Prisoner’s Dilemma – Cooperation and Civilization

We all use game theory as unconsciously as sticklebacks or bats. A human society is a group interacting repeatedly. Some interactions pose choices between self and group interest. How often mutual cooperation occurs is a measure of how effectively the society is functioning.

The paramount importance of civilization in human history rests with its role in promoting cooperation. With the discovery of agriculture, people formed permanent settlements. Once people became rooted to cultivated plots of earth, society changed. For the first time, People had neighbors, fellow beings that they would have dealings with again and again. A person who cheats his neighbor could not expect cooperation in the future. A person who cheated all his neighbors would be an outcast. With corps in the ground or an urban business with a stock of good will, it was no longer so easy to pick up and move on. For most people, most of the time, it was easier to cooperate.

Many of the trappings of civilization promote cooperation. Inventions such as names, language, credit card, license plates, and ID cards help connect a person with his past behavior. That permits the use of conditional strategies. Most laws proscribe defection of various kinds. In their 1957 book, Luce and Raiffa observed that “some hold the view that one essential role of government is to declare that the rules of certain social ‘games; must be changed whenever it is inherent in the game situation that the players, in pursuing their own ends, will be forced into a socially undesirable position.

Human history is not one of ever-increasing cooperation, though. Game theory may help to understand that, too. TIT FOR TAT is not the only conditional strategy that is evolutionarily stable or nearly so. Once entrenched, other strategies can be highly stable.

Game theorists Steve Rytina and David L. Morgan investigated the role of labels. A label is any category that can be used to distinguish players. In human societies, it may be gender, race, social class, nationality, club membership, union membership, or other attributes.

Imagine a society divided into two groups, the blues and the reds. Nearly everyone in the society follows a strategy that can be called “DISCRIMINATORY TIT FOR TAT” (DTFT). This strategy is just like TIT FOR TAT except when dealing with someone of a different color group. Then you always defect.

When two reds interact for the first time, each cooperates. When two blues with no history interact, both cooperate. But when a red and blue interact, each defects (“because you can’t trust those guys”).

Rytina and Morgan demonstrated that this arrangement is stable. An individual who tries to play regular, color-blind TIT FOR TAT is worse off than the one who conforms. Suppose a red and blue interact for the first time, and the blue contemplates cooperating (as in regular TIT FOR TAT). The red player, however, is almost certainly playing DTFT and will defect. The blue player will get the sucker payoff and do less well than a conformist playing DTFT.

This does not mean that DTFT is more successful than TIT FOR TAT would be if everyone played TIT FOR TAT. It’s not. Every time players of different colors interact they end up with the punishment rather than the reward. But DTFT is stable once entrenched because it punishes individual efforts to establish TIT FOR TAT.

The label that is in the minority is hurt more by DTFT than the majority. If reds are greatly in the majority, then most of a red player’s interaction will be with other reds. In that case, DTFT is not much different from TIT FOR TAT. Only in a few cases will an interaction be with a blue. But blues, being in the minority, will interact frequently with reds, and in each case will get the punishment payoff. In the limiting case of an arbitrarily small minority, its members will almost always received the punishment payoff, while the majority almost always receives the reward.

This provides a game-theoretic rationale of separatist movements. Such diverse phenomena as “Chinatowns” and ghettos, India’s partition into Moslem and Hindu states, the Pilgrims’ founding of the Massachusetts Bay Colony, the separation of Marcus Garvey and Black Muslims, and the Mormons’ founding of Utah all have or had the effect of limiting a minority’s interaction with outsiders distrustful of them.

Prisoner’s Dilemma – J. Nash’s Biography

In due course Nash followed von Neumann’s example by juggling a bicoastal career as RAND consultant and professor at the Massachusetts Institute of Technology. In the late 1940s and early 1950s, Nash extended game theory in a direction von Neumann and Morgenstern had not taken it. Nash studied “noncooperative” games where coalitions are forbidden.

 

Von Neumann and Morgenstern’s treatment of games of more than two persons focuses on coalitions, groups of players who chose to act in concert. They suppose that rational players would hash out the results of joining every possible coalition and choose the one most advantageous. This approach makes sense given von Neumann and Morgenstern’s grand aim, which was to treat economic conflicts as n-person games. Businesses team up to fix prices or drive a competitor out of business; workers join unions and bargain collectively. In each case it is reasonable to expect that parties will form coalitions whenever it is to their advantage. In effect, this is the definition of a free-market, laissez-faire economy.

 

The only kind of noncooperative games von Neumann treated were two-person, zero-sum games – which are necessarily noncooperative. When one player’s gain is another’s loss, there is no point in forming a coalition. That case, however, was already covered by von Neumann’s minimax theorem. Nash’s work was primarily concerned with non-zero-sum games and games of three or more players.

 

With the minimax theorem, von Neumann struck a great blow for rationality. He demonstrated that any two rational beings who find their interest completely opposed can settle on a rational course of action in confidence that the other will do the same. This rational solution of a zero-sum game is an equilibrium enforced by self-interest and mistrust – and the mistrust is reasonable in view of the antithetical aims of the players.

 

Nash extended this by showing that equilibrium solutions also exist for non-zero-sum two-person games. It might seem that when two person’s interests are not completely opposed – where by their actions they can increase the common good – it would be even easier to come to a rational solution. In fact it is often harder, and such solutions may be less satisfying.

“The technology has to be considered as larger than just the inanimate pieces of hardware,” said Felsenstein. “The technology represents inanimate ways of thinking, objectified ways of thinking. The myth we see in WarGames and things like that is definitely the triumph of the individual over the collective dis-spirit. [The myth is] attempting to say that the conventional wisdom and common understanding must always be open to question. It’s not just an academic point. It’s a very fundamental point of, you might say, the survival of humanity, in a sense that you can have people [merely] survive, but humanity is something that’s a little more precious, a little more fragile. So that to be able to defy a culture which states that ‘Thou shalt not touch this,’ and to defy that with one’s won creative powers is… the essence.”

The essence, of course, of the Hacker Ethic.

Treatment of Tuberculosis Infection

1. Preventive therapy with isoniazid given for 6 to 12 mo is effective in decreasing the risk of future tuberculosis in adults and children with tuberculosis infection demonstrated by a positive tuberculin skin test reaction. The appropriate criterion for defining a positive skin test reaction depends on the population being tested.

For adults and children with HIV infection, close contacts of infectious cases, and those with fibrotic lesions on chest radiograph,

A reaction of >= 5 mm is considered positive. For other at-risk adults and children, including infants and children younger than 4 yr of age, a reaction of >= 10 mm is positive. Persons who are not likely to be infected with Mycobacterium tuberculosis should generally not be skin tested. If a skin test is performed on a person without a defined risk factor for tuberculosis infection, >= 15 mm is positive.

2. Persons with a positive skin test and any of the following risk factors should be considered for preventive therapy regardless of age: persons with HIV infection; persons at risk for HIV infection with unknown HIV status; close contacts of sputumpositive persons with newly diagnosed infectious tuberculosis; newly infected persons (recent skin test convertors); and persons with medical conditions reported to increase the risk of tuberculosis (i.e., diabetes mellitus, adrenocorticosteroid therapy and other immunosuppressive therapy, intravenous drug users, hematologic and reticuloendothelial malignancies, end-stage renal disease, and clinical conditions associated with rapid weight loss or chronic undernutrition). In some circumstances persons with negative skin tests should also be considered for preventive therapy. These include children who are close contacts of infectious cases and anergic HIV-infected adults at increased risk of tuberculosis. Tuberculin- positive adults with abnormal chest films that show fibrotic lesions likely representing old healed tuberculosis and adults with

silicosis should usually receive 4-mo multidrug chemotherapy although 12 mo of isoniazid preventive therapy is an acceptable alternative.

Persons who are known to be HIV-infected and who are contacts of patients with infectious tuberculosis should be carefully evaluated for evidence of tuberculosis. If there are no findings suggestive of current tuberculosis, preventive therapy with isoniazid should be given. Because HIV-infected contacts are not managed

in the same way as those who are not HIV-infected, HIV testing is recommended if there are known or suspected risk factors for acquisition of HIV infection.

3. In the absence of any of the above risk factors, persons younger than 35 yr of age with a positive skin test in the following high incidence groups should also be considered for preventive therapy: foreign-born persons from high-prevalence countries; medically undersewed low-income persons from high-prevalence populations (especially blacks, Hispanics, and Native Americans); and residents of facilities for long-term care (e.g., correctional institutions, nursing homes, and mental institutions).

4. Twelve months of preventive therapy is recommended for adults and children with HIV infection and other conditions associated with immunosuppression. Persons without HIV infection should receive at least 6 mo of preventive therapy. The American Academy of Pediatrics recommends that children receive 9 mo

of therapy.

5. In patients who have a positive tuberculin skin test and either silicosis or a chest radiograph demonstrating old fibrotic lesions, and who have no evidence of active tuberculosis, acceptable regimens include: (7) 4 mo of isoniazid plus rifampin, or (2) 12 mo of isoniazid, providing that infection with drug-resistant organisms is judged to be unlikely.

6. In persons younger than 35 yr of age, routine monitoring for adverse effects of isoniazid should consist of a monthly symptom review. For persons 35 yr of age and older, hepatic enzymes should be measured prior to starting isoniazid and monitored monthly throughout treatment, in addition to monthly symptom reviews. Other factors associated with an increased risk of hepatitis include daily use of alcohol, chronic liver disease, and injection drug use. There is also evidence to suggest that postpubertal black and Hispanic women are at greater risk for hepatitis.

Certain medications taken concurrently with isoniazid may increase the risk of hepatitis or drug interactions. More careful monitoring should be considered in these groups, possibly including more frequent laboratory monitoring.

7. Persons who are presumed to be infected with isoniazidresistant organisms should be treated with rifampin rather than with isoniazid.

8. As with treatment of tuberculosis, the key to success of preventive therapy is patient adherence to the prescribed regimen. Although not evaluated in clinical studies, directly observed, twice-weekly preventive therapy may be used for at-risk adults and children who cannot or will not reliably self-administer therapy.