"As you know, sir, in the heat of action, men are likely to forget where their best interests lie and that their emotions carry them away." (The Maltese Falcon (1941))
On Thursday, my game theory professor gave three reasons why people fail to behave rationally in the real world (the theory of "bounded rationality"): inability to calculate a rational course of action, inability to implement a rational course of action, and emotion overcoming a rational course of action.
Emotion definitely has the capability to overcome rational-seeming courses of action. And that's not always a bad thing (even though some part of me still wants to believe that it is). "Le cœur a ses raisons que la raison ne connaît point." I would suspect that in interacting with other people, emotion is a much larger barrier to acting rationally than inability to calculate or implement a rational choice.
So, I am currently taking a course of action that could definitely be perceived as irrational. Is it? Who knows. And I don't really care. Living life is a lot more fun than analyzing it.
Saturday, April 14, 2007
Wednesday, February 14, 2007
Game Theory and Relationships
The prisoner's dilemma is a well-known construct in game theory, describing a game in which each player has the choice to "cooperate" or "defect". In the classic construction, the players are suspects in some crime. The prosecutors offer each of them a deal: if one person betrays the other ("defects") and one stays silent ("cooperates"), the defector will go free while the cooperator gets ten years in jail. However, if both defect, each will get five years. If each stays silent, the prosecutors don't have enough evidence to convict, and each receives a sentence of one year on a minor charge.
Clearly, both players would be best off if each chose to cooperate (the Pareto efficient outcome). However, the best strategy is for each to defect. Why? Consider one player. If his accomplice cooperates, his best strategy is to defect, receiving zero years in jail instead of one. If his accomplice defects, his best strategy is again to defect, receiving five years instead of ten. Since both players face the same choices, the equilibrium result is that both players defect.
I suspect that a similar situation arises when two people are deciding whether to start a relationship or not. Consider the following situation: If both players choose "relationship", each receives a utility (or well-being or satisfaction) of 50. If both players choose "no relationship", each receives utility of 40. However, if one chooses "relationship" and one chooses "no relationship", the "relationship" player, broken-hearted, receives utility of -30, while the "no relationship" player, free to pursue a new relationship and glad the other person is finally out of the situation, receives utility of 60. This set-up leads to the same outcome; both players will choose "no relationship" even though they would both be better off by choosing "relationship". Thus no rational person should ever start a relationship. This seems to be a rather depressing outcome.
There is a possibility, however, in a prisoner's dilemma situation, that both players choosing to cooperate is an equilibrium outcome (that is, one from which neither player has an incentive to deviate). If the game is played repeatedly (an infinite or unknowable number of times), each player's choice in the current round will likely have an effect on the other player's choice in future rounds. That is, suppose one player violates the trust of the other by choosing to defect. While this player may obtain a better outcome this round, the other player is likely to "punish" him in the future by also defecting. This leads to an incentive for both players to cooperate every round, and this will work as long as both players continue to cooperate every time.
One of the best possible strategies for this "iterated" prisoner's dilemma is called "tit-for-tat". Essentially, the strategy is to cooperate in the first round, then in each future round, do whatever the other player did the round before. If both players choose tit-for-tat, each will cooperate forever. However, any deviation is likely to lead to an endless string of defections. Tit-for-tat was the "winner" in a tournament of strategies submitted by various academics, conducted in the 1980s. It turns out that a slightly better strategy is "tit-for-tat with forgiveness". This allows a small probability of choosing to cooperate even though the other player has defected, potentially breaking a long string of defections.
So what does this mean for relationships? It means that a "relationship" outcome is possible. Making the reasonable assumption that each person will re-evaluate their status in the relationship from time to time, a strategy of "always choose relationship" may be viable in the long run. The game certainly has the potential to be played an infinite or unknowable number of times, continuing through this life and beyond.
However, this strategy depends on one's ability to trust the other person to follow the same strategy. This trust can be difficult to establish, and once broken, can be very difficult to re-establish, potentially leading to the suboptimal outcome. Also, it's generally at the beginning of a relationship when each person has the most difficulty learning to trust the other, and potentially leading to an early loss of trust and permanent outcome of "no relationship". It may be that a rational person always chooses "no relationship" to avoid ever receiving the negative utility of a broken heart.
But clearly this is not what I'd like to believe (I don't think anyone would). Do people simply act irrationally when it comes to these things? I don't like that answer either. Perhaps it just takes a circumstance in which each person somehow decides to have perfect (or almost-perfect) trust in the other. I'm not sure. Perhaps someday I'll figure it out.
Clearly, both players would be best off if each chose to cooperate (the Pareto efficient outcome). However, the best strategy is for each to defect. Why? Consider one player. If his accomplice cooperates, his best strategy is to defect, receiving zero years in jail instead of one. If his accomplice defects, his best strategy is again to defect, receiving five years instead of ten. Since both players face the same choices, the equilibrium result is that both players defect.
I suspect that a similar situation arises when two people are deciding whether to start a relationship or not. Consider the following situation: If both players choose "relationship", each receives a utility (or well-being or satisfaction) of 50. If both players choose "no relationship", each receives utility of 40. However, if one chooses "relationship" and one chooses "no relationship", the "relationship" player, broken-hearted, receives utility of -30, while the "no relationship" player, free to pursue a new relationship and glad the other person is finally out of the situation, receives utility of 60. This set-up leads to the same outcome; both players will choose "no relationship" even though they would both be better off by choosing "relationship". Thus no rational person should ever start a relationship. This seems to be a rather depressing outcome.
There is a possibility, however, in a prisoner's dilemma situation, that both players choosing to cooperate is an equilibrium outcome (that is, one from which neither player has an incentive to deviate). If the game is played repeatedly (an infinite or unknowable number of times), each player's choice in the current round will likely have an effect on the other player's choice in future rounds. That is, suppose one player violates the trust of the other by choosing to defect. While this player may obtain a better outcome this round, the other player is likely to "punish" him in the future by also defecting. This leads to an incentive for both players to cooperate every round, and this will work as long as both players continue to cooperate every time.
One of the best possible strategies for this "iterated" prisoner's dilemma is called "tit-for-tat". Essentially, the strategy is to cooperate in the first round, then in each future round, do whatever the other player did the round before. If both players choose tit-for-tat, each will cooperate forever. However, any deviation is likely to lead to an endless string of defections. Tit-for-tat was the "winner" in a tournament of strategies submitted by various academics, conducted in the 1980s. It turns out that a slightly better strategy is "tit-for-tat with forgiveness". This allows a small probability of choosing to cooperate even though the other player has defected, potentially breaking a long string of defections.
So what does this mean for relationships? It means that a "relationship" outcome is possible. Making the reasonable assumption that each person will re-evaluate their status in the relationship from time to time, a strategy of "always choose relationship" may be viable in the long run. The game certainly has the potential to be played an infinite or unknowable number of times, continuing through this life and beyond.
However, this strategy depends on one's ability to trust the other person to follow the same strategy. This trust can be difficult to establish, and once broken, can be very difficult to re-establish, potentially leading to the suboptimal outcome. Also, it's generally at the beginning of a relationship when each person has the most difficulty learning to trust the other, and potentially leading to an early loss of trust and permanent outcome of "no relationship". It may be that a rational person always chooses "no relationship" to avoid ever receiving the negative utility of a broken heart.
But clearly this is not what I'd like to believe (I don't think anyone would). Do people simply act irrationally when it comes to these things? I don't like that answer either. Perhaps it just takes a circumstance in which each person somehow decides to have perfect (or almost-perfect) trust in the other. I'm not sure. Perhaps someday I'll figure it out.
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