In game theory, the solution concept is a formal rule to predict how the game will be played. These predictions are called "solutions", and describe which strategies will be adopted by the player and, therefore, the outcome of the game. The most commonly used solution concept is the concept of equilibrium, the most famous of which is the Nash equilibrium.
Many concept solutions, for many games, will result in more than one solution. This puts one solution in doubt, so a game theorist can apply enhancements to narrow the solution. Each consecutive solution concept presented below improves its predecessor by eliminating unreasonable equilibria in richer games.
Video Solution concept
Definisi formal
In the concept of this solution, players are assumed to be rational and so strongly dominated strategies are omitted from sets of strategies that may be eligible to play. The strategy is very strict when there are several other strategies available for players who always have higher results, regardless of strategy chosen by other players. (A completely dominated strategy is also important in the search for game-minimax trees.) For example, in the prisoner's dilemma (one period) (shown below), work closely is dominated by defects for both players because one player is always better off playing disabled , regardless of what his opponent does.
Maps Solution concept
Nash equilibrium
Nash equilibrium is a strategy profile (strategy profile determines strategy for each player, for example in the game the above convict dilemma ( working , defects ) specifies that prisoner 1 plays work same and player 2 plays defects ) in which each strategy is the best response to any other strategy being played. A player's strategy is the best response to another player's strategy if no other strategy can be played that will result in higher payouts under any circumstances where other player strategies are played.
Induced retreat
There are some games that have some Nash equilibria, some of which are unrealistic. In the case of a dynamic game, Nash's unrealistic equilibria may be eliminated by applying reverse induction, which assumes that the game of the future will be rational. Therefore it eliminates unreliable threats because the threat is unreasonable to do if a player is called to do so.
For example, consider a dynamic game where players are the ruling companies in industry and prospective entrants in the industry. As it stands, the incumbent has a monopoly over the industry and does not want to lose some of its market share to participants. If the participant chooses not to go in, the payout to the incumbent is high (keep the monopoly) and the participant does not lose or profit (the result is zero). If a participant enters, the incumbent may resist or accommodate the participants. It will struggle with lowering its price, running the participant out of business (and paying out - the negative outcome) and damaging its own profits. If it accommodates the participant will lose some of its sales, but high prices will be retained and will receive a greater profit than by lowering the price (but lower than monopoly profits).
If a participant enters, the best response from the incumbent is to accommodate. If the incumbent accommodates, the best response from the participants is to enter (and make a profit). Therefore, the strategy profile in which the petahana candidate accommodates if the participant enters and the participant enters if the punggawa accommodates is Nash's equilibrium. However, if the incumbent will play against, the best response from the participant is not to enter. If the participant does not go in, it does not matter what the holder of the position (because no other company is doing it - note that if the participant does not go in, fight and accommodate the same result for both players, the incumbent will not lower the price if the participant is not logged in). Therefore the fight can be regarded as the best response of the incumbent if the participant does not enter. Therefore a strategy profile in which incumbent fights if the participant does not go in and the participant does not enter if the incumbent fights are Nash's equilibrium. Because the game is dynamic, any claims by the adventure will be a tremendous threat because once the decision reaches the point at which it can decide to fight (ie, the participant has entered), it does not make sense to do so. Hence Nash's equilibrium can be eliminated by reverse induction.
See also:
- Theory of monetary policy
- Stackelberg Competition
The sub-subtitle equilibrium Nash is perfect
A generalized reverse induction is the perfection of subgame. The backward induction assumes that all future games will be rational. In the perfect subgame balance, playing in each subgame is rational (especially Nash's equilibrium). Backward induction can only be used in ending (up to) games of a certain duration and can not be applied to games with incomplete information. In this case, subgame perfection can be used. The omitted Nash equilibrium described above is an imperfect subgame because it is not the Nash equilibrium of the subgame that begins at the vertex achieved after the participant enters.
Perfect Bayesian Equilibrium
Sometimes the subgrame of perfection does not impose considerable restrictions on unreasonable results. For example, since sub-subtitles can not truncate sets of information, the game of imperfect information may have only one sub-game - itself - and hence the subgame perfection can not be used to remove Nash equilibrium. A perfect Bayesian balance (PBE) is the player's strategy specification and beliefs about which knot in the collection of information that the game has gained. Confidence about decision nodes is the probability that certain players think that nodes are or will be played (on the path of balance ). In particular, the PBE's intuition is that it determines a rational player's strategy given the belief that the player determines and that belief determines consistent with his determined strategy.
In Bayesian games, a strategy determines what players play in each set of information controlled by the player. The requirement that confidence is consistent with strategy is something that is not determined by the perfection of the subgame. Therefore, PBE is a condition of consistency in players' beliefs. Just as in Nash's equilibrium, no player strategy is really dominated, in a PBE, for whatever information is set, there is no player strategy that really dominates from that set of information. That is, for every belief that a player can hold the information set there is no strategy that results in a larger expected payment for that player. Unlike the concept of the above solutions, there is no player strategy that really dominates from any given information even if it is out of the equilibrium path. So in the PBE, players can not threaten to play a strategy that is completely dominated from any information that triggers the balance path.
The Bayesian in the name of the concept of this solution alludes to the fact that players renew their beliefs according to Bayes's theorem. They calculate the probability of remembering what has happened in the game.
Forward induction
Forward induction is so called because only as a backward induction assumes future games to be rational, forward induction assumes the game of the past is rational. Where a player does not know what type the other player is (ie there is imperfect and asymmetric information), the player can form a belief what kind of player it is by observing the player's actions in the past. Therefore the belief formed by the player about what the opponent's chances of being a particular type is based on the past game of a rational opponent. A player can choose to hint at his type through his actions.
Source of the article : Wikipedia
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