Perfect Game Theory of Equilibrium - Essay Example

This may be bad for player 1 so he decides to play W, but also would be bad for player 2. Now, given the opportunity to move, player 2 will prefer to play 1 since it is the remaining Nash equilibrium. One has to bear in mind the tree diagram of probability when handling game perfect equilibrium theory. In game 1, the correct sub-game starts with player2’s decision to join; the condition that 2’s choices are Nash equilibrium strategy lowers or reduces the prerequisite that 2 takes the action that yields in the highest induce, thus, player 2 must play 1; these deductions are only possible because there exists a finite extensive form of the game, therefore exists a sub-game perfect Nash equilibrium. In addition, the Nash sub-perfect game equilibrium can be joined to the tree diagram of probabilities (McCain, 55). A different problem with sub-game excellence is that the concept is not in an alternative unnecessary changing of the game tree. For instance, a tree diagram has the same form as that of the normal form in game 2 but has sub-game completeness (McCain, 56).

When manipulating for equilibrium in zero, some games will not take into account the challenger playoff; this is because the opponents are implicitly known, and they are ever diametric. On the other hand, in non-zero games, one has to put in mind the opponents' playoff. These will always yield different outcomes. A relevant example is that of the innovation of Blu-ray by Toshiba and Sony companies, if both companies go for the same innovation, the results may be more convenient for only Toshiba, but if the two companies don’t involve in the same kind of coordination (if only has a greater probability or chance of winning in the innovation). The game in comparison is Blu-ray for Sony to that of Toshiba, now, if the two companies happen to pick an option, then Sony will have a big payoff compared to Toshiba. Consequently, if Toshiba Company reconsiders the option of HD DVD will leave the Sony Company with a play of o. this will be considered as that playoff 1 for the selection of Blu-ray. However, (HD DVD, HD DVD) is another strategic equilibrium. The game theories will term these as pure strategy equilibrium in the non-zero game of Nash equilibrium (McCain, 78).

The coordination between the companies will bear some common problems in the scope of business and innovations. Although it is better to understand that solutions reached as a result of Nash equilibrium; solutions obtained are of the beneficiary to the companies; Sony and Toshiba. Therefore, it is important to understand the mixed strategy of Nash equilibrium; this case will put the guiding principle based on any of the players or companies this means that the mixed equilibrium must yield some payoff outcomes (McCain 123). For instance, if we take the mixed strategy for Sony company to be y for choosing Blu-ray and (1-y) for Toshiba company for choosing HD DVD, we can use Toshiba’s payoff to manipulate the values for HD DVD and Blu-ray.

In this example, Sony’s strategy is to have an unsystematic choice of Blu-ray (4/5) and the same time (1/5) to that HD DVD. Now, there will be a mixed strategy of (x, 1-x) of Toshiba Company against that of Sony.

As illustrated, Toshiba Company will find some convenience to choose Blu-ray (1/5) and leave HD DVD (4/5). The Nash strategy for both Toshiba and Sony is based on 1/5 and 4/5 respectively. Therefore, one can determine the average of the strategy's equilibriums. Despite this, one must have related the two players in terms of their probabilities, for example, relating the strategy for Sony.

Unfortunately, if Sony Company discovers this mixed equilibrium strategy, it will put the company in a worse condition than it had gone for HD DVD. Thurs, this game is considered symmetric due to the fractions or probabilities. Finally, this theory put more emphasis on the merits of making or picking but is based on chances of failing or winning due to the differences in chances or probabilities; this theory can, however, be put into a real-life situation to improve the management of an organization.