Game types
A game is cooperative whether the players are a person engaged or qualified in a profession. to form binding commitments externally enforced e.g. through contract law. A game is non-cooperative if players cannot form alliances or if any agreements need to be self-enforcing e.g. through credible threats.
Cooperative games are often analyzed through the model of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take, and the resulting collective payoffs. this is the opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. The focus on individual payoff can statement in a phenomenon invited as Tragedy of the Commons, where resources are used to a collectively inefficient level. The lack of formal negotiation leads to the deterioration of public goods through over-use and under provision that stems from private incentives.
Cooperative game theory gives a high-level approach as it describes only the structure, strategies, and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will impact the distribution of payoffs within regarded and listed separately. coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory the converse does non hold submitted that sufficient assumptions are made to encompass all the possible strategies usable to players due to the opportunity of external enforcement of cooperation. While using a single theory may be desirable, in numerous instances insufficient information is usable to accurately utility example the formal procedures available during the strategic bargaining process, or the resulting model would be too complex to ad a practical tool in the real world. In such(a) cases, cooperative game theory provides a simplified approach that allows analysis of the game at large without having to make any assumption about bargaining powers.
A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. That is, if the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. Many of the usually studied 2×2 games are symmetric. The requirements representations of ] scholars would considerasymmetric games as examples of these games as well. However, the almost common payoffs for each of these games are symmetric.
The most ordinarily studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the ultimatum game and similarly the dictator game have different strategies for each player. It is possible, however, for a game to have identical strategies for both players, yet be asymmetric. For example, the game pictured in this section's graphic is asymmetric despite having identical strategy sets for both players.
Zero-sum games more generally, constant-sum games are games in which choices by players can neither add nor decrease the available resources. In zero-sum games, the or situation. benefit goes to all players in a game, for every combination of strategies, always adds to zero more informally, a player benefits only at the live expense of others. Poker exemplifies a zero-sum game ignoring the possibility of the house's cut, because one wins precisely the amount one's opponents lose. Other zero-sum games put matching pennies and nearly classical board games including Go and chess.
Many games studied by game theorists including the famed prisoner's dilemma are non-zero-sum games, because the outcome has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another.
Constant-sum games correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential gains from trade. It is possible to transform any constant-sum game into a possibly asymmetric zero-sum game by adding a dummy player often called "the board" whose losses compensate the players' net winnings.
Simultaneous games are games where both players come on simultaneously, or instead the later players are unaware of the earlier players' actions creating them effectively simultaneous. Sequential games or dynamic games are games where later players have some knowledge about earlier actions. This need not be perfect information about every action of earlier players; it might be very little knowledge. For instance, a player may know that an earlier player did not perform one particular action, while they do not know which of the other available actions the first player actually performed.
The difference between simultaneous and sequential games is captured in the different representations discussed above. Often, normal form is used to make up simultaneous games, while extensive form is used to represent sequential ones. The transformation of extensive to normal form is one way, meaning that corporation extensive form games correspond to the same normal form. Consequently, notions of equilibrium for simultaneous games are insufficient for reasoning about sequential games; see subgame perfection.
In short, the differences between sequential and simultaneous games are as follows:
The Cournot competition model involves players choosing quantity of a homogenous product to produce independently and simultaneously, where marginal cost can be different for each firm and the firm's payoff is profit. The production costs are public information and the firm aims to find their profit-maximising quantity based on what they believe the other firm will produce and behave like monopolies. In this game firms want to produce at the monopoly quantity but there is a high incentive to deviate and produce more, which decreases the market-clearing price. For example, firms may be tempted to deviate from the monopoly quantity if there is a low monopoly quantity and high price, with the intention of increasing production to maximise profit. However this option does not afford the highest payoff, as a firm's ability to maximise profits depends on its market share and the elasticity of the market demand. The Cournot equilibrium is reached when each firm operates on their reaction function with no incentive to deviate, as they have the best response based on the other firms output. Within the game, firmsthe Nash equilibrium when the Cournot equilibrium is achieved.
The Bertrand competition, assumes homogenous products and a fixed marginal cost and playersthe prices. The equilibrium of price competition is where the price is equal to marginal costs, assuming complete information about the competitors' costs. Therefore, the firms have an incentive to devate from the equilibrium because a homogenous product with a lower price will gain all of the market share, so-called as a cost advantage.