Strategic dominance

The dominant strategy in game theory models is a strategy that provides the highest utility among all possible strategies, regardless of what the other actors (players, agents) do. The concept of dominant strategy appears to both classical decision theory and game theory, allowing it to recognize behaviors of actors in a play. The dominant strategy is in simultaneous as well as sequential games application.

• 3.3.1 Application Example

Demarcation

The dominant strategy is in contrast to the dominant strategy one of the worst strategies dar. Again, regardless of what the other players do, is the dominant strategy of an ever better, the so-called dominant strategy dominates.

A player's dominant strategy is for this is of no use and will also again no strict best response to any strategy of the opponent. If you compare the dominant strategy of the dominant strategy compared, it is clear that the dominant strategy is always consistently better than any other strategy. In contrast, the dominant strategy is always consistently worse than all other strategies. Removal of the dominated strategy (s) shall be carried out accordingly.

Definition of Terms

The concept of dominant strategy identifies a series of actions, which is better than all other options, regardless of what the other players do. What a strategy dominates another strategy if the dominant never worse, but sometimes better than the dominated strategy. A rational agent should choose a strategy when an alternative strategy exists, which leads to a higher benefit over all possible strategies. If there is a dominant strategy, then this standard applies. However, not always all players a dominant strategy, not even for one of the actors. The dominance is the exception and not the rule.

Methodology of the dominant strategy

Application

In contrast to the sequential play a simultaneous game through lack of communication of the exogenous factors is characterized within a game. It can be played only once. However, the steps of the opponent are normally known in a sequential game. This is ensured through communication, although still a degree of information asymmetry may exist. Accordingly, if there is a dominant strategy for any given decision of her opponent, the dominant strategy would be selected for sequential trains always. However, could be as the inverted case occur, causing the opponent is only the second train of the series. Here, the opponent can calmly await the decision and adapt to the situation. Here it is advisable to choose a person other than the dominant strategy. One speaks in this case of self- binding on game-theoretical basis. For sequential trains the use of collaboration solutions can also be considered by the use of dominant strategies in game theory.

Streng / strictly dominant strategy

Player A strategy is a strictly dominant strategy if they for him has a greater benefit for all possible strategy combinations of the other players, more than all his other strategies. Since this property can only be true in each case on a strategy, there are at most a strictly dominant strategy for each player. A player with a strictly dominant strategy does not need to cooperate in order to achieve the greatest benefit for themselves.

The condition for a strictly dominant strategy can be described by a mathematical formula. Be a player's possible strategies and the possible strategy combinations of his teammates. Of player A strategy is called strictly dominant when

Applies to all other strategies of player, and all strategy combinations of his teammates. This means that players left the strategy combination rated higher than the right.

Is there a utility function in a game and a player has a strictly dominant strategy, then this strategy is the one with the highest payout for him.

Example of use

The scenario in Figure 1 illustrates the two competing sporting goods manufacturer Nike and Adidas that their sales could change more use of advertising, depending on the decision strategy by possibly. The goal of both is here in the maximization of sales.

For Nike, it is always better to invest more advertising to increase sales: Invests Adidas in more advertising, so Nike still achieved an increased turnover of 4000 €. If Adidas unchanged however uses a lot of advertising, so Nike made ​​an even higher turnover of 5000 €. Nike, however, could also opt for unchanged lot of advertising, but would therefore accept as in the use of more advertising a lower turnover.

No matter what Adidas is doing: For Nike, it is always better to invest more advertising. The strategy more advertising is strictly best response to every conceivable strategy by Adidas for Nike. The Alternative same amount of advertising from the alternative more advertising is dominated. The alternative is more advertising for Nike therefore a strictly dominant strategy.

Weak dominant strategy

Player A strategy is a weakly dominant strategy, if they for him has the greatest benefit for all possible strategy combinations of his teammates. In general, a player can have multiple dominant strategies that have all the same benefits for him. A player with a weakly dominant strategy does not need to cooperate in order to achieve the greatest benefit for themselves.

The condition for a weakly dominant strategy can be described by a mathematical formula. A strategy of a player is called weakly dominant when

For all other strategies of player, and all strategy combinations of other players and

Applies to at least one of these strategy combination. This means that players left the strategy combination is at least as highly rated as the right.

Is there a utility function in a game and a player weakly dominant strategies, these strategies have the highest payout for him.

Example of use

The scenario illustrated in Figure 2 is based on two accused who have actually committed a crime. The imprisonment may be different depending on the decision strategy. This is a simultaneous game in which the defendants are not entitled to be informed of the decision of each other in experience. The goal of both is here in the minimization of their own imprisonment.

It can be noted that for Kuno, there is no dominant strategy: not confess dignity Uwe, so it would be best for Kuno to confess. Selects confess Uwe, then both strategies are equally good for Kuno. Kuno is indifferent between and confess not confess. It can be stated, therefore, that for Kuno to confess the strategy never worse than the strategy not to confess; in the event that Uwe does not confess, even better. After identification of the weakly dominated strategy can not confess therefore be assumed that Kuno will confess.

Solution concepts in dominant strategies

The dominant strategy in game theory provides a solution concept dar. in a game, each player has a strictly dominant strategy, so it is rational for each player to play this strategy configuration as a non- cooperative solution. However, this does not guarantee that the resulting payoffs are also collectively rational. Due to the composition of the rational chosen strategy combination, the game is in a dominant strategies equilibrium. Each dominant equilibrium strategies at the same time makes just a Nash equilibrium visible.

Another solution of a game in game theory with dominant strategies, the elimination of dominated strategies dar. Although the dominated strategy is not a benefit for each player, so it is nevertheless clear from this a way to reduce the complexity of a game. Thus, the number of possible game results can limit the number of possible game results using the elimination of strictly dominated strategy (s). The choice of the utility-maximizing strategy is facilitated.