The allocation of any resource requires decisions on how the resource will be used at any given time, and how intensely it will be used. Since many resources are only available in limited amounts, any consumption of these resources today will partially or totally destroy them for future use. Therefore, we must decide on the most efficient and optimal resource allocation. This means that we must decide on a rate of consumption that is neither too fast nor too slow, so that we will not deplete the resources too quickly. These problems are solved through market institutions that privatize goods and define property rights over resources. Fortunately these conditions exist over most economic goods; unfortunately, in the area of natural resources they usually do not. These resources are called ‘public goods’. A lawn is an example of such a good. It can be private yet simultaneously have unclear property rights. When property rights are clearly established on the lawn, the owner decides how to use the lawn, and what resources to use to allocate its upkeep. The owner also solely reaps the costs and benefits of the lawn. However, when the lawn is jointly owned, the individuals have incentives to overuse the lawn and under-allocate resources in its upkeep. If this situation is extended to a public park, a lake, or an ocean, the seriousness of the problem is clear. This problem is known as the ‘tragedy of the commons’ and is the subject of this paper.

Before understanding the phenomenon of the tragedy of the commons, it is important to understand the commons itself. A common property resource is a resource that everyone can use. The terminology comes from sixteenth-century England. Villages had a section of grassy land in the center of town, called the commons, which all the townspeople could use. An "international water" is a current example of a common property resource. There are two defining characteristics of a commons: unrestricted access and resource depletability. Because of the unlimited access of the commons, the resource may get overused. If it is overused, the resource will be destroyed completely or not be able to regenerate for future generations. These consequences result in the tragedy of the commons. Familiar examples of the tragedy of the commons include the near extinction of the American buffalo, global warming, and the Internet jam. In the nineteenth century, nearly anyone could hunt and kill the herds of buffalo. When the hunting became widespread, the buffalo could not regenerate enough to meet the needs of the hunters. This overuse of a common resource caused the buffalo to almost become extinct. Global warming is caused by carbon dioxide trapped in the atmosphere. The carbon dioxide is released when coal, oil, or gas is burnt. When energy consumers use these products and release carbon dioxide into the atmosphere (which is a commons), we all share in the warmer temperatures that result. Finally, consider the Internet as a commons. Usually we can be connected to a website almost immediately. However, we experience the tragedy of the commons when many people are online at the same time, and we have to wait through slower connections before getting online.

Many possible, but incomplete, solutions have been offered to solve the tragedy of the commons. Still, "the question that many economists and other social scientists grapple with is how to balance the private desire for utility or profits against the social imperative of sustainable resource use" (Dutta 98). In a socially optimal situation, there would be enough of the resource saved for regeneration for future generations. Some of the proposed solutions include privatization of the resource ownership, fees or taxes paid for usage of the resource, and limits on the number of resource users. Problems with these solutions include difficulty in implementation, inefficiency, and in the case of privatization, common access is taken away. However, these imperfect solutions are preferable to unregulated tragedy of the commons. When searching for answers to the tragedy, it is important for decision-makers to take into account the actions of others. One way to understand the interdependency of all decision-makers is to apply game theory to the commons problem.

Game theory is concerned with the way individuals make decisions when they know and take into account the fact that their actions affect each other. "It is the interaction among individual decision-makers, all of whom are behaving purposefully, and whose decisions have implications for other people that makes strategic decisions different from other decisions" (Dutta 4). Many decisions that we make everyday can be thought of as games. For example, if we need to buy some groceries, do we go to the expensive gourmet store right down the street or should we go to the inexpensive grocery store across town? All market games have a list of players, their strategies, and their payoffs for each strategy. Consider two children's clothing stores in a small city selling similar merchandise to similar clientele. One store is Tiny Treasures (TT) and the other is All the Little Ones (AL)--the list of players. The store-owners must decide if they are going to sell their merchandise at high or low prices--the strategies. Every decision made affects the profits of each store--the payoffs. This type of game is often shown in a payoff table similar to the one below.

Daily Profits (in dollars)

TT

high low

high (850,850) (500,1000)

AL

low (1000,500) (750,750)

AL's payoffs are always the left number in the pair, and TT's payoffs are always the right. It is important to remember that the players act simultaneously and neither player has advance information on their opponent's move. Therefore, assuming both players will act in their own self-interest, they must form an assumption of a move by their opponent. It would be better for everyone if both players chose the high strategy, with each receiving $850. However the safer strategy is to chose low, regardless of how the other player acts. Because of this dominant strategy, both players will chose low even though profits will only be $750.

The strategic interaction between the two stores will continue as long as the stores operate. Therefore, this type of game has become an infinitely repeated game where the players are very familiar with the strategies of their opponents. The players could then suggest an agreement in which they commit to always sell at high prices, therefore ensuring higher payoffs for everyone. However, there are strong incentives to cheat. For example, if AL and TT agreed to sell high, but AL cheated and sold low, AL would get $1000 payoff while TT would only get $500. TT must have a credible threat of punishment that will enforce the agreement, preventing AL from cheating. In situations like this one, the punishment is often that the cooperative player will never again agree to sell high. Everyone will be forced to sell low and therefore get lower payoffs. However, the incentive to cheat does not end with this threat of punishment. The player considering cheating would only cooperate if the payoffs from cheating, once added to the payoffs of forever playing low, are less than or equal to the payoffs from cooperating forever. This idea is shown mathematically by the following. The interest rate is represented by i, and it is used to discount the inflation on the future value of the payoffs.

cooperate cheat

850 + (850 / i) = 1000 + (750 / i)

solving for i: (100 / i) = 150

i = .67 or 67%

If interest rates are below 67%, the players will cooperate. If they are above 67%, the players will cheat. A collusive agreement such as this one only works when players have a sufficient incentive and take into account that their current actions affect future periods.

Similar problems occur when resources are commonly owned, such as a fishing lake. In this case, all players have an incentive to overuse the lake by taking out too many fish -- more than they would if they owned the lake. This action is observed because the individual will only bare part of the costs of this overuse, yet receive all the benefits. The total cost of the consumption is split between all the users; thus no individual bears full responsibility for over-extraction. Similarly, if the individual fisherman tried to conserve fish, he would assume extra costs because what he did not take for himself, another fisherman would take. However, if the resource is private, the owner assumes responsibility for all the benefits and costs of the lake. This fisherman would take out fewer fish, leaving enough for the resource to regenerate. While privatization solves the commons problem, many resources cannot be privatized for either technical or political reasons. Therefore, we must come up with other solutions to solve the tragedy of the commons.

The following description of a series of classroom experiments demonstrates over-harvesting of a common property resource (Hazlett 1). The experiment was run in a principles of economics course, a game theory course, and with a group of sixth through eighth graders. The resource is a plate of M&Ms. At the beginning of the experiment, the plate contains a number of M&Ms equal to ten times the number of students in the class. This number is the carrying capacity of the plate (it can hold no more than this number of M&Ms). Every period, the students privately record the number of M&Ms that they want to harvest for that period; but, no student will be allowed to harvest more than twenty M&Ms in one period. Then, they simultaneously reveal their desired harvest to the whole class. If the total desired harvest is less than or equal to the number of M&Ms on the plate, the students take their desired harvests. If the total desired harvest is greater than the number of M&Ms on the plate, then the students get a portion of their desired harvests (every student gets his desired harvest times the number of M&Ms on the plate divided by the total desired harvest). After the harvest, the remaining M&Ms will reproduce if there are enough of them to form a viable population. "At least eight M&Ms must remain after harvest to provide enough genetic diversity for reproduction" (Hazlett 1). If eight M&Ms are left, each M&M will have one offspring and the number of M&Ms on the plate will double, assuming the carrying capacity permits. After reproduction, the process will begin again. If ever there are less than eight M&Ms left after reproduction, the population is crashed and the experiment is terminated. If the cycle is able to continue, it will be ended by the instructor. The students should not know the number of periods determined for the experiment.

In the first experiment, the students are not allowed to communicate with each other. All of the groups crashed the experiment within four periods. In the second experiment, communication is allowed to try to avert the tragedy of the commons--mixed results occurred. The principles group never agreed on a harvesting rule, but the communication did lead to more restrained harvests than in experiment one. The game theory group agreed to harvest the maximum sustainable yield for three periods, then they jointly crashed the experiment in period four. The maximum sustainable yield is the socially optimal solution. For this population, the students should harvest half of the initial number of M&Ms each period (five M&Ms per person), therefore allowing the plate to return to the carrying capacity for the next period.

The middle school grade group also agreed to harvest five per person, but one student cheated and harvested nineteen. In the next period, the cheater was asked not to harvest while the others took three. The group had returned the plate to its carrying capacity when the instructor ended the experiment. In the third and final experiment, the students are assigned individual property rights. Each student owns a portion of the plate which has its own carrying capacity, equal to ten M&Ms. As long as there are at least eight M&Ms on the whole plate after harvest, the M&Ms in each portion will double according to the carrying capacity of that portion. This structure gives the students a personal incentive to conserve M&Ms. The results were that each group harvested the maximum sustainable yield each period. Some students harvested all their M&Ms when they thought the instructor would end the experiment.

A factor that differentiates this experiment from the example of the children's clothing stores is that this game has an end period, with the probability of the game ending being equal to the interest rate. Even though the students were able to cooperate in some of the experiments, cheating is still observed. The high interest rate and the threat of the game ending caused some students to harvest all their M&Ms rather than lose them when the game ended. The possibility of a terminal period will destroy the cooperative agreements that were supported by the infinitely repeated games.

Although privatization of the resource led the results of experiment three to be nearly socially optimal, privatization is not a possible answer to every commons problem. Take international fishing waters as an example. Given the current state of technology, it is not necessary to privatize the world's seas. Therefore, it is the responsibility of the fishermen to conserve the resource of fish. However, any expense an individual fisherman would undertake to conserve fish stock would yield him a negligible return. Other fishermen would take advantage of the additional catches or other improvements this concerned fisherman could bring. "Where no individual is able to recoup an investment made in fish stock, everyone will personally incline to neglect the future of the resource" (Butlin 58). Because of this fact, the government is often called upon to help regulate similar types of commons problems.

Even with assistance from the government through laws and regulations, averting the tragedy of the commons is a complicated task. When dealing with exhaustible resources, there are many questions that need to be answered. How is the supply of resources likely to be depleted over time and will this rate change as prices and interest change? Also, how do we decide on an optimal rate of depletion? This question is particularly difficult because it involves value judgments. Because all individuals do not share the same value judgments about what is good or bad for society, there will be no rate of depletion on which everyone agrees is good. Applying game theory to the commons problem, such as in the M&Ms experiment, can help us find possible solutions to the problem of limited resources and unlimited time to use them. "Encapsulated in environmental and natural resource management is the problem of time. It permeates each resource utilization problem with which man is faced" (Butlin 60).

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This page updated Decmber 20, 2001