In the The Evolution of Cooperation you will learn:
Consider cooperation in a few different forms. If you are in a long-term relationship with another person, does it make the most sense in terms of your personal goals to cooperate with that individual? Do you gain any advantage by showing kindness to someone who never reciprocates? What could your business gain by working with another company if it was soon going to go bankrupt? How should your country react to an overt hostile action by an enemy nation? Can your country deal with – or manipulate – this enemy so that it will cooperate? A helpful way to portray and answer such questions is to use an iterated (repeating) “Prisoner’s Dilemma.”
The original conundrum is: The police capture two criminals and separately offer them a deal. The men are not allowed to confer. If one informs against the other and confesses, he will be released from prison, and the other will get a 10-year prison term. If they both remain silent, they each will get a minor, six-month term. If both inform against the other, they each get a two-year term. The dilemma is, if both inform, they each gain less than if they remain silent. In game theory, a Prisoner’s Dilemma again provides three possible outcomes between two players: 1) Both players benefit modestly when they cooperate with each other; 2) One betrays the other and benefits handsomely if, at the same time, the other player is trying to cooperate (that player gains nothing); and 3) Both players receive minimal benefits if they betray each other simultaneously.
The Prisoner’s Dilemma always has two players. Both have two distinct choices: cooperate or betray (that is, defect or inform against the other player). Each player chooses to cooperate or not without knowing what the other player will do. Defection always pays better than cooperation. The dilemma? If both players defect, they each gain less than if they both decide to cooperate.
To visualize the Prisoner’s Dilemma graphically, think of a simple matrix, like a box, with two rows and two columns resulting in a square cut vertically and horizontally to form four adjoining boxes. One player selects a horizontal row, either betraying or cooperating. The choices are symbolized by letters: “R” for reward, “T” for temptation to defect, “S” for sucker’s payoff and “P” for punishment for mutual defection. The other player chooses a vertical column. Together, these choices provide one of four separate outcomes as shown in each box of the matrix:
• Box 1: Cooperation column and cooperation row – When both players cooperate, each receives R, the reward for mutual cooperation, worth three points.
• Box 2: Defection column and cooperation row – When the column player chooses to defect and the row player chooses to cooperate, the defecting column player wins. This player receives T, for yielding to temptation and defecting. This is worth five points. The row player earns S, the sucker’s payoff, worth zero points.
• Box 3: Cooperation column and defection row – When the column player chooses to cooperate and the row player chooses to defect, the winner is the defecting player. This player receives T, worth five points. The column player earns S, worth zero points.
• Box 4: Defection column and defection row – If both players defect, each receives P, the punishment for mutual defection. This is worth one point each.
As the breakdown shows, the game assigns points based on each prisoner’s specific choices. A set number of points accompany each choice, that is, R (3), S (0), T (5) and P (1). Considering these payoffs, if you are the horizontal row player, defecting is always to your advantage, no matter what choice you think the other player plans to make. Thus, defection, not cooperation, is your sensible, strategic choice. This logic also applies to the other player, who should always choose to defect, too. Thus, it is always logical for both you and your opponent to defect. However, in such a scenario (Box 4), you and your opponent receive only one point each. This is a smaller payoff than if you both cooperate, which earns three points each (Box 1). What a conundrum! Rational choices lead to poorer individual payoffs. Thus the dilemma.
There is no way around this fix. If you and your opponent take turns defecting, the outcome will, nevertheless, always be worse than if mutual cooperation prevails. The three-point reward for mutual cooperation is greater than the average (two-and-a-half points) each player gets if one earns five points for defecting and the other earns zero points for being a sucker. When the Prisoner’s Dilemma is played only once, both players logically choose defection, and win one point each, a less successful payoff than if both had cooperated. If two people play the game a finite number of times, defection remains a logical, rational choice for both. Each player assumes defection on the other player’s part based on the last move and, by extension, the next to the last move. Thus, cooperation makes no sense. In such a scenario, it just isn’t the logical choice.
This logic changes if the game is played repeatedly and indefinitely. In that case, a cooperative strategy can emerge if the individual players are not certain when the game (that is, the interaction) will reach its last move. With that unknown, cooperation may make more sense than defection. This indefinite scenario is more realistic and lifelike than one in which two individuals (or groups or businesses or nations) precisely plan a finite number of interactions. In an indefinite scenario, cooperation becomes possible because both players understand that they may be interacting with one another again and again. Choices that individual players make now can influence subsequent choices. Thus, the future affects the present. But as in life, present payoffs are always more attractive than future ones. Therefore, the payoff for the current move always seems more valuable than the payoff for the next move.
Considering all of this, what is the best strategy for an individual player in an iterated Prisoner’s Dilemma of indefinite length? To find out, researchers organized a tournament. They invited psychologists, economists, political scientists, mathematicians and sociologists to submit computer programs that would compete with one another. They received 14 entries.
The winning program – which also was the simplest submitted – was “Tit for Tat,” entered by Anatol Rapoport, a University of Toronto professor. Tit for Tat’s first move is cooperation. After that, it always mimics the other player’s previous moves. In a 200- move game, Tit for Tat averaged 504 points per game. Other programs that did well in the tournament all shared a common characteristic with Tit for Tat: They all were nice. They never defected on the first move. It makes sense that the nice programs performed well. The tournament included a large enough number of them to demonstrate that they worked well with each other, thus raising their average scores. Tit for Tat incorporates a high degree of what can be termed “forgiveness.” If the other player defects, and subsequently then cooperates, Tit for Tat does the same. Plus, Tit for Tat is virtually nonexploitable. If the other player defects, so does Tit for Tat, quite remorselessly.
A subsequent, actual open-for-all-entries Prisoner’s Dilemma tournament drew 62 proposals from six countries. Tit for Tat was the clear winner in the first and second rounds. Its simplicity gave it an edge over other tactics. In the second tournament, as before, “Nice guys finished first.” The programs that did best against Tit for Tat capitalized on its niceness. A hypothetical “Tit for Two Tats” game would have done even better than the actual Tit for Tat program. In it, defection would occur only if the opposing player defected on the two previous moves.
If researchers projected a large number of Prisoner’s Dilemma tournaments, the results would show that the nice programs would thrive, while the other programs (called the “meanies”) would tend to drop out eventually. Thus, cooperation, in effect, evolves over time to become a dominant strategy when repeated interactions occur. Indeed, in such circumstances, it is logical that Tit for Tat would become a universal strategy that everyone would apply.
In addition to the artificial construct of the Prisoner’s Dilemma, the efficacy of Tit for Tat applies in far more practical realms. Consider the value of reciprocity (Tit for Tat’s ruling principle) in the U.S. Congress, where “you vote for my bill and I will vote for your bill” is a philosophy that has been in play for years. Individual congressmen cannot succeed without their colleague’s assistance. Their bills would never pass. Eventually, their constituents would deem them ineffective and vote them out of office.
Other examples of the logic and sensibleness of cooperation abound, not only in terms of human relations, but also widely throughout nature. Consider the relationship of ants to acacia trees (also known as thorn trees). The acacias provide food and domicile for the ants inside their inflated thorns; the ants protect the acacias from hungry herbivores and trim competing plants. Similarly, alga and fungus join in symbiosis to form lichen. Even bacteria sometime employ a conditional strategy to thrive. Cooperation, based on reciprocity (Tit for Tat), evolves even among nonthinking life forms.
Activity at the Western Front in France and Belgium during World War I provided a vivid example of the all-consuming cooperative power of reciprocity among human beings. Enemy soldiers shooting from trenches fought gruesome and bloody battles against each other for years, often for gains of only a few small yards of territory. But in between the actual battles, enemy soldiers commonly exhibited remarkable restraint about attacking each other. German soldiers would walk about, in clear sight and within rifle range, but the Allies would not shoot at them. This applied equally to Allied troops. Often, shelling on both sides would cease precisely at meal times. Snipers and artillery gunners knew not to attack certain areas marked by flags. Often, between battles, riflemen and artillery operators on both sides would purposely shoot to miss each other. And, the troops would not fire on each other when bad weather prevailed.
Both German and Allied troops honored such unspoken rules. Indeed, this “live and let live” philosophy, while not formalized in any way between the deadly trench combatants, was nevertheless starkly evident across the entire 500-mile Western Front. One British veteran explained it this way to a comrade who was new to the trenches, “Mr. Bosche ain’t a bad fellow. You leave ’im alone; ’e’ll leave you alone.”
What took place in those trenches was nothing less than an iterated Prisoner’s Dilemma. Since the opposing soldiers routinely attacked each other’s trenches, a policy of mutual defection (always shooting and shelling to kill) was the sensible choice in the short term. This would weaken the enemy. However, the enemy troops that faced each other across that No Man’s Land did so for extended time periods. Thus, the combatants could develop conditional strategies that fit their lengthy interactions. Therefore, it should come as no surprise that, given these circumstances, a mutually cooperative policy based upon reciprocity developed among the enemy combatants.
In the trenches, reciprocity was the controlling factor. If the Germans began shelling the British at the dinner hour, then the British would immediately follow by shelling the Germans at dinner, and also at breakfast. If the British snipers suddenly become accurate marksmen in between battles, then so would the German sharpshooters. This was essentially Tit for Tat with machine guns. Throughout most of WWI, cooperation was a spontaneous, self-replicating and evolving phenomenon along the entire Western Front. This proves that cooperation is an immensely powerful strategy. In fact, it can quickly take shape, unspoken, amongst the deadliest of enemies.
- What is game theory’s Prisoner’s Dilemma
- How it proves that a “Tit-for-Tat” strategy is effective;
- Why an even more forgiving strategy could achieve even better results;
- How this applies to the concept of cooperation; and
- How a spirit of cooperation can prevail even in unpromising situations.
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| The Evolution of Cooperation Summary |
The Prisoner’s Dilemma
Consider cooperation in a few different forms. If you are in a long-term relationship with another person, does it make the most sense in terms of your personal goals to cooperate with that individual? Do you gain any advantage by showing kindness to someone who never reciprocates? What could your business gain by working with another company if it was soon going to go bankrupt? How should your country react to an overt hostile action by an enemy nation? Can your country deal with – or manipulate – this enemy so that it will cooperate? A helpful way to portray and answer such questions is to use an iterated (repeating) “Prisoner’s Dilemma.”
The original conundrum is: The police capture two criminals and separately offer them a deal. The men are not allowed to confer. If one informs against the other and confesses, he will be released from prison, and the other will get a 10-year prison term. If they both remain silent, they each will get a minor, six-month term. If both inform against the other, they each get a two-year term. The dilemma is, if both inform, they each gain less than if they remain silent. In game theory, a Prisoner’s Dilemma again provides three possible outcomes between two players: 1) Both players benefit modestly when they cooperate with each other; 2) One betrays the other and benefits handsomely if, at the same time, the other player is trying to cooperate (that player gains nothing); and 3) Both players receive minimal benefits if they betray each other simultaneously.
The Prisoner’s Dilemma always has two players. Both have two distinct choices: cooperate or betray (that is, defect or inform against the other player). Each player chooses to cooperate or not without knowing what the other player will do. Defection always pays better than cooperation. The dilemma? If both players defect, they each gain less than if they both decide to cooperate.
Picturing the Prisoner’s Dilemma
To visualize the Prisoner’s Dilemma graphically, think of a simple matrix, like a box, with two rows and two columns resulting in a square cut vertically and horizontally to form four adjoining boxes. One player selects a horizontal row, either betraying or cooperating. The choices are symbolized by letters: “R” for reward, “T” for temptation to defect, “S” for sucker’s payoff and “P” for punishment for mutual defection. The other player chooses a vertical column. Together, these choices provide one of four separate outcomes as shown in each box of the matrix:
• Box 1: Cooperation column and cooperation row – When both players cooperate, each receives R, the reward for mutual cooperation, worth three points.
• Box 2: Defection column and cooperation row – When the column player chooses to defect and the row player chooses to cooperate, the defecting column player wins. This player receives T, for yielding to temptation and defecting. This is worth five points. The row player earns S, the sucker’s payoff, worth zero points.
• Box 3: Cooperation column and defection row – When the column player chooses to cooperate and the row player chooses to defect, the winner is the defecting player. This player receives T, worth five points. The column player earns S, worth zero points.
• Box 4: Defection column and defection row – If both players defect, each receives P, the punishment for mutual defection. This is worth one point each.
As the breakdown shows, the game assigns points based on each prisoner’s specific choices. A set number of points accompany each choice, that is, R (3), S (0), T (5) and P (1). Considering these payoffs, if you are the horizontal row player, defecting is always to your advantage, no matter what choice you think the other player plans to make. Thus, defection, not cooperation, is your sensible, strategic choice. This logic also applies to the other player, who should always choose to defect, too. Thus, it is always logical for both you and your opponent to defect. However, in such a scenario (Box 4), you and your opponent receive only one point each. This is a smaller payoff than if you both cooperate, which earns three points each (Box 1). What a conundrum! Rational choices lead to poorer individual payoffs. Thus the dilemma.
There is no way around this fix. If you and your opponent take turns defecting, the outcome will, nevertheless, always be worse than if mutual cooperation prevails. The three-point reward for mutual cooperation is greater than the average (two-and-a-half points) each player gets if one earns five points for defecting and the other earns zero points for being a sucker. When the Prisoner’s Dilemma is played only once, both players logically choose defection, and win one point each, a less successful payoff than if both had cooperated. If two people play the game a finite number of times, defection remains a logical, rational choice for both. Each player assumes defection on the other player’s part based on the last move and, by extension, the next to the last move. Thus, cooperation makes no sense. In such a scenario, it just isn’t the logical choice.
The Emergence of Cooperation
This logic changes if the game is played repeatedly and indefinitely. In that case, a cooperative strategy can emerge if the individual players are not certain when the game (that is, the interaction) will reach its last move. With that unknown, cooperation may make more sense than defection. This indefinite scenario is more realistic and lifelike than one in which two individuals (or groups or businesses or nations) precisely plan a finite number of interactions. In an indefinite scenario, cooperation becomes possible because both players understand that they may be interacting with one another again and again. Choices that individual players make now can influence subsequent choices. Thus, the future affects the present. But as in life, present payoffs are always more attractive than future ones. Therefore, the payoff for the current move always seems more valuable than the payoff for the next move.
“Tit for Tat”
Considering all of this, what is the best strategy for an individual player in an iterated Prisoner’s Dilemma of indefinite length? To find out, researchers organized a tournament. They invited psychologists, economists, political scientists, mathematicians and sociologists to submit computer programs that would compete with one another. They received 14 entries.
The winning program – which also was the simplest submitted – was “Tit for Tat,” entered by Anatol Rapoport, a University of Toronto professor. Tit for Tat’s first move is cooperation. After that, it always mimics the other player’s previous moves. In a 200- move game, Tit for Tat averaged 504 points per game. Other programs that did well in the tournament all shared a common characteristic with Tit for Tat: They all were nice. They never defected on the first move. It makes sense that the nice programs performed well. The tournament included a large enough number of them to demonstrate that they worked well with each other, thus raising their average scores. Tit for Tat incorporates a high degree of what can be termed “forgiveness.” If the other player defects, and subsequently then cooperates, Tit for Tat does the same. Plus, Tit for Tat is virtually nonexploitable. If the other player defects, so does Tit for Tat, quite remorselessly.
A subsequent, actual open-for-all-entries Prisoner’s Dilemma tournament drew 62 proposals from six countries. Tit for Tat was the clear winner in the first and second rounds. Its simplicity gave it an edge over other tactics. In the second tournament, as before, “Nice guys finished first.” The programs that did best against Tit for Tat capitalized on its niceness. A hypothetical “Tit for Two Tats” game would have done even better than the actual Tit for Tat program. In it, defection would occur only if the opposing player defected on the two previous moves.
If researchers projected a large number of Prisoner’s Dilemma tournaments, the results would show that the nice programs would thrive, while the other programs (called the “meanies”) would tend to drop out eventually. Thus, cooperation, in effect, evolves over time to become a dominant strategy when repeated interactions occur. Indeed, in such circumstances, it is logical that Tit for Tat would become a universal strategy that everyone would apply.
What about the Real World?
In addition to the artificial construct of the Prisoner’s Dilemma, the efficacy of Tit for Tat applies in far more practical realms. Consider the value of reciprocity (Tit for Tat’s ruling principle) in the U.S. Congress, where “you vote for my bill and I will vote for your bill” is a philosophy that has been in play for years. Individual congressmen cannot succeed without their colleague’s assistance. Their bills would never pass. Eventually, their constituents would deem them ineffective and vote them out of office.
Other examples of the logic and sensibleness of cooperation abound, not only in terms of human relations, but also widely throughout nature. Consider the relationship of ants to acacia trees (also known as thorn trees). The acacias provide food and domicile for the ants inside their inflated thorns; the ants protect the acacias from hungry herbivores and trim competing plants. Similarly, alga and fungus join in symbiosis to form lichen. Even bacteria sometime employ a conditional strategy to thrive. Cooperation, based on reciprocity (Tit for Tat), evolves even among nonthinking life forms.
“Live and Let Live”
Activity at the Western Front in France and Belgium during World War I provided a vivid example of the all-consuming cooperative power of reciprocity among human beings. Enemy soldiers shooting from trenches fought gruesome and bloody battles against each other for years, often for gains of only a few small yards of territory. But in between the actual battles, enemy soldiers commonly exhibited remarkable restraint about attacking each other. German soldiers would walk about, in clear sight and within rifle range, but the Allies would not shoot at them. This applied equally to Allied troops. Often, shelling on both sides would cease precisely at meal times. Snipers and artillery gunners knew not to attack certain areas marked by flags. Often, between battles, riflemen and artillery operators on both sides would purposely shoot to miss each other. And, the troops would not fire on each other when bad weather prevailed.
Both German and Allied troops honored such unspoken rules. Indeed, this “live and let live” philosophy, while not formalized in any way between the deadly trench combatants, was nevertheless starkly evident across the entire 500-mile Western Front. One British veteran explained it this way to a comrade who was new to the trenches, “Mr. Bosche ain’t a bad fellow. You leave ’im alone; ’e’ll leave you alone.”
What took place in those trenches was nothing less than an iterated Prisoner’s Dilemma. Since the opposing soldiers routinely attacked each other’s trenches, a policy of mutual defection (always shooting and shelling to kill) was the sensible choice in the short term. This would weaken the enemy. However, the enemy troops that faced each other across that No Man’s Land did so for extended time periods. Thus, the combatants could develop conditional strategies that fit their lengthy interactions. Therefore, it should come as no surprise that, given these circumstances, a mutually cooperative policy based upon reciprocity developed among the enemy combatants.
In the trenches, reciprocity was the controlling factor. If the Germans began shelling the British at the dinner hour, then the British would immediately follow by shelling the Germans at dinner, and also at breakfast. If the British snipers suddenly become accurate marksmen in between battles, then so would the German sharpshooters. This was essentially Tit for Tat with machine guns. Throughout most of WWI, cooperation was a spontaneous, self-replicating and evolving phenomenon along the entire Western Front. This proves that cooperation is an immensely powerful strategy. In fact, it can quickly take shape, unspoken, amongst the deadliest of enemies.
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