Public goods game

Last updated
In this diagram of a public goods game, three players choose to contribute their full $20 while the fourth player chooses to contribute $0. The $60 is multiplied by a factor of 1.2 and the resulting $72 is distributed equally among the four players. Public Goods Game.png
In this diagram of a public goods game, three players choose to contribute their full $20 while the fourth player chooses to contribute $0. The $60 is multiplied by a factor of 1.2 and the resulting $72 is distributed equally among the four players.

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 tokens in this pot are multiplied by a factor (greater than one and less than the number of players, N) and this "public good" payoff is evenly divided among players. Each subject also keeps the tokens they do not contribute.

Contents

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.

Results

The group's total payoff is maximized when everyone contributes all of their tokens to the public pool. However, the Nash equilibrium in this game is simply zero contributions by all; if the experiment were a purely analytical exercise in game theory it would resolve to zero contributions because any rational agent does best contributing zero, regardless of whatever anyone else does. This only holds if the multiplication factor is less than the number of players, otherwise, the Nash equilibrium is for all players to contribute all of their tokens to the public pool. [1]

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 (anywhere from 0% to 100% of initial endowment can be chipped in). [2] The average contribution typically depends on the multiplication factor. [3] 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. [4]

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". [1]

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, [5] they compared linear public goods games without comparison (PG), with comparison but without incentives to win (XPG), or with incentives to win (CPG).

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 (increases) in response to wins (losses).

On a cognitive level, intergroup comparisons can enhance (diminish) the salience of the group (individual) 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 (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. [6] [7] 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".

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). [8] 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. [9] 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. [10] However, if the amount contributed by each group member is not hidden, the amount contributed tends to be significantly higher. [11] 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. [12] However, since punishment is costly, it tends to lead to (marginally) lower payoffs, at least initially. [13] In contrast, in the long term, punishment seems to be more efficient, since costs decrease. [14] [15] On the other hand, a 2007 study found that rewards alone could not sustain long-term cooperation. [16] 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 [12] [16] as well as in identical groups. [13]

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. [17]

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. [18]

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. [19]

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. [20]

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. [21]

Multiplication factor

For contribution to be privately "irrational" the tokens in the pot must be multiplied by an amount smaller than the number of players and greater than 1. Other than this, the level of multiplication has little bearing on strategy, but higher factors produce higher proportions of contribution.

With a large group (40) and a very low multiplication factor (1.03), almost no one contributes anything after a few iterations of the game (a few still do). However, with the same size group and a 1.3 multiplication factor the average level of initial endowment contributed to the pot is around 50%. [22]

Implications

The name of the game comes from economists' definition of a "public good". One type of public good is a costly, "non-excludable" project that everyone can benefit from, regardless of how much they contribute to create it (because no one can be excluded from using it—like street lighting). Part of the economic theory of public goods is that they would be under-provided (at a rate lower than the "social optimum") because individuals had no private motive to contribute (the free rider problem). The "public goods game" is designed to test this belief and connected theories of social behaviour.

Inequality in the public goods game

Previous studies on public goods games have explored the effect inequality in endowment has on the contributions made by individuals. The effects of inequality cause some individuals to shirk and free-ride on the other players of the game. This has far-reaching consequences for the equality of wealth in the game. [23] The evidence provided from studies is that often contributions are lower when there is inequality in endowment.

Through another lens, inequality influences the contributions that individuals are making to the game. A study demonstrated that the inequality in endowment and contributions creates an asymmetry of punishment in the game, which introduced an asymmetry in power for players. This has further applications to modern-day workplace arrangements and notably, the issue of shirking in group projects.

Shirking

The influence of the free-riding in the public goods game and the influence this has on cooperation. The free riding issue in the Public Goods game.png
The influence of the free-riding in the public goods game and the influence this has on cooperation.

Shirking in the public goods game may arise through an asymmetry in power created by the punishment in the game. An additional influence in this is the role of inequality in wealth in the public goods game. In this, an individual may shirk and use their higher wealth to punish the group members with lower wealth. [24] Their goal from this is to increase their own wealth and gains from their decisions. Shirking is evident in many workplace arrangements and is studied in the field of managerial economics.

Game theory

The empirical fact that subjects in most societies contribute anything in the simple public goods game is a challenge for game theory to explain via a motive of total self-interest, although it can do better with the "punishment" variant or the "iterated" variant; because some of the motivation to contribute is now purely "rational" if players assume that others may act irrationally and punish them for non-contribution.

Applications

Applications to organisations

The public goods game explores the role of an incentive in decisions and the actions of players. An application of this is incentives and how workers respond to different projects. These incentives may extend to institutional incentives, including bonuses and financial rewards. [25] An application of this is workforce incentives for team projects. The public goods game is relevant to this situation as it analyses the contribution employees are willing to make to team projects when there is an incentive to contribute. Resultant of this incentive, the public goods game may create punishments for individuals who do not contribute effectively.

Applications to sociology

The sociological interpretation of these results emphasizes group cohesion and cultural norms to explain the "prosocial" outcomes of public goods games.

Additional contributing factors in the public goods game

Rational choice theory

Previous studies have demonstrated the role of behavioural economics—particularly personality traits—and their influence on players' behaviour. However, minimal studies are investigating the role of rationality in player's decision making. Applying rational choice theory to public goods games offers benefits in understanding the contributions players are willing to make and the trends that arise across players and their behaviour. A study that explored this found that rationality has a statistically significant effect on the public goods game. Furthermore, the study found that rational individuals are more likely to contribute fewer resources to public goods. [26]

Pareto optimality in the public goods games

As there is a Nash equilibrium established in the linear public goods games, there are opportunities to create a Pareto optimal allocation. Michael Pickhardt began research into applications of the linear public goods games and their relationship to Pareto optimal allocations. His findings evidenced that smaller groups in the public goods games are more likely to have higher optimal ratios over the total ratios. [27] This finding demonstrates the applicability of Pareto optimality in understanding the provision of public goods in the public goods game. The conclusions drawn from these findings show the impacts teams have on workplace projects and their ability to meet the overall requirements of their task.

Incentives in the public goods game

Incentives are fundamental in the public goods game as they provide an opportunity to understand the decisions and actions of the players. Examples of incentives may include financial, economic, and incentives or negative responses such as punishment. The type of incentive offered varies across organisations. An example includes donations made to support a corporate social responsibility initiative of a company. [28]

The incentives in the public goods game also offer benefits in understanding the decisions behind an individual choosing to cooperate. A study exploring the role of social incentives discussed that donations made to charities increase the cooperation between players when in one-shot public goods games. [29] Through a different lens, negative incentives also influence the behaviour and decisions of the players. As punishment is often an incentive in the public goods games, it impacts the cooperation of others in the public goods games. A study conducted by Ernst Fehr and Simon Gachter found that contributions are often higher with punishment than those made without punishment. [30]

See also

Related Research Articles

Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science. Traditional game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 21st century, game theory applies to a wider range of behavioral relations, and it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers.

In the social sciences, the free-rider problem is a type of market failure that occurs when those who benefit from resources, public goods and common pool resources do not pay for them or under-pay. Examples of such goods are public roads or public libraries or services or other goods of a communal nature. Free riders are a problem for common pool resources because they may overuse it by not paying for the good. Consequently, the common pool resource may be under-produced, overused, or degraded. Additionally, it has been shown that despite evidence that people tend to be cooperative by nature, the presence of free-riders causes cooperation to deteriorate, perpetuating the free-rider problem.

Managerial economics is a branch of economics involving the application of economic methods in the organizational decision-making process. Economics is the study of the production, distribution, and consumption of goods and services. Managerial economics involves the use of economic theories and principles to make decisions regarding the allocation of scarce resources. It guides managers in making decisions relating to the company's customers, competitors, suppliers, and internal operations.

<span class="mw-page-title-main">Loss aversion</span> Overall description of loss aversion theory

Loss aversion is a psychological and economic concept, which refers to how outcomes are interpreted as gains and losses where losses are subject to more sensitivity in people's responses compared to equivalent gains acquired. Kahneman and Tversky (1992) suggested that losses can be twice as powerful psychologically as gains.

Experimental economics is the application of experimental methods to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law.

<span class="mw-page-title-main">Ultimatum game</span> Game in economic experiments

The ultimatum game is a game that has become a popular instrument of economic experiments. An early description is by Nobel laureate John Harsanyi in 1961. One player, the proposer, is endowed with a sum of money. The proposer is tasked with splitting it with another player, the responder. Once the proposer communicates their decision, the responder may accept it or reject it. If the responder accepts, the money is split per the proposal; if the responder rejects, both players receive nothing. Both players know in advance the consequences of the responder accepting or rejecting the offer.

In psychology and behavioral economics, the endowment effect is the finding that people are more likely to retain an object they own than acquire that same object when they do not own it. The endowment theory can be defined as "an application of prospect theory positing that loss aversion associated with ownership explains observed exchange asymmetries."

In game theory, the centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either to take a slightly larger share of an increasing pot, or to pass the pot to the other player. The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes the pot on the next round, one receives slightly less than if one had taken the pot on this round, but after an additional switch the potential payoff will be higher. Therefore, although at each round a player has an incentive to take the pot, it would be better for them to wait. Although the traditional centipede game had a limit of 100 rounds, any game with this structure but a different number of rounds is called a centipede game.

The dictator game is a popular experimental instrument in social psychology and economics, a derivative of the ultimatum game. The term "game" is a misnomer because it captures a decision by a single player: to send money to another or not. Thus, the dictator has the most power and holds the preferred position in this “game.” Although the “dictator” has the most power and presents a take it or leave it offer, the game has mixed results based on different behavioral attributes. The results – where most "dictators" choose to send money – evidence the role of fairness and norms in economic behavior, and undermine the assumption of narrow self-interest when given the opportunity to maximise one's own profits.

Inequity aversion (IA) is the preference for fairness and resistance to incidental inequalities. The social sciences that study inequity aversion include sociology, economics, psychology, anthropology, and ethology. Researches on inequity aversion aim to explain behaviors that are not purely driven by self-interests but fairness considerations.

Backward induction is the process of determining a sequence of optimal choices by employing reasoning backward from the end of a problem or situation to its beginning, choice by choice. It involves examining the last point at which a decision is to be made and identifying the most optimal choice of action at that point. Using this information, one can then determine what to do at the second-to-last point of decision. This process continues backward until the best action for every possible point along the sequence is determined. Backward induction was first utilized in 1875 by Arthur Cayley, who discovered the method while attempting to solve the secretary problem.

Quantal response equilibrium (QRE) is a solution concept in game theory. First introduced by Richard McKelvey and Thomas Palfrey, it provides an equilibrium notion with bounded rationality. QRE is not an equilibrium refinement, and it can give significantly different results from Nash equilibrium. QRE is only defined for games with discrete strategies, although there are continuous-strategy analogues.

A collective action problem or social dilemma is a situation in which all individuals would be better off cooperating but fail to do so because of conflicting interests between individuals that discourage joint action. The collective action problem has been addressed in political philosophy for centuries, but was most clearly established in 1965 in Mancur Olson's The Logic of Collective Action.

In game theory, the traveler's dilemma is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals wins; the lowball player receives the lowball payoff plus a small bonus, and the highball player receives the same lowball payoff, minus a small penalty. Surprisingly, the Nash equilibrium is for both players to aggressively lowball. The traveler's dilemma is notable in that naive play appears to outperform the Nash equilibrium; this apparent paradox also appears in the centipede game and the finitely-iterated prisoner's dilemma.

Strong reciprocity is an area of research in behavioral economics, evolutionary psychology, and evolutionary anthropology on the predisposition to cooperate even when there is no apparent benefit in doing so. This topic is particularly interesting to those studying the evolution of cooperation, as these behaviors seem to be in contradiction with predictions made by many models of cooperation. In response, current work on strong reciprocity is focused on developing evolutionary models which can account for this behavior. Critics of strong reciprocity argue that it is an artifact of lab experiments and does not reflect cooperative behavior in the real world.

Social preferences describe the human tendency to not only care about one's own material payoff, but also the reference group's payoff or/and the intention that leads to the payoff. Social preferences are studied extensively in behavioral and experimental economics and social psychology. Types of social preferences include altruism, fairness, reciprocity, and inequity aversion. The field of economics originally assumed that humans were rational economic actors, and as it became apparent that this was not the case, the field began to change. The research of social preferences in economics started with lab experiments in 1980, where experimental economists found subjects' behavior deviated systematically from self-interest behavior in economic games such as ultimatum game and dictator game. These experimental findings then inspired various new economic models to characterize agent's altruism, fairness and reciprocity concern between 1990 and 2010. More recently, there are growing amounts of field experiments that study the shaping of social preference and its applications throughout society.

Third-party punishment, or altruistic punishment, is punishment of a transgressor which is administered, not by a victim of the transgression, but rather by a third party not directly affected by the transgression. It has been argued that third-party punishments are the essence of social norms, as they are an evolutionarily stable strategy, unlike second-party punishments. It has also been shown that third-party punishments are exhibited in all examined populations, though the magnitude of the punishments varies greatly, and that costly punishment co-varies with altruistic behavior. Differences between within-group and inter-group altruistic punishments have also been observed.

Behavioral game theory seeks to examine how people's strategic decision-making behavior is shaped by social preferences, social utility and other psychological factors. Behavioral game theory analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness, and framing effects. As a research program, the subject is a development of the last three decades.

Urs Fischbacher is a Swiss economist and professor of applied economic research at the University of Konstanz. He is director of the Thurgau Economic Institute, an affiliated institute of the University of Konstanz. He pioneered the field of software tools for experimental economics.

The gift-exchange game, also commonly known as the gift exchange dilemma, is a common economic game introduced by George Akerlof and Janet Yellen to model reciprocacy in labor relations. The gift-exchange game simulates a labor-management relationship execution problem in the principal-agent problem in labor economics. The simplest form of the game involves two players – an employee and an employer. The employer first decides whether they should award a higher salary to the employee. The employee then decides whether to reciprocate with a higher level of effort due to the salary increase or not. Like trust games, gift-exchange games are used to study reciprocity for human subject research in social psychology and economics. If the employer pays extra salary and the employee puts in extra effort, then both players are better off than otherwise. The relationship between an investor and an investee has been investigated as the same type of a game.

References

  1. 1 2 Hauert, C. (January 2005). "Public Goods Games". University of Vienna. groups of rational players will forego the public good and are thus unable to increase their initial endowment. This leads to a deadlock in a state of mutual defection and economic stalemate.
  2. ↑ Janssen, M.; Ahn, T. K. (2003-09-27). "Adaptation vs. Anticipation in Public-Good Games". American Political Science Association. Archived from the original on 2012-03-28. Retrieved 2011-10-03. - (This paper, from researchers at Indiana University and Florida State University summarizes the experimental findings of earlier research before comparing theoretical models against these results.)
  3. ↑ Gunnthorsdottir, A.; Houser, D.; McCabe, K. (2007). "Dispositions, history and contributions in public goods experiments". Journal of Economic Behavior and Organization. 62 (2): 304–315. CiteSeerX   10.1.1.15.3807 . doi:10.1016/j.jebo.2005.03.008.
  4. ↑ Capraro, V (2013). "A Model of Human Cooperation in Social Dilemmas". PLOS ONE. 8 (8): e72427. arXiv: 1307.4228 . Bibcode:2013PLoSO...872427C. doi: 10.1371/journal.pone.0072427 . PMC   3756993 . PMID   24009679.
  5. ↑ Tan, J.H.; Bolle, F. (2007). "Team competition and the public goods game". Economics Letters. 96 (1): 133–139. doi:10.1016/j.econlet.2006.12.031.
  6. ↑ Levitt, Steven D.; List, John A. (2007). "What Do Laboratory Experiments Measuring Social Preferences Reveal About the Real World?" (PDF). The Journal of Economic Perspectives. 21 (7): 153–174. doi:10.1257/jep.21.2.153.
  7. ↑ McGinty, Matthew; Milam, Garrett (March 2012). "Public Goods Contribution by Asymmetric Agents: Experimental Evidence". Social Choice and Welfare. 40 (4): 1159–1177. doi:10.1007/s00355-012-0658-2. S2CID   38375522.
  8. ↑ Fehr, E.; Schmidt, K. M. (1999). "A Theory of Fairness, Competition, and Cooperation" (PDF). Quarterly Journal of Economics. 114 (3): 817–868. doi:10.1162/003355399556151. hdl:10535/6398.
  9. ↑ Fiala, Lenka and Sigrid Suetens. "Transparency and cooperation in repeated dilemma games: a meta study" Experimental economics vol. 20,4 (2017): 755-771.
  10. ↑ Fiala, Lenka, and Sigrid Suetens. "Transparency and Cooperation in Repeated Dilemma Games: a Meta Study." SpringerLink, Springer, 24 Feb. 2017, link.springer.com/article/10.1007/s10683-017-9517-4.
  11. ↑ Rege, Mari; Telle, Kjetil (July 2004). "The impact of social approval and framing on cooperation in public good situations". Journal of Public Economics. 88 (7–8): 1625–1644. doi:10.1016/s0047-2727(03)00021-5.
  12. 1 2 Andreoni, James; Harbaugh, William; Vesterlund, Lise (2003). "The Carrot or the Stick: Rewards, Punishments, and Cooperation". The American Economic Review . 93 (3): 893–902. CiteSeerX   10.1.1.588.378 . doi:10.1257/000282803322157142. punishments improved cooperation by eliminating extremely selfish offers, pushing proposers in the Stick treatment to modest degrees of cooperation.
  13. 1 2 Rand, David G.; Dreber, Anna; Ellingsen, Tore; Fudenberg, Drew; Nowak, Martin A. (2009-09-04). "Positive Interactions Promote Public Cooperation". Science. 325 (5945): 1272–1275. Bibcode:2009Sci...325.1272R. doi:10.1126/science.1177418. PMC   2875121 . PMID   19729661.
  14. ↑ Gächter, Simon; Renner, Elke; Sefton, Martin (2008). "The Long-Run Benefits of Punishment". Science. 322 (5907): 1510. Bibcode:2008Sci...322.1510G. doi:10.1126/science.1164744. PMID   19056978. S2CID   28478770.
  15. ↑ Frey, Ulrich J.; Rusch, Hannes (2012). "An evolutionary perspective on the long-term efficiency of costly punishment". Biology & Philosophy. 27 (6): 811–831. doi:10.1007/s10539-012-9327-1. S2CID   254282497.
  16. 1 2 Sefton, M.; Shupp, R.; Walker, J. M. (2007-04-16). "The Effect of Rewards and Sanctions in Provision of Public Goods" (PDF). Economic Inquiry. 45 (4): 671–690. doi:10.1111/j.1465-7295.2007.00051.x. S2CID   14861767.
  17. ↑ Cui, Pengbi; Wu, Zhi-Xi (2014-11-21). "Selfish punishment with avoiding mechanism can alleviate both first-order and second-order social dilemma". Journal of Theoretical Biology. 361: 111–123. arXiv: 1408.2610 . Bibcode:2014JThBi.361..111C. doi:10.1016/j.jtbi.2014.07.021. ISSN   0022-5193. PMID   25088776. S2CID   2266522.
  18. ↑ Graves, P. E. (September 2010). "A Note on the Design of Experiments Involving Public Goods" (PDF). doi:10.2139/ssrn.1687570. SSRN   1687570.{{cite journal}}: Cite journal requires |journal= (help)
  19. ↑ Gächter, Simon; Mengel, Friederike; Tsakas, Elias; Vostroknutov, Alexander (2017). "Growth and inequality in public good provision". Journal of Public Economics. 150: 1–13. doi: 10.1016/j.jpubeco.2017.03.002 . hdl: 11572/220727 .
  20. ↑ Dufwenberg, Martin; Gächter, Simon; Hennig-Schmidt, Heike (November 2011). "The framing of games and the psychology of play". Games and Economic Behavior. 73 (2): 459–478. CiteSeerX   10.1.1.187.3821 . doi:10.1016/j.geb.2011.02.003.
  21. ↑ Willinger, Marc; Ziegelmeyer, Antohny (December 1999). "Framing and cooperation in public good games: an experiment with an interior solution" (PDF). Economics Letters. 65 (3): 323–328. doi:10.1016/s0165-1765(99)00177-9.
  22. ↑ Isaac, R. Mark; Walker, James M.; Williams, Arlington W. (May 1994). "Group Size and the Voluntary Provision of Public Goods: Experimental Evidence Utilizing Large Groups". Journal of Public Economics. 54 (1): 1–36. doi:10.1016/0047-2727(94)90068-X.
  23. ↑ Hargreaves Heap, Shaun P; Ramalingam, Abhijit; Stoddard, Brock V (2016-09-01). "Endowment inequality in public goods games: A re-examination". Economics Letters. 146: 5. doi:10.1016/j.econlet.2016.07.015 . Retrieved 2021-04-23.
  24. ↑ Gächter, Simon; Mengel, Friederike; Tsakas, Elias; Vostroknutov, Alexander (2013-01-01). "Growth and Inequality in Public Good Games" (PDF). Externe publicaties SBE; Microeconomics & Public Economics; RS: GSBE ETBC. Retrieved 2021-04-22.
  25. ↑ Kosfeld, Michael; Okada, Akira; Riedl, Arno (2009-09-01). "Institution Formation in Public Goods Games". The American Economic Review. 99 (4): 1335–1355. doi:10.1257/aer.99.4.1335. hdl: 10419/25839 . S2CID   14023837 . Retrieved 2021-04-21.
  26. ↑ Lang, Hannes; DeAngelo, Gregory; Bongard, Michelle (2018-06-01). "Explaining public goods game contributions with rational ability". Games. 9 (2): 36. doi: 10.3390/g9020036 .
  27. ↑ Pickhardt, Michael (2012-01-01). "Pareto meets Olson — A Note on Pareto-optimality and Group Size in Linear Public Goods Games". ORDO: Jahrbuch für die Ordnung von Wirtschaft und Gesellschaft. 63: 195–201. doi:10.1515/9783828260214-014. hdl: 10419/51369 . ISBN   9783828260214. JSTOR   23745715 . Retrieved 2021-04-24.
  28. ↑ Butz, Britta; Harbring, Christina (2020-04-01). "Donations as an incentive for cooperation in public good games". Journal of Behavioral and Experimental Economics. 85: 3. doi:10.1016/j.socec.2019.101510. S2CID   213597084 . Retrieved 2021-04-24.
  29. ↑ Butz, Britta; Harbring, Christina (2020-04-01). "Donations as an incentive for cooperation in public good games". Journal of Behavioral and Experimental Economics. 85: 7. doi:10.1016/j.socec.2019.101510. S2CID   213597084 . Retrieved 2021-04-24.
  30. ↑ Fehr, Ernst; Gächter, Simon (2000-09-01). "Cooperation and Punishment in Public Goods Experiments". The American Economic Review. 90 (4): 80–94. doi:10.1257/aer.90.4.980. hdl: 20.500.11850/146553 . S2CID   11045470 . Retrieved 2021-04-21.

Further reading

The mean contribution rate among the 60 Japanese subjects was 80%
The mean contribution rate among the 39 American subjects was 69%
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.