Friday, February 08, 2008

Game theory

An interesting article on game theory and the effects of U.S. foreign policy on the trust and confidence that other countries have in the U.S.... the article argues that in a game of tolerant tit for tat, the injured party retaliates once. In the case of Iran, for instance, the current stance is the retaliation for U.S. actions in the 1950s and that it is wrong of the U.S. to consider this reason for a renewed confrontation...

How U.S. Policy Is Undermining
the Prospects for World Peace
Hendrik van den Berg
UNL Professor of Economics
War is the failure of more cooperative forms of mutually beneficial interaction between groups. Despite the many gains from cooperating in trade, sharing the earth's common resources, and spreading useful knowledge and technology, nations have repeatedly squandered these gains by resorting to war. As an economist, I have studied the successes and failures of economic and social interaction at great length. The field of economics that has provided especially interesting insight into how humans can peacefully deal with each other more effectively is game theory.

Game theory looks at how specific sets of rules and strategies increase or decrease the gains from economic and social interaction among groups of people and nations. In the real world, we act under a wide array of rules, laws, customs, cultures, and other types of institutions that reward and constrain our actions. The large differences between wealthy and poor societies are largely the result of differences in the way members of societies play out their lives. Now, in our global society, the well-being of the world's 6.5 billion citizens largely depends on how nations deal with each other. By examining the outcomes under alternative sets of rules and strategies, game theory helps us understand how our global society might best achieve peace and prosperity.

Cooperation vs. Conflict
Humans are social animals. Given their particular abilities and characteristics, people survive and reproduce better as part of a group than they would living in isolation. Total output per person is greater when people work together, when they specialize across tasks, and when they put their heads together to solve problems. However, maintaining group cooperation is difficult because people face many short-run situations where they can improve their personal well-being by not cooperating with others. For example, thieves find stealing easier than working hard, the owners of Enron gained by defrauding others, and oppressors of all sorts continue to gain by forcing others to sacrifice their own interests in favor of those of the oppressor.

Economists have shown that, in the long run, a cooperative society provides a much higher level of well-being to its members than a society of thieves and oppressors. However, because individuals, groups and individual countries often find it beneficial to 'deviate' from rules of cooperation to, instead, steal or enslave, it is not easy to maintain a cooperative and peaceful world community. Why work hard toward the cooperative effort if it is easier to steal what others have worked to produce? People and countries quickly find themselves in an adversarial relationship, and resources are increasingly allocated to defense and preparation for conflict rather than welfare-enhancing productive activity. When countries do not trust each other, cooperative outcomes like specialization in production, trade and the sharing of knowledge are lost.

The Game of Tit for Tat
To find the strategies that work best to maximize human well-being in the "game of economic interaction," the economist Robert Axelrod organized a now-famous tournament for game theorists in 1984. Game theorists were invited to play each other in the Prisoner's Dilemma game. This game involves a pair of prisoners accused of having jointly committed a serious crime. Each prisoner is isolated from the other and offered the following choice: (1) confess and implicate the other in exchange for a reduced prison sentence of one year, or (2) remain silent and admit nothing. In the latter case, the prisoner will go free, provided the other prisoner also remains silent and does not confess. However, if the second prisoner does confess and testifies against the first, the silent prisoner will be sentenced to ten years behind bars. Obviously, the optimal outcome is for each prisoner to remain silent and walk out free. However, such an outcome is only possible if the two prisoners trust eac!
h other to remain silent. If either prisoner believes the other will confess in order to guarantee themselves a oneyear sentence rather than the possible ten-year sentence, the optimal strategy is to also confess and at least avoid the onerous ten-year prison term.

This prisoner's dilemma is similar to the example described above where people face the choice of (1) working hard to add to national production without worrying about anyone stealing the fruits of labor, or (2) devoting extensive resources to protecting themselves against theft. Everyone would be better off if they could trust each other - they would not have to waste resources on national defense and preparing for war. But, in the absence of trust, the best choice is to engage in a costly expansion of the military and prepare for the worst.

Axelrod had each pair of players repeat the game over and over in 100 successive rounds. Overall, hundreds of thousands of rounds of the Prisoner's Dilemma were played. The winner of the game was the one who accumulated the least amount of jail time over the 100 games played with each of the nearly 100 other players. The winner was an economist who played the game according to the strategy known as "tolerant tit for tat:"

a. Unless provoked, remain silent (that is, 'cooperate' with your fellow prisoner)

b. If the other implicates you, retaliate by doing exactly the same thing to the other player in the next round

c. Forgive and cooperate again on the subsequent round

The term tit for tat implies that a player responds by doing to the other exactly what the other did to her in a previous round. Thus, one player's silence and refusal to confess triggers similar cooperation by the other player the following round. A violation of trust triggers a confession and implication of the other in the following round. The game is tolerant because a player quickly forgives the other's lack of cooperation and goes back to not confessing after the one-time retaliation under the assumption that the retaliation made the other player see the futility in not cooperating.

The fact that the "tolerant tit for tat" strategy won the tournament surprised some observers. They had expected that tolerant tit for tatters would be exploited and repeatedly made to serve ten-year jail sentences. They should have realized, however, that the prevalence of the 'golden rule,' 'an eye for an eye,' and other similar tolerant tit for tat rules across all cultures throughout history suggests that societies have in fact found this game strategy successful.

Evolutionary biologists have in fact found that many animal species follow the rules of tit for tat. There is also overwhelming evidence that humans are 'pre-programmed' to not only accord some degree of trust to others, but also to retaliate when others do not cooperate. Most people naturally smile when they meet a stranger for the first time. And, you feel anger when someone takes advantage, cuts into a waiting line, cheats or violates what you perceive as the rules of the game you are playing. Such anger serves a useful purpose; if there was no retaliation, violations would quickly escalate and all would suffer. However, to keep society in a cooperative mode, the retaliation must be proportional to the violation. Overreaction causes an escalation of conflict and makes a return to cooperation more difficult. Psychological studies also show that humans have an innate biological tendency to forgive others, especially as time passes. Forgiveness has proved to be useful behavioral!
characteristic because the group gains when other players return to the fold and cooperate with others.

The Lessons
In general, international law has supported the principle that countries should not initiate war, but they are justified in retaliating against those who violate that principle. The tit for tat strategy effectively describes Cold War nuclear policy. Each side promised to refrain from using its weapons so long as the other side also refrained. It worked because the consequences of first strike and retaliation were so awful.

History also warns against an alternative strategy of overreaction to a deviation from the tolerant tit for tat strategy. When the retaliation exceeds the damage done by the initial deviation from cooperation, the overreaction involves both a 'fair' response and a new violation that must be retaliated against by an opponent. Hence, conflict tends to escalate when tit for tat principles are violated. An historical example is the imposition of reparations payments on Germany by Britain and France at the end of World War I even though there was little evidence that Germany was any more to blame for the war than some of the allied victors. Hitler not only exploited this 'injustice' to get elected, he also used it to gain support for retaliation through rearmament and eventual war. On the other hand, the willingness of the allied countries to admit Germany and Japan into the Western coalition after World War II, despite the obvious violations of trust by those countries, resulted in !
a long period of cooperation and peace that continues through today.

The 'pre-emptive' invasion of Iraq is a clear violation of the rules of tit for tat. Threats to bomb Iran are also a violation. Repeated violations of the rules by the U.S. constitutes war, and it may trigger aggression by other countries.

The Surprise of the 2004 Tournament
The Prisoner's Dilemma tournament was repeated in 2004. In order to better reflect the real world, participants were allowed to enter more than one player (strategy) in the competition. Players could form coalitions and carry out joint strategies with other players. A team from Southampton University in the U.K. submitted a whole set of players with distinct strategies and won the competition. When the Southampton players recognized each other, they assumed 'master and slave' roles under which one would sacrifice itself so the other could win repeatedly. If one of the 'slave' players did not recognize the other player as a Southampton player, it would immediately play the role of spoiler and do a lot of damage to the other player by not cooperating. Southampton ended up with the top performer, and a large number of utter failures at the bottom of the table. Does this then show that tit for tat is not the best strategy for countries to follow?

The lesson to be drawn from the 2004 competition is that when players do not play the game as equals - that is, when there is oppression or enslavement by some players of other players - the tit for tat strategy no longer works to maximize the well beingof all the players. The growth of colonial powers in the 18th and 19th centuries provides an example of this outcome. The colonial powers strived to control as many foreign colonies as possible so that they could 'serve' the colonist and thereby gain an advantage over other countries. The gains from international interaction were diminished for the colonized countries (except for a few leaders of colonized governments) and the other countries, but, of course, the winning colonial power gained cheap resources, a captive market for its industries and soldiers for its colonial army.

Today, we see the U.S. effectively using other governments to further its aims, to the detriment of the populations of the 'slave' countries and other competing countries. Tit for tat only raises all nations' wellbeing in a competition among equals, and without the possibility of forcing other players to act against their own interests.

How to Achieve Peace
The continued denial on the part of Americans that our government has done anything wrong, in part because the rest of the world is not powerful enough to retaliate against us for our actions, is most problematic. Americans tend to see the Iranian government's aggressive rhetoric in isolation and, therefore, as a violation of the rules of the game of tit for tat that we subconsciously play. Rather, we should see Iran's actions as their retaliation against our 1952 overthrow of their democratically elected government, the arming of Saddam Hussein to attack Iran in the 1980s, our unwarranted isolation of Iran as an "Axis of Evil" country, and the continual threats of bombing by the Bush/Cheney Administration. The danger is that we are likely to use the tit for tat retaliation that Iran sees as perfectly justified as a justification for our 'retaliating' against them.

Our own government and news media work hard to obscure history and discourage the American public from viewing Iran and global strategy from the more appropriate long-term 'repeated game' perspective. This constitutes a clear indication that our government has no intention of encouraging a globally beneficial strategy of tolerant tit for tat. We seem to have adopted an imperial strategy, in which 'slave players' support us. This is morally wrong, given human evolution and the tendency for people to behave in accordance with the tolerant tit for tat strategy. Our imperial strategy can be successful for a period of time, as the 2004 tournament showed, but in the long run it escalates conflict. Sooner or later, China, Russia, India, Pakistan, Iran and all other countries disadvantaged by our strategy will retaliate. It is human nature to do so. And we will pay the price.

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