section 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 has decided to do. Note that no rows or columns are strictly dominated here.
We represent such games using the device of information sets. Trees are used to represent sequential games, because they show the order in which actions are taken by the players.
After my house is finished, I can make your labour free to me simply by reneging on my promise. The players, and analysts, can predict this outcome using a mechanical procedure, known as iterated elimination of strictly dominated strategies.
As previously noted, games of perfect information are the logically simplest sorts of games. It was said above that the distinction between sequential-move and simultaneous-move games is not identical to the distinction between perfect-information and imperfect-information games.
In fact, neither of us actually needs to be immoral to get this chain of mutual reasoning going; we need only think that there is some possibility that the other might try to cheat on bargains. Following the general practice in economics, game theorists refer to the solutions of games as equilibria.Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question.Download