Public Goods Games

The public goods game is a measure of experiment used in experimental economics. The game is played by a number of subjects who chose how many of the tokens that they have that is private they would wish to withhold. They additionally chose how many tokens they would wish to place in the public pot. The tokens that are placed in the pot are then multiplied by a factor that is greater than one. The public benefit that is realized is finally divided amongst the players equally. The tokens that the players did not wish to contribute are kept back by each individual. The group’s total outcome is usually multiplied. It becomes even higher, if the players contributed all the tokens that they had. This is termed as maximization. Consequently, the Nash equilibrium is no contributions by all players. If the theory were put into practice in a real case point, the contributions by any rational agent would be zero. This is regardless of how other agents contribute. In fact, the equilibrium by Nash is usually never seen in any actual experiment. This is because players tend to add a token into the pot. The actual contribution by each agent is usually from 0% to 100%. The players who do not contribute to the game are termed as defectors or rather free riders. The players who hand in their chips are termed as cooperators. There are five variants to the game. The first one is the iterated public goods games. It is termed as the repeat play; the game involves same group of participants in the same game who contest in a series of rounds. The usual results in the game are the reduction in contribution as the game proceeds. When the players who are termed as trusted see that there is no contribution from certain players, they tend to hold back their contributions in the next round.

If the action continues, the amount of cash is usually reduced in the cash pot. However, the token that is usually put into the pot never reaches  zero. This is because the players have to contribute some amount to the pot. The reason some players hold back their contributions to the game, is that they view other players getting higher dividends from putting a small amount of money in the pot. This happens even though the identities of the free riders are usually unknown. Those who contribute something nothing in some round do not continue contributing even if they see the other players doing so. The second variant is open public, goods games. In this type of variant, the amount that is contributed to the pot is usually high since it is not hidden from the players. This is sometimes made possible by let us say there are two contributors in the game. The contributions by each agent are made public. The third variant is the public goods with a punishment. This is the subject in this paper. The option given here is that the defaulters will have to be punished. This type of variant is usually played more as compared to the others. The punishment is usually put into place to even the contributions and the earned points. This leads to higher contributions, and in result, it leads to more contributions. The other variant is games with rewards, the agents who contribute are rewarded than those who are defecting. Some studies have shown it is somehow more profitable than the punishment variant. The paper discusses coalition and communication in public good games because of the punishment.    

Literature Review

Ostrom (1992) was the first to introduce the punishment of individuals as a way of ensuring collective bargain in the public goods games. The experimental design that they carried out, helped in making punishment quite productive and rational. The experimental hypothesis that they carried out, made punishing a positive rather than a negative aspect of creating responsibility. The strategy that they used, led to profit maximization. During the experiments, they kept the subjects in constant public goods games and did not reveal the total  number of rounds that they would play (Univie, 2009, p.  2). Since the players knew that they would interact with other players for some time, they, therefore, knew that they knew they could punish the free riders. With so doing, they knew that they would face greater cooperation in the future. The cooperation would be coupled with greater pay offs in the subsequent rounds. The rational players in the game would punish the offenders with an aim of increasing the financial pull in the next round. Therefore, to the free riders would contribute more to avoid punishment in the subsequent rounds. The cooperators would also incur costs while punishing the non-cooperators in the game. They used the basis that when individuals know the depth that the punishment and the number of rounds that they are playing. They would be willing to take risks. It can be clear in the last round, as the players will know that there are no future rounds, and the rational players would not punish the offenders seeing no future, but the offenders would commit crime seeing no future repercussions (Vecon Lab, 2010, p. 1). When looked in a background mode, this is evident that the players will avoid punishment at all costs. Nonetheless, the observation that is made is that individuals may fail to punish even when they knew the possible consequences. The first experimenters of the irrational behavior were first experimented by Fehr and Gachter. They found out that even when the rounds are obvious, and the players in the game are anonymous, the agents would still administer costly punishments on the free riders. Consequently, this mode of punishment reduces the number of free riders. Without the punishment, the mean contributions reduced with every round. This trend went on to nearly zero. On the other hand, the mean contribution when the players were aware of the punishment, they maintained the mean above zero. In another pioneer experiment, Decker noticed that even though punishing is usually for the public good, it is not usually administered. The punishment cost to some instances is usually equal to the cost of non-contribution by free riders (Diverse thoughts, 2009, p. 12).

The research was mainly carried out to decipher the effectiveness of punishment and cost of distribution whenever it is carried out. The groups that put a collective power, and shared equally the cost of punishment, survived in their undertaking. However, the group that administered heavy punishment was ready and easy to administer justice. Justice in this point is termed as the positive correlation between the payments and the realizations. However, this hypothesis is usually not carried out to the fullest due to the high costs of administering punishments. In theory, agents in a public good game will avoid punishment because they perceive no gains from punishing. Usually this case leads to an overall rational participation. On the other hand, players do not administer punishment fully for monetary gains. Several researches have been carried out to determine the motives in those punishments (Surhone, 2011, p. 13). In a research presented forth by Nikiforakis, he found out that the free rides do not necessarily find reason to punish other offenders. However, a high number of punishers administer the punishment for monetary gains. The free rides are involved in the cheating themselves, and they find no reason of punishing an offender since they will gain future favors if the hold in subsequent rounds. The punishment might also be held back when participants see that the punishment will generally affect the group. In a subsequent research, Decker found out that sometimes punishment is usually administered through emotions and not the perceived gains in it. Researchers of this theory carry out several public goods games using collective or individual punishment regimes. The overall report is that the punishment is usually very high at the end of the games. This is because there are monetary gains perceived in those rounds and there are no subsequent rounds. The free riders at this moment have no future prospects and the way that they perform greatly affects their future decisions although they have no chance of changing. This feeling of revenge creates a motivation of punishment with no financial gains perceived. The punishment behavior in most instances is usually not directly connected to price, and, therefore, there is a negative relation. This is usually consistent with the inequality aversion model. The severity of the punishment leads to cooperation, and formation of sub groups under the whole group to protect financial gains, and to act as the protectors of each other, just in case there is a future punishment for one of the members (Hasson, 2009, p. 46).         


What have others/done/found?

When a public good game is played with punishment, it creates numerous strategies in the players. This leads to the formation of a coalition is some players and communication is enabled. The cooperation is usually formed between people who are usually strangers. This aspect is usually studied in sciences and economics. In a research carried out by Hannelore Brandt, she tried to decipher the relation of public game and the cooperation diverse people form (Brandt, 2003, p. 1). The study used three individuals to study out the possibilities of cooperation and interaction.  The author writes that there is a possibility that territoriality promotes cooperative behavior. This is the case of prisoners. In addition, the punishment that is formed usually brings out a sense of responsibility. The researcher presumes that, when there is an action of three people who are socially oppressed, then they have to devise ways and means of coming out with good results. If there is a will to punish, there is always formation of cooperation. This reduces the results of exploitation. Thus, the individuals in the game become more and more cooperative. In the research, the author reviews the book of public goods by Binmore and ultimatum game. She concludes that there is always an altruistic, cooperative mode. It is created after players in a game decide to form cooperation due to either fear or lack of option. The author writes that there is a possibility that people can be made to collaborate through either rewards or punishment. The case example is when she takes three players and decides to play a game of possibilities using various variations. She takes three sample players and does not introduce the punishment, but when the punishment is introduced, the results are as follows: after there is an introduction of punishment, there is the possibility that the players will start to be keener in each subsequent round (Offerman, 1997, p. 697). This is because the punishment is usually very costly since the fee of punishment must be paid and the actual fines. Therefore, the author concludes that punishment is usually an unselfish behavior.  In addition, it increases the contributions by the players. It in return leads to cooperation amongst them. In the experiment, she concludes that human beings form a pronounced nature of punishing offenders. The readiness to punish usually increases with the rate that the offenders commit crime. It also remains after there is a stop by the agents to commit a crime. The defectors are the ones who determine the rate of punishment. For a case of simplification, the researcher decides that there, it is best to employ the use of binary options.  The players decide after every round, to punish or not to punish the perpetrators. To punish these players, the agent who punishes involves a cost labeled g on the offender. For people who have done the mistake, the cost reflects as b for each one of them. This in return leads to four basic strategies for three groups (Kosfeld, 2006, p. 127).

Another research carried by Gordwin Craft, to find the results of punishment and conditions in the public goods games. He found out that when there is no anonymity the results tend to e different. The researcher said that, in realistic scenarios, the effects of the game are controlled by the environment. This can lead them to having information about the potential future partners in the game (Repec, 2009, p. 5 ). Therefore, there will be conniving punishment trend in the newfound group. Therefore, a cooperator who is then matched in the same group with people that he or she knows pretty well is not punishers may be tempted to take an advantage. Consequently, he or she may be tempted to defect this is of course without the fear of repercussions. Therefore, not all the players who carry some sort of reputation may be the best partners. He in return observed that the probability m of a cooperator knowing that the partners are lax at punishing (Discover Magazine, 2009, p. 4). Therefore, he consequently falls to the temptation of joining the defaulters. Therefore, a single cooperator is paired with two non-punishers. The new strategy labeled also as G1 is greatly affected by reputations. It is then consequential when a defector is paired up with strict punishers he or she will be intimated by their presence. Therefore, he or she will be forced to cooperate. The defectors were labeled as n. The effects are sometimes not that hard. Therefore, the interaction by two groups labeled as G1 and G4 with clear knowledge of reputation helps to understand the mode of operation of the each player (Shaklee, 1977, p. 15). The cooperators, case in point G1 when they are coupled with the less severe punishers G4 they are likely to defect. It is evident that reputation of an agent is the key factor in determining the player. The figure below summarizes the behavior:

The relationship and reputation is a key factor in determining the bistability. This is usually since the introduction of a punishment is always a deterring factor in the way an agent performs. The range r is usually responsible for the possibility of cooperation. Then the threshold is lowered to rc <1.25. As the incomplete strategy of G2 is vanishes and the configuration of r in the vicinity rc <1.25 time evolution sensitivity will depend on the initial configuration (Matros, 2003, p. 75). That means that the appearance in high numbers of technical reputable agents who are punishers will determine the performance of G1 and G3. This is because the players will refrain from cooperating for the matching. The minor changes in rc in return leads to higher changes in r. therefore, the researcher proved that the outcome of knowing the underlying of another player results to changes in the game plan. The ideology can be summarized in the figure below.

In yet another research that was carried out in Harvard University, it was found that when there are three players in a game cooperators succeeded when they form groups and this reduces the way they interrelate with the defectors.  This can be equated with the prisoners relations each other. The agreement forms seclusions. However, the relations between the groups are usually conditional and require a high number of multiplication factors. Therefore in an arranged meeting, a case example that has a threshold of rc <2.07. The rc that is the number of cooperators and defectors will coexist in a diverse but equal setting (Zack, 2010, p. 845).  The average size of the cooperators will then increase with r until they will eventually eliminate the defectors. Introducing a punishment is fundamental as it changes the game in a certain way or the other. The system then becomes bistable and the existence between the cooperators and the defectors becomes intolerable. At the same time the opportunities of punishment render the cooperation between the agents hard but renders the opportunity and reduces the threshold rc <1.35. In any system that is finite, the existence of key players may require an adjustment to know whether they will cooperate or defect. This strategy performs very well.  The r for the group that has a low or mild punishment spreads to nearly 85% (Kung, 2010, p. 580). This in return increases the costly task of defeating the social behavior and leaves it to a few individuals. Something interesting is that when the fines represented by b are increased, the fines represented by rc is usually lowered until it comes to a low r <1. Consequently, the net benefit when there is cooperation is (r21). This becomes negative. Therefore, it is possible that a punishment can leave a person in a more cooperative state. However, it will be worse off than a social state (ALGER, 2001, p. 296). This is eventually another dilemma. Therefore, combining reputation and punishment may clearly help in the public goods games but may prove fatal to some extent. Therefore, reputation may help since the players will alter the way that they actually behave to suit the characters of the people that the people that they are interacting with. Consequently, reputation alters the dynamics in a leaner way. The system remains bistable and therefore, the threshold is only slightly lowered down. It is figuratively written as rc <1.25. The figure below shows depicts the situation.

In yet another research, the researchers tried to link the feature of altruism to public good games. This was proven through an assortment of matching in the games. The researcher starts by identifying the way animals are always dependent on each other. Therefore, communication is an essential part of the daily lives of human beings. Therefore, the researcher embarks on a mission to find out the reason and ways of making a sustainable relationship between people in times of need. In the paper, the researcher proposes new theoretical ideas that can explain the changes in the public goods games after the introduction of rules. Humans are animals with imaginative thinking and strong memory. Therefore, the cooperation that they show in many instances is due to the situation that they are in (Cadigan, 2011, p. 525). cooperation is usually sustained via reciprocity. The author is consistent with the findings of other researchers that human beings tend to punish the people that they feel do not cooperate in any endeavors that they take, case in point the public goods game. Consequently, large numbers of people tend to form a cooperative stand if they are faced with risk or material interest. Such a suggestion shows that human beings sometimes form a preference due to the selfish ideas that they have. The theory is also supported by the recent researches in the field of neuroscience (Clemens, 2011, p. 412). Therefore, the big question in this case is if the material nature of human beings makes them cooperative, does it mean that the altruistic nature of humans survives. The researcher proposes the theory of endogenous creation of altruistic features. The individuals in the study are paired o play a game of public goods. The researcher notes that the game requires a lot of cooperation in the form unity. The analysis is divided into two steps. The first one is the examination of the material benefit that a person gains from cooperation. The second one is assuming that the success of the player is dependent on the way that he or she plays in the game. The researcher studies two individuals who take part in the game of public goods and are unselfish. The individuals in the research are altruistic meaning that they really care about the material gains. This nature therefore, increases the projected benefit by the player in the contribution pool (Cartwright, 2010, p. 700). Therefore, the contributions by the agents increase with each round so that they can gain big in the game. This decreases the contribution that the other player who does not wish to release the token. The higher the contributions made by one player the lower the contribution by the other due to the altruistic nature. The analysis that is employed uses the methodology put forth by Alger and Weibull. The individuals who had an upper hand in the game are seen as those who hold back their tokens. In conclusion, the author found out that the strategy employed y each player in a game is usually essential in bringing out the collective sense by the players.

In another research carried out by Devlin Foltz, the researcher uses the public goods game to see the reactions of the participants if they are punished. The paper also examines what the reactions of the players when they are punished. The paper further researches the effects of free riding even after the punishment against certain players proves to hold a loss. The paper also proves the fact that sometimes not punishing is profitable. The paper also establishes why the punishment is usually severe if one of the team members is allowed to punish all the players instead of all of them. It also implies that the individuals who punish the free riders for no apparent reason are always non-rational in the game. The paper also establishes why the individual responsibility is usually important in the game of public good. John Nash was an influential economist and his study about the effects of disagreement between individuals is usually a big source of cooperation. This was through the game theory. The concepts are widely used by modern day economists to study the effects of holding back in determining the market plan. In the part about behavioral economics and free-ridership, the researcher tackles the question of the basis of how to well to avail goods that are of social interest but are much costly to individuals. The goods that are discussed are public goods that are not easily substituted (Shinohara, 2009, p.. 896). Therefore, these goods are easily prone to free ridership. In other words, the researcher concludes that the people who consume these goods are always susceptible to free-ridership since the gains that are perceived from it are numerous. Consequently, a free rider is able to capitalize on this moment for they can wait for other people to contribute and hold back their tokens. The types of public goods that are susceptible to this are national defense and highway systems. Through experimental research, the researcher was able to know the and clearly understand the behavior of public goods. The institutions that are regarded as public goods are those ones that that encourage social optimal goals. In the contribution to these institutions, there are the risks of coming across free riders who halt the development plans. These institutions therefore introduce ways and means of punishing the offenders. The researcher used experiments that literally mimicked the public good setting to depict the way that they affect a system. Fehr and Gachter found out that when there is the risk of punishment, the contributors tend to play along well in those games to avoid the scenarios. They therefore, raise their contributions to the common pull. This in the end increases the fund in the societal welfare. Though the punishment is effective, the institutions that are meant to punish may also be involved in the same of harboring free riders (Anderson, 2010, p. 169).

Punishing the free riders is beneficial to the society as a whole. However, it requires a lot of common pull to maintain it. This makes the running of the punishment institution a public goods game indirectly. The participants who free ride may use the same opportunity to ride freely on the punishment of other people. The study generally studied the effect of an assigned and diffused duty in relation to punishment in a public goods game. The aim was to prove that punishment might act positively to the public good and the extent in which it is beneficial (Volk, 2011, p. 811). Specifically, the researcher wanted to find out whether the opportunity to punish is usually severe if the responsibility rest with one punisher or several. The first part of the paper reviews the earlier researches and the implications of punishment on public good games. The next phase reviews the outcomes of other experiments and the design used. The final part of the research reviews the results and implications. The research further offers the advice on how further research can be conducted. In a research carried out by Anderson and Putterman in the year 2006, they found out the motive of punishing is usually ambiguous. In previous researches before this, it was found out that sometimes punishment is usually carried out because the offended parties wish to avenge the free rider or they just wish to establish some form of organization or even to ward off any would be offenders. The study carried out by the two researchers is however incomplete without the involvement of financial gains. If the view of financial gains is held back, the researchers found out that the participants were satisfied with the results after a punishment. In public good settings, many individuals are usually more concerned with the maximization of profit when they are playing a game of chance (Alonso-Meijide, 2010, p. 533). The utility of every cooperator is usually achieved through the financial and emotional satisfaction. The cost of punishment also forces the young people to play a key role in the game since they cannot bear the cost of punishment. In the experiment that the two researchers carried out, the subjects were arranged in groups of and given some token to act as an overall endowment. They could either keep these tokens or contribute them to the public game. Contributed tokens would benefit all of the participants but they had little benefit on the contributor. This is because the tokens benefit every person equally regardless of the amount put in.

The number of rounds was made public to ensure that there were no planned punishments on some players. There were two treatments in the groups with each group a different way of punishing the offenders. In the group that had unrestricted treatment, the members were allowed to punish an offender collectively. In the group, that only one person punishes, only a single person was chosen to conduct the punishment for every offender. This was a strategy in seeing which of the two groups had the most severe punishment. The selection of a single punisher was done randomly in different rounds so that the players would not be biased. Considering the number of rounds there was no possibility, that one person could punish more than twice (Alger I. , 2010, p. 799). Twelve participants were divided into three different groups. The treatment order was switched in the groups to avoid the sequencing that might be experienced. Each session in the game was conducted in five rounds and in two occasions, they lasted for thirty minutes. The contributions of the game were displayed in the personal computer screens of each participant. The researcher read loud the amount of contribution by each player after every round. The research team automatically assigns an identification number to the participants. This is useful as they log in to experiment their game. After the experiment, the results were as follows:

What is interesting in this area?

This field of economics is usually interesting due to the facts that are offered in the research. Human beings are generally group animals. This is because they tend to form groups when they are faced situations. The public goods game is an interesting subject in the field of research since it is used to determine the behavior of human beings when they are faced with a situation that needs overall contributions. The examples above show how people tend to react to issues when they are faced with punishment. The groups of players are given a chance to play their roles and to give out results if they wish to control a public good. The people who participate in the games are given tokens to contribute to a common pull and they are tested on whether they can hold back or play. To make sure that those who hold back face repercussions (Wang, 2010, p. 100). The rules and punishment forces the players to form a coalition. The coalition is used to help the free riders who are the player who do not contribute regularly into the pull and many players do not utilize this tactic. The public goods game is a game that requires tactic and being precise. The other interesting part of this game is the fact that the players are forced to know each other’s behaviors in order to survive in the game. Many researchers have studied this phenomenon to come out with an explanation as to why human beings behave in the way that they do in the game situation. The game is in testing as it captures the essence of classical economy and the reactions that the player have is usually outstanding.   

What behavior have they observed?

The behavior that is being observed in this research is usually the relations of human beings in relations. The major being observed is usually to see the characteristic of human beings in the event that one of them is found to be an impediment to the success of the pull (Kempf, 2010, p.769 ). The observed behavior is beneficial in giving the right direction in the research to know how to come out with ideas to further the research. This is a basic element in creating a way through which a person can create a basic idea in public goods games are played. Public goods games uses biological and economic data to bring out the basic thinking of the players.        

When communication is allowed and how it is facilitated

Communication is usually accepted when there is the introduction of punishment (Anya Skatova, 2011, p. 240). It is accepted to facilitate the formation of strategy so that the players can be given a chance to strategies on their next moves.  The communication that is allowed is facilitated through a mediator who monitors the way the participants carry out the information that they have. This is essential in creating a raptor that will ensure there is no malice in between the players.

What is different to having no communication or no punishment?

When there is no communication or punishment, the players are usually not progressive. This creates a way of free riders joining the game and taking unfair advantage over other players.

What else could be interesting here?

The other interesting future of this hypothesis is that it creates a clear image in the knowledge of how to survive in the competition.

How can the experiments and their results be tied into the existing literature?

The experiments and results can be tied to the existing literature by building a common standing point. The research has all concluded that the way people relate is usually fostered by the restrictions that they are given by the environment.  


In conclusion, the public goods game is a fantastic way of creating a pull of fund by several individuals for the public good. The development of collaboration amongst unconnected persons in human being and animal societies remains a demanding subject transversely in all disciplines. In this framework, two forms have gained the largest part of concentration: the prisoner’s predicament for pair wise connections and public goods game for a faction of connections. The two games share numerous features as established by the close up association of their foundations. In excellent-mixed populations with unsystematic run into connecting individuals, cooperators are destined and disappear quickly. However, in spatially prearranged populations with incomplete restricted connections, cooperators are capable of continued existence and co-exist with defectors in an established symmetry. Spatial additional rooms enable cooperators to structure collections and by this, means lessen mistreatment by defectors. The geometry (four-sided figure in opposition to honeycomb), i.e. the association, has well-defined and strong effects on the providence of cooperators. For a case in point, in pair wise communications, cooperators prosper more straightforwardly on honeycomb lattices but for assemblage communications including all neighbors, it becomes progressively more complicated to encourage teamwork in superior groups. This is essential in knowing the concept of unity in public goods games.

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