Public goods game
Encyclopedia
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 the public pot. The tokens in the pot are multiplied by a factor (>1) and this "public good
" payoff is evenly divided among players. Each subject also keeps the tokens they do not contribute.
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.
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).
Those who contribute nothing are called "defectors" or "free rider
s", as opposed to the contributors who are called "cooperator
s".
" 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 trust
ing 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 tend to remain a hard core of ‘givers’.
One explanation for the dropping level of contribution is inequity aversion
; once it is realized that others are receiving 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.
can vary among players; the standard game (with a fixed initial endowments) allows no work effort variation and cannot capture the marginal substitutions
among three factors: private goods, public goods, and leisure.
, but higher factors produce higher proportions of contribution.
With a large group (40) and 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%.
’s definition of a “public good
”. One type of public good is a costly, "non-excludable" project that every one 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.
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.
" outcomes of Public goods games.
Experimental economics
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...
. In the basic game, subjects secretly choose
Information asymmetry
In economics and contract theory, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. This creates an imbalance of power in transactions which can sometimes cause the transactions to go awry, a kind of market failure...
how many of their private
Private good
A private good is defined in economics as "an item that yields positive benefits to people” that is excludable, i.e. its owners can exercise private property rights, preventing those who have not paid for it from using the good or consuming its benefits; and rivalrous, i.e. consumption by one...
tokens to put into the public pot. The tokens in the pot are multiplied by a factor (>1) and this "public good
Public good
In economics, a public good is a good that is non-rival and non-excludable. Non-rivalry means that consumption of the good by one individual does not reduce availability of the good for consumption by others; and non-excludability means that no one can be effectively excluded from using the good...
" payoff is evenly divided among players. Each subject also keeps the tokens they do not contribute.
Results
The group's total payoff is maximized when everyone contributes all of their tokens to the public pool. However, the Nash equilibriumNash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
in this game is simply zero contributions by all; if the experiment were a purely analytical exercise in game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
it would resolve to zero contributions because any rational agent
Rational agent
In economics, game theory, decision theory, and artificial intelligence, a rational agent is an agent which has clear preferences, models uncertainty via expected values, and always chooses to perform the action that results in the optimal outcome for itself from among all feasible actions...
does best contributing zero, regardless of whatever anyone else does.
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
Endowment
-Finance:*Financial endowment, relating to funds or property donated to institutions or individuals *Endowment mortgage, a mortgage to be repaid by an endowment policy*Endowment policy, a type of life insurance policy...
can be chipped in).
Those who contribute nothing are called "defectors" or "free rider
Free rider problem
In economics, collective bargaining, psychology, and political science, a free rider is someone who consumes a resource without paying for it, or pays less than the full cost. The free rider problem is the question of how to limit free riding...
s", as opposed to the contributors who are called "cooperator
Cooperation
Cooperation or co-operation is the process of working or acting together. In its simplest form it involves things working in harmony, side by side, while in its more complicated forms, it can involve something as complex as the inner workings of a human being or even the social patterns of a...
s".
Iterated public goods games
"Repeat-playRepeated game
In game theory, a repeated game is an extensive form game which consists in some number of repetitions of some base game . The stage game is usually one of the well-studied 2-person games...
" 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 trust
Trust (sociology)
In a social context, trust has several connotations. Definitions of trust typically refer to a situation characterised by the following aspects: One party is willing to rely on the actions of another party ; the situation is directed to the future. In addition, the trustor abandons control over...
ing 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 tend to remain a hard core of ‘givers’.
One explanation for the dropping level of contribution is inequity aversion
Inequity aversion
Inequity aversion is the preference for fairness and resistance to incidental inequalities. The social sciences that study inequity aversion include sociology, economics, psychology, anthropology and ethology.-Human studies:...
; once it is realized that others are receiving 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
If the amount contributed isn't hidden it tends to be higher. In a typical public goods game there might be six subjects contributing to the pot so concealing the level of contribution isn't difficult. In "pairwise iterations" with only two players the other player's contribution level is always known.Public goods games with punishment
The option to punish non-contributors after a round of the public goods game is widely exercised, even at a cost. In most experiments this leads to greater group cooperation, and fewer defections in subsequent rounds.Public goods games with reward
The option to reward co-operation (rather than punish defection) is less often exercised by players, but some studies have shown that it can be more effective at enforcing co-operation than punishing. The evidence comparing reward with punishment is mixed; a 2007 study found that rewards could not sustain long-term cooperation.Income variation
A public goods games variant suggested as an improvement for researching the free rider problem is one in which token incomeHousehold income
Household income is a measure of the combined incomes of all people sharing a particular household or place of residence. It includes every form of income, e.g., salaries and wages, retirement income, near cash government transfers like food stamps, and investment gains.Average household income can...
can vary among players; the standard game (with a fixed initial endowments) allows no work effort variation and cannot capture the marginal substitutions
Marginal rate of substitution
In economics, the marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility.-Marginal rate of substitution as the slope of indifference curve:...
among three factors: private goods, public goods, and leisure.
Multiplication factor
In order 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 strategyStrategy
Strategy, a word of military origin, refers to a plan of action designed to achieve a particular goal. In military usage strategy is distinct from tactics, which are concerned with the conduct of an engagement, while strategy is concerned with how different engagements are linked...
, but higher factors produce higher proportions of contribution.
With a large group (40) and 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%.
Implications
The name of the game comes from economistEconomist
An economist is a professional in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy...
’s definition of a “public good
Public good
In economics, a public good is a good that is non-rival and non-excludable. Non-rivalry means that consumption of the good by one individual does not reduce availability of the good for consumption by others; and non-excludability means that no one can be effectively excluded from using the good...
”. One type of public good is a costly, "non-excludable" project that every one 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
Free rider problem
In economics, collective bargaining, psychology, and political science, a free rider is someone who consumes a resource without paying for it, or pays less than the full cost. The free rider problem is the question of how to limit free riding...
problem). The “public goods game” is designed to test this belief and connected theories of social
Social
The term social refers to a characteristic of living organisms...
behaviour.
Game theory
The empirical fact that subjects in most societies contribute anything in the simple public goods game is a challenge for game theoryGame theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
to explain via a motive of total self-interest
Psychological egoism
Psychological egoism is the view that humans are always motivated by self-interest, even in what seem to be acts of altruism. It claims that, when people choose to help others, they do so ultimately because of the personal benefits that they themselves expect to obtain, directly or indirectly,...
, 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 to sociology
The sociological interpretation of these results emphasizes group cohesion, and cultural norms to explain the "prosocialProsocial behavior
Prosocial behavior, or "voluntary behavior intended to benefit another", consists of actions which "benefit other people or society as a whole," "such as helping, sharing, donating, co- operating, and volunteering." These actions may be motivated by empathy and by concern about the welfare and...
" outcomes of Public goods games.
See also
- Ultimatum gameUltimatum gameThe ultimatum game is a game often played in economic experiments in which two players interact to decide how to divide a sum of money that is given to them. The first player proposes how to divide the sum between the two players, and the second player can either accept or reject this proposal. ...
- Trust game
- Prisoner's dilemmaPrisoner's dilemmaThe prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...
- Robert AxelrodRobert AxelrodRobert M. Axelrod is an American political scientist. He is Professor of Political Science and Public Policy at the University of Michigan where he has been since 1974. He is best known for his interdisciplinary work on the evolution of cooperation, which has been cited in numerous articles...
, The Evolution of CooperationThe Evolution of CooperationThe evolution of cooperation can refer to:* the study of how cooperation can emerge and persist as elucidated by application of game theory,* a 1981 paper by political scientist Robert Axelrod and evolutionary biologist W. D...
External links
- The evolution of strategies in public goods games: Three interactive simulations of the spread of defection among automated players choosing between strategies. (This is a model of experimental economics, rather than an actual experiment.)
- Voluntary Participation and Spite in Public Good Provision Experiments: An International Comparison. This is an Economic Science Association paper from 2002 detailing the methodology and results used in an experiment comparing the performance of JapanJapanJapan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese and American subjects in public goods games. They reject the hypothesis of international equality in overall efficiency:
- The mean contribution rate among the 60 Japanese subjects was 80%
- The mean contribution rate among the 39 American subjects was 69%