Public Goods Game

The Public Goods Game ( also Public - goods game ) is part of game theory and is the subject of Experimental Economics. As a model, it is used in the provision of public goods to be analyzed. This analysis is important because public goods in contrast to private can multiply and simultaneously be consumed, but no one can be excluded from consumption. Because no one can be excluded, it is rational to carry any costs of providing ( free rider problem ).

• 2.1 explanations
• 2.2 criticism

• 3.1 Repeated Games
• 3.2 Transparent / Open Games
• 3.3 reward and / or punishment
• 3.4 Asymmetric costs and / or benefits
• 3.5 framing

Game play

In the standard version of the game, the participants decide in secret how much of their initial endowment they want in a public pot ( public good ) invest. This pot is easily multiplied at the end and then distributed to all players equally. It will also get their share of players who have done nothing for the provision of the good. The winnings of a player results from the public and payment of withheld initial endowment. This gain was after the match, usually at a known exchange rate in real currency, rarely also in eg Coursework exchanged.

Multiplication factor

In the standard version of the multiplication factor for the public good between 1 and the number of players is. A factor equal to one means that each player gets back exactly a contribution if all make the same contribution. In this case, the player would be indifferent between the public good and the simple restraint of their total assets. A factor equal to the number of players means that the payout ratio and multiplication ratio are equal. A higher factor would thus result in each case to a win for all depositors.

Regardless of group size and contribution reflux, the group as a whole stands there best when all participants their entire private facilities contribute to the public good. This result would be the Pareto optimum: Pays each player from the beginning of its entire initial endowment, which group receives the maximum possible payout by the game leader.

Expected and actual results

The standard economic theory said out with the Nash equilibrium that no player makes group contributions if the game is finite. This dominant strategy any player regardless of how each of the other player behaves. Since it is rational not to cooperate even in the last round of finitely repeated games, it is because of backward induction and rational, something to contribute in any round. This free-rider problem leads to the tragedy of the commons: Although everyone in the group have the public good and would like to use, no one pays ( voluntarily ) for it. As a result, there is an undersupply of the public good compared to the state of the Pareto optimum. The Nash equilibrium also predicts that larger groups and / or lower returns led ( by a lower multiplication of the public good ) to less cooperation because the incentives for the provision of the public good always continue to fall.

In fact, the deficiency associated with the Nash equilibrium rarely in experiments not before up; the participants tend to invest at least a small part of their private facilities. The extent of participation of individuals thereby varies greatly. However, the social optimum (complete cooperation of all participants ) is rarely if ever achieved, are more frequent in non- repeated games. Contrary to popular opinion and economic theory, a larger group or a higher multiplication factor does not necessarily lead to more cooperation and higher individual contributions to the public good. The sociological interpretation of these findings emphasizes the group cohesion and cultural norms to explain the results of pro-social public goods games.

Explanations

The interest of science focused after the first public - goods games on why the game players of the economic rationality differ or whether rather the theory which has shortcomings. Practically oriented studies explored in addition to induce group cooperation with an appropriate incentive system. From this evidence for many solutions to problems in society can derive (see variations).

Obowohl discussion of results is not complete, some explanations crystallized early out:

• Among other things, put the game theoretic Nash equilibrium complete information on returns from the public good and the level of initial endowment of all players ahead. However, variations with more and less information to show no difference in behavior.
• As tends to be a higher cooperation than was observed in repeated games in individual games, the learning hypothesis was formed: At least some players have to first learn how they rationally behaving in optimization problems, and build their strategy. A delayed adjustment of the dominant strategy was also observed in other games. The learning hypothesis could be verified either in public goods games even in other games.
• Players do not act according to the rational logic of backward induction repeated playing. (?)
• Game theory based on the fact that players maximize their utility solely on monetary returns. Some economists turned therefore one that the theory is too narrow, and players maximize their utility by other concomitants: So players would (hot glow engl.) also benefit from the " warm glow " of giving, or incorporate fairness calculi in their decisions leave.

Criticism

However, it was also criticized how simple, abstract, short and finite laboratory experiments are useful in small groups, to give predictions for human behavior in complex everyday situations. In reality, we can not exclude that meet market players again and then possibly the consequences of their actions from previous actions - get to feel - such as non- co-operation.

Variations

Repeated Games

Repeated games means that the same game is repeated in the same composition or modified for a certain number of rounds. A typical result is a decreasing share of contributions to the public good in comparison to the one-off game. Players tend to contribute even less than in the first round when they see that others give less. In the next round, the effect is repeated, but now from a lower base. However, never contributed anything of all, because a hard core remains of ' donors '.

One explanation for this is the inequality aversion (English inequity aversion ). In repeated games, players have the opportunity to build reputation, as observed by others. On the other hand, players can learn certain properties of the entire group know and adapt their behavior continuously. More precisely adjust their expectations about future payments of the other group members, because nobody wants alone contribute to the public good. Watching players that other players get a larger refund for a smaller contribution, this contradicts their sense of justice.

Transparent / Open Games

If the amount of contributions or even the identity of the player is made transparent, individual contributions are regularly higher. This result is independent of the specific experimental setup, so whether players are known from the beginning, are mentioned only in pairs, or at the end of the experiment, etc.

This fact make charity events on a regular basis as its own, where the donors are called regularly and be honored in part according to their contribution goal.

Reward and / or punishment

The use of rewards or punishment is the subject of numerous studies. As a rule, the players punish each other after the public good was provided. Here, a player is randomly selected, the punished at his own expense a group member. Rewards function analogously. Alternatively, rewards or punishments are carried out automatically by the game leader by a known rule. A key result is that rewards and punishments are used as different means: Rewards are not the same as non- punishment, while a penalty does not apply as the absent reward.

Penalties be carried out even in cost and lead in most experiments to higher contributions or to higher cooperation. The effect of rewards alone, however, is weaker. This should not be confused with higher payouts group: As punishment cost, means increased cooperation is not necessarily higher payouts from the public pot. At least in the first round, so the fines can lead to ( marginally ) lower group payouts.

Therefore, many studies emphasize the combination of punishments and rewards. It leads both to increased cooperation as well as to higher posts. This applies to both repeated games in alternating groups, as well as for identical groups.

Asymmetric costs and / or benefits

Asymmetry with respect to the private cost of provision or payment from the public pot have a direct impact on player behavior. Although they are more sensitive to monetary incentives and behave rationally according to the economic theory. However, even here more is contributed to the public good than in the Nash equilibrium.

Framing

Different representation of the same structure or the same game ( engl. ' framing ') which deviates from the original game behavior. A variant of the ' framings ' is the association with real problems in which public goods must be provided. This may be the climate change negotiations, the construction of a road or gift to a private party. This allows the players information to draw conclusions about the preferences of other players, probability estimates of their actions and perception.

The effect of association (attribute - framing) is different and depends on the personal experience of the players. This is especially true for single games, where players predict the behavior of other players just because of their own experiences in the real world ( can ). Even players from the same culture can have the same attribute, different terms and react with both higher and lower contributions.

In addition, can be represented as a choice between gains or losses choice between basically every game. Because of the framing effect players react completely differently: If public - good games are presented as a loss instead of a profit ( ie, a contribution to a private good reduces the payoffs of other players ) contributions are significantly smaller.