Iterated public goods games "
Repeat-play" public goods games involve the same group of subjects playing the basic game over a series of rounds. The typical result is a declining proportion of public contribution, from the simple game (the "One-shot" public goods game). When
trusting contributors see that not everyone is giving up as much as they do they tend to reduce the amount they share in the next round. If this is again repeated the same thing happens but from a lower base, so that the amount contributed to the pot is reduced again. However, the amount contributed to the pool rarely drops to zero when rounds of the game are iterated, because there tends to remain a hard core of "givers". This effect is called the end-game effect. One explanation for the dropping level of contribution is
inequity aversion. During repeated games, players learn their co-players inequality aversion in previous rounds on which future beliefs can be based. If players receive a bigger share for a smaller contribution the sharing members react against the perceived injustice (even though the identity of the "free riders" are unknown, and it's only a game). Those who contribute nothing in one round, rarely contribute something in later rounds, even after discovering that others are.
Open public goods games (transparency) Transparency about past choices and payoffs of group members affects future choices. Studies show individuals in groups can be influenced by the group leaders, whether formal or informal, to conform or defect. Players signal their intentions through transparency which allows "conditional operators" to follow the lead. If players are informed of individual payoffs of each member of the group it can lead to a dynamic of players adopting the strategy of the player who benefited the most (contributed the least) in the group. This can lead a drop in cooperation through subsequent iterations of the game. However, if the amount contributed by each group member is not hidden, the amount contributed tends to be significantly higher. The finding is robust in different experiment designs: Whether in "pairwise iterations" with only two players (the other player's contribution level is always known) or in nominations after the end of the experiment.
Public goods games with punishment and/or reward The option to punish non-contributors and to reward the highest contributions after a round of the public goods game has been the issue of many experiments. Findings strongly suggest that non-rewarding is not seen as a sanction, while rewards don't substitute punishment. Rather they are used completely differently as a means to enforce cooperation and higher payoffs. Punishing is exercised, even at a cost, and in most experiments it leads to greater group cooperation. However, since punishment is costly, it tends to lead to (marginally) lower payoffs, at least initially. In contrast, in the long term, punishment seems to be more efficient, since costs decrease. On the other hand, a 2007 study found that rewards alone could not sustain long-term cooperation. Many studies, therefore, emphasize the combination of (the threat of) punishment and rewards. The combination seems to yield both a higher level of cooperation and payoffs. This holds for iterated games in changing groups
Asymmetric costs and/or benefits Researchers conducted experiments in different scenarios where endowments are symmetric, weak-asymmetric, strong-asymmetric, etc. The result shows that strong-asymmetric groups tend to contribute less to the public. It could be explained intuitively by "The super-rich player tends to contribute an amount that is not significantly different from the average contribution of the poor players". It could be concluded that for strong asymmetric scenario, the poor would gain much less profit with higher
Gini coefficient. There are other researches on the effect of "kings and bosses", especially on whether they would affect the outcome and could be rationalized.
Income variation A public goods games variant suggested as an improvement for researching the free-rider problem is one in which endowment are earned as
income. The standard game (with a fixed initial endowment) allows no work effort variation and cannot capture the
marginal substitutions among three factors: private goods, public goods, and leisure. Researchers have found that in an experiment where an agent's wealth at the end of period t serves as their endowment in t+1, the amounts contributed increase over time even in the absence of punishment strategies.
Framing A different framing of the original neutral experiment setting induces players to act differently because they associate different real-life situations. For example, a public good experiment could be presented as a climate negotiation or as contributions to private parties. The effect of associations (label frame) depends on the experience pool the player made with similar real-life frames. This is especially true for one-shot (not iterated) games where players can only infer others' behaviour and expectations from their life experiences. Therefore, the same frame can induce more and also less contribution, even in similar cultures. Label frames move beliefs i.e. about other player's behaviour, and these beliefs subsequently shape motivation and choice. Also, the same game structure can always be presented as a gain or a loss game. Because of the
framing effect players respond completely differently when it is presented as a gain or a loss. If public good games are presented as a loss, i.e. a player's contribution in a
private engagement diminishes other player's payoff, contributions are significantly lower. ==Multiplication factor==