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Public goods game

Public goods game is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Public goods game rather than just read about it. In short: 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.

Public goods game — main illustration
Public goods game — illustration

Key takeaways

  • Public goods game belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Public goods game to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Public goods game from memory before moving on to harder problems.

Reference excerpt

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 their "private consumption" (their endowment minus their contribution) plus their benefit from the "public good" (the sum of contributions multiplied by a factor). 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" (public good). The payoff of each individual i is

π i = M − g i + a ∑ j = 1 n g j {\displaystyle \pi _{i}=M-g_{i}+a\sum _{j=1}^{n}g_{j}}

where g i {\displaystyle g_{i}} is the contribution of individual i to the public good, and therefore, M − g i {\displaystyle M-g_{i}} is her private consumption and a ∑ j = 1 n g j {\displaystyle a\sum _{j=1}^{n}g_{j}} is her benefit from the public good.

Optimum To find the optimal contribution we shall maximize the payoff of the representative individual:

M a x g ( M − g + a n g ) {\displaystyle {\underset {\ g}{\ Max}}(M-g+ang)}

The derivative with respect to g is − 1 + a n {\displaystyle -1+an} . Note that if a n > 1 {\displaystyle an>1} then the optimal contribution is M since the first derivative is positive.

Nash equilibrium If a < 1 {\displaystyle a<1} 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 a < 1 {\displaystyle a<1} . 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 (or egoism). 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). 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 (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

… excerpt ends here. Continue reading the full article.

Illustrations

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

Worked examples

Example 1 — a first encounter with Public goods game

Start with the simplest possible case. Write down what Public goods game claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Public goods game before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Public goods game ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Public goods game

In research
Public goods game appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Public goods game in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Public goods game is common in secondary-school and first-year university syllabi. It links to neighbouring topics Moral psychology, Non-cooperative games, Public sphere, so understanding it makes those chapters shorter.
In everyday life
Look for Public goods game outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Public goods game in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Public goods game means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Public goods game out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Public goods game in simple terms?

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.

Why does Public goods game matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Public goods game?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Public goods game.

Tags

  • Moral psychology
  • Non-cooperative games
  • Public sphere
  • Social psychology
  • Social science experiments

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