Public goods game
The public goods game is a standard of experimental economics. In the basic game, subjects secretly choose how many of their private tokens to put into a public pot. The payoff of each player is her "private consumption" plus her benefit from the "public good". The game is used to study degree of altruism and cooperation between individuals.
Introduction
Public goods games are fundamental in experimental economics. The nature of the experiment is incentives and the problem of free riding. Public goods games investigate the incentives of individuals who free-ride off individuals who are contributing to the common pool.A public goods game investigates behavioural economics and the actions of the players in the game. In this process, it seeks to use behavioural economics to understand the decisions of its players. It extends further to free-riding, which has far-reaching applications to environmental, managerial and social economics. Public goods games are valuable in understanding the role of incentives in an individual's behaviours. They arise from behavioural economics and have broad applications to societal challenges. Examples of applications include environmental policy, legal and justice issues and workplace and organisational structures.
Description of the game and result
Consider a group of individuals consists of n identical individuals. Each individual is endowed with M tokens and must decide how many tokens to allocate to a public "pot".The payoff of each individual i is
where is the contribution of individual i to the public good, and therefore, is her private consumption and is her benefit from the public good.
Optimum
To find the optimal contribution we shall maximize the payoff of the representative individual:The derivative with respect to g is. Note that if then the optimal contribution is M since the first derivative is positive.
Nash equilibrium
If then given other individuals' contributions individual i maximizes her payoff by contributing 0. If she contributes 1 token her private consumption decreases by 1 and her benefit from public consumption increases by. Therefore, at the Nash equilibrium each individual contributes 0.The public good game is easily translated to a laboratory experiment. If individuals are purely egoistic then we will end up in no contributions. If individuals are pure altruistic then we will end up in individuals contributing their entire endowments. An experimental result between the two extremes, shows the degree of altruism.
In fact, the Nash equilibrium is rarely seen in experiments; people do tend to add something into the pot. The actual levels of contribution found varies widely. The average contribution typically depends on the multiplication factor. Capraro has proposed a new solution concept for social dilemmas, based on the idea that players forecast if it is worth to act cooperatively and then they act cooperatively in a rate depending on the forecast. His model indeed predicts increasing level of cooperation as the multiplication factor increases.
Depending on the experimental design, those who contribute below average or nothing are called "defectors" or "free riders", as opposed to the contributors or above-average contributors who are called "cooperators".
We can take a deeper look at the public goods game. In fact, intergroup competition has a large effect on the public goods game. In Jonathan et al.'s experiment, they compared linear public goods games without comparison, with comparison but without incentives to win, or with incentives to win.
Throughout the experiment, they found that in one-shot games, competition increases cooperation with/out incentives, while in finitely repeated games, cooperation is sustained with incentives. Cooperation decreases in response to wins.
On a cognitive level, intergroup comparisons can enhance the salience of the group objective – a common goal – and also how closely one identifies with the group. In turn, the more a rational individual "reasons for the team" i.e., behave as a component of a profile maximizing the group's objective, the more cooperation is expected. Linking monetary incentives to group success further enhances the salience of the group objective, and thus intra-group cooperation.
Variants
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. 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. 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 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 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 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 punishment and rewards. The combination seems to yield both a higher level of cooperation and payoffs. This holds for iterated games in changing groups as well as in identical groups.
Not limited to rewards, the combination of punishment mechanisms and other strategies can also show an effect on directing to cooperation in a promising way.
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 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 depends on the experience pool the player made with similar real-life frames. This is especially true for one-shot 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.