Operations Research - Game Theory

by

Elmer G. Wiens

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Nonnegotiable Two Person Generalized (Non-Zero) Sum Games

Free Rider Problem

Frontier Petroleum Exploration

In 1966 geologists believed the Sverdrup Basin in the Canadian Arctic Islands held vast quantities of hydrocarbons; however, the extent of these oil and gas reserves had not been proven through the drilling of wells. A large number of firms held the exploration permits issued by the Canadian Government. The Canadian Government and the permit holders wanted this area explored. Each permit holder wanted to know how much oil and/or gas lay under the acreage covered by his permit.

Drilling a well in the Arctic is very expensive. If a specific firm drilled a well on its property, it would incur the exorbitant cost alone. But, the information obtained from its drill would be available to all the other firms, improving their estimates of the probability of oil and gas under their acreage. Each permit holder had an incentive to delay drilling, hoping the other firms would drill first. But then all firms delayed drilling.

The solution was to "unitize" exploration by forming a consortium to drill a series of test wells, to provide information about the entire region, and to pool the expenses.

Without doing too much violence to the facts (see Wiens), suppose twenty firms each hold an equal number of acres under permit. A series of five test wells will cost 20 million dollars to drill. Geologists estimate the value of the information on oil and gas reserves from the test wells to be 40 million dollars. So the net gain to each firm is one million dollars, if all twenty firms join the consortium.

The twenty firms hold meetings to see if they can form a consortium to drill the wells, with each firm investing one million dollars. A given firm has two options. Join the consortium and share in the costs and benefits, or, do not join and "free-ride" on the benefits of the consortium's activities.

The benefits are there, but they cannot reach an agreement. What is the problem? The following game tableau shows the payoffs to a given firm and to the consortium.

 Game Tableau Consortium Do Not Drill Drill Y1 Y2 Free-Rider Do Not Join X1 0, 0 2 million, 18 million Join X2 0, 0 1 million, 19 million

Analyzing his payoff, the free-rider — a hardheaded realist — will chose the first row — Do Not Join. Let the others form the consortium and drill the test wells. Reap the benefits, but do not incur the costs.

The remaining nineteen members in the consortium will chose the second column. Each member gets 1 million if the free-rider joins; about .95 million if the free-rider does not join. Group rationality suggests that they proceed with the drilling project.

However, each firm is potentially a free-rider. Individual rationality suggests that each firm abstain from joining the consortium.

The net result is that the consortium does not form and no wells are drilled.

In the case of the Canadian Arctic Islands, a consortium called Panarctic Oils Ltd. formed (see Wiens). Panarctic Oils was created in December of 1967, but not before the Canadian Government invested nine million dollars for a 45% equity in the company. The remaining eleven million dollars was provided by 19 other shareholders.

Free Rider Problem

Canada's democracy is based on politicians and political parties. During an election, citizens who reside in a constituency vote for a particular candidate (politician) representing a particular political party. The political party that elects the most candidates forms the government. The leader of the party that forms the government becomes the Prime Minister of Canada, who has vast powers under the Canadian Constitution.

The benefits to a political party forming a government are clear. However, only a small percentage of the Canadian population actually belong to any political party. Even a smaller percentage of the population bother to work for their party during an election.

Some individuals promote a political party based on shared political beliefs. Other people support a political party expecting to benefit directly if their party is elected. Often the latter hope to get some contract with the government, which they would not have received otherwise. Their work is conditional on them obtaining a benefit, either for themselves or for their firm. In effect, they work as lobbyists within the party.

Individuals who want to contribute to the democratic process of Canada can easily be discouraged. If they join a political party, they must pay a fee, albeit nominal, and give up some of their free time if they are to be actively involved. Often their names just become an entry on a membership list to be solicited from time to time for money. Even their volunteer work often goes unappreciated. Why bother?

The individual's contribution to the political party's success pales in comparison to that of the well-healed law firm anticipating some lucrative government litigation, or the large corporation desiring some propitious change in legislation.

For the average person, individual rationality dictates they not join a political party. Collective rationality suggests people join political parties in great numbers to offset the influence and power of lobbyists, and to obtain good government. In Canada it is individual rationality that dominates; few people, in fact, ever join a political party.

References

• Black, Max. Perplexities. Cornell: Ithaca, 1990.
• Howard, Nigel. Paradoxes of Rationality: Theory of Metagames and Political Behavior. Cambridge: MIT, 1971.
• Intriligator, Michael D. Mathematical Optimization and Economic Theory. Englewood Cliffs: Prenctice-Hall, 1971.
• Nash, John F. "Noncooperative Games." Annals of Mathematics. 54 (1951): 286-295.
• Mulgrew, Ian. "Ex-Justice Minister 'Offered Contracts.'"  The Vancouver Sun 10 April 2009: B1.
• Oxford Dictionary: The Concise Oxford Dictionary of Current English. 5th ed. Ed. H.W. Fowler and F.G. Fowler. Oxford: Oxford UP, 1964
• Owen, Guillermo. Game Theory, 2nd Edition. New York: Academic, 1982.
• Rapoport, Anatol. Two-Person Game Theory: The Essential Ideas. Ann Arbor: U Michigan: 1966.
• Thomas, L. C. Games, Theory and Applications. New York: John Wiley, 1984.
• Wiens, Elmer G. "Petroleum Exploration, Property Rights and Externalities in the Canadian Arctic Islands." Center for the Study of Organizational Innovation, University of Pennsylvania, Discussion Paper #45, 1979.