I found the articles on Game Theory rather fun to see the outcomes. It seems to me the natural flow of a Game and its termination rules, what the Brams article called Alternative, would be a natural assessment of how rational beings would play Game Theory. In the same article it also addresses that Kennedy and his advisers, as well as the Soviets, acted as rational players for the Cuban Missile Crisis. This is obvious since we did not attack with nukes and the Soviet players did not set up us the bomb during the Cuban Missile Crisis.
One of the articles I believe addressed this by reporting that the U.S. advising committee for the crisis evaluated all possible out come with Game Theory and all possible avenues, effectively creating what Nash called a Game Tree. In the two by two schematics that the articles proposed the Nash equilibrium occurred when both sides had an equal ordinal value. Nash equilibria of the Cuban Missile Crissis occurred when both sides stood down, a compromise, or when nuclear war happened. Then if one were to take into account how the world views the actions one would change the dynamic of Game Theory into Alternative Theory. This involves even more rationality on both sides to show a dynamic flow of what choice will result to.
But suppose that neither side was rational, and that instead of nuclear warfare you have two prisoners. If both were rational beings and both are being interrogated for a crime they are suspects for then the rational outcome would be both "ratting" out the other. Both would get a reduced sentence but neither would be ultimately free. If both withheld snitching then both would walk away scott-free. The other 2 possibilities are one rats but the other doesn't. In 3 out of the 4 outcomes someone admits to the crime so the other, rational person, would opt for also admitting. This is all fun and games (theory) but what happens if humans aren't rational?
In the post I made prior to this I referenced a web article on a Scientific American addressing the uncertainty of irrational people. It comes from a phenomena in real life situations of the prisoner's dilemma that there is a significant non-zero occurrence of both parties not snitching on the other party. Classical (rational) thought says this to be the least probable occurrence yet the article states it to happen about 40% of the time. That leaves the other 60% to be split up among 3 other options resulting in the phenomena opposing that of the classical thought. While Game and Alternative Theory are great tools to appraise an ordinal relation (to steal a term coined by Nash) between two cases there is a certain uncertainty due to human actions that it fails to encompass.
Which begs the question; was the game theory used during the Cuban Missile Crisis a lucky fluke? Or were so many lives and variables on the line that both sides were forced to be the most rational beings possible to make game theory work? Or is there a deeper side to game theory that has yet to be found/refined?
I think you allude to a major problem in relying on game theory to solve serious problems when you said that "there is a certain uncertainty due to human actions that it fails to encompass". I mean, using Nash's equilibrium kind of assumes that all players are looking at the problem through the same lens; their strategies for "winning" the game are the same. But what defines a strategy? And how can we tell which kind (if any) of real world situation game theory should be applied to? On paper, game theory seems like a wonderful way of predicting behavior, but in reality there is no way to know for certain what another player is going to do. It is a great tool for understanding and predicting "logical behavior", but in comparison to real world human behavior it falls short. Personally, I think that attempting to predict human behavior is a waste of time; game theory needs not to be refined any further, at least in regards to predicting human behavior becuase it is simply impossible to predict with 100% accuracy.
ReplyDeleteI thought it was interesting when pride got brought into the prisoners’ dilemma. It ties in a human characteristic into mathematics,having pride changes the outcomes of benefits and losses. Through this how it couldn’t be redone or if the prisoners’ were able to communicate how this would affect the outcomes. I agree with Brandon it is a way to predict logical behavior, but how often do humans work on logical behavior? Through education I think it’s been easier to see that you have no real control on a students behaviors. You can try to influence, reinforce, model appropriate behaviors but there is nothing another human can to do control or predict another humans response every time or trial. Each and every individual has the choice, most of the time, to control how they will respond or act. I think this can also be tied in to how in game theory we have to understand how good people can make the world worse, and how if we change how we behave this could negatively affect our society. They give the example of forgiving and forgetting crimes, however there is no way of knowing how individuals would actually react. Last comment, reading about game theory is all probability of how humans will react in drastic events. It makes me nervous while reading about all of the situations, and what could happen and where how far will we take mathematics.
DeleteLike you all have said, game theory does have its shortcomings and a lot of analysts realize that. My paper for this class involves game theory and talks about some of the issues with game theory, primarily that the human variable is, well, too variable, much like Jamison is saying. Dr. Crist said in class on Tuesday that the assumption that all players in the game are rational actors is a simplifying assumption because otherwise things would be too complex to model via game theory. This makes me curious why people are so insistent on using game theory. I’ll admit that I am one of those people that finds game theory intriguing, and I think that it is a good method to roughly estimate which outcomes are more likely and what responses are best, but I don’t think I would ever rely on it to dictate my decisions. As ironic as this might sound, there is too much uncertainty in this predictive model for my liking. We like to think we are rational beings, but in reality we are not and that adds a completely different spin to game theory.
ReplyDeleteIn response to Brandon: Although there is always a degree of uncertainty in human behavior, I think it is important to realize that game theory is not an attempt to fully predict behavior but instead evaluate probable actions and outcomes. Based on my understanding, game theory is used to decipher the consequences of a move and the potential progression of the game following that move. I like the chicken analogy of game theory for the Cuban missile crisis and would like to point out that the players in this particular game could only play chicken because they had cars, a.k.a. missiles and nukes. This relates to the race between the Soviets and the U.S. for nuclear bombs and the super nuke, as mentioned in the previous readings. The necessity for nuclear weapons seemed to stem from the likelihood of the Soviets possessing such weapons. In this way, nuclear weapons were more for defensive purposes and to look tough. Human reason makes us think twice about swinging a bat at someone who also has a bat, especially if his or her bat is bigger. Due to the number of variables and tools available to both the Americans and Soviets I would argue game theory in the Cuban missile crisis was more like a game of chess than a game of chicken. It is the rationality of humans that makes game theory relevant to various events and although irrational behavior occurs occasionally, it is in our nature to act in a rational manner, which is why game theory is so useful and applicable to real life situations.
ReplyDeleteAll the prior discussion was great. One aspect of analyzing the results of game theory that I feel was left out was the trust you must have (or lack there of) in your fellow "player." The decisions of the players are mainly thought in terms of the relationship between their consequences. However an overlooked aspect in the decision making is the amount of trust someone displays in the other.
ReplyDeleteKruschev's article highlights the importance of trust in fellow players, just as his father and Eisenhower started to trust one another. I understand that game theory excepts both players as rational, but is there a mathematical model out there that relates the person-person relationship of trust? Furthermore, can we base the trustworthiness of someone on mathematics? It seems like this model should incorporate past behavior, but is it fair to judge people on past behavior using an equation?
On this point, it seems game theory would advocate that the consequences of a player's decisions are tied to the player. It can make a value judgement of who someone is based on how they act. Mathematics seems to have a hard time handing out second chances.
Trust is a huge part of game theory. I was thinking about the simplified version of game theory Dr. Christ gave us in class and it seemed like in order to get anywhere, there needed to be a certain level of understanding of the opponent. I don't know if you necessarily need to 'trust' your opponent but you definitely need to know how their minds work. I think it's safe to say that in the simplified version the best option for both parties is the 'no war' option. However, this is difficult because it leaves each party with a sense of vulnerability. The better you understand your opponent, the less vulnerable you will feel. If there are communications between the two parties then I think trust comes into play as you have to trust your opponents word that they will do what was promised.
DeleteJamison, that’s interesting that you suggest that the game theory used during the Cuban Missile Crisis could have been a lucky fluke. Game theory is effective as a predictive measure only so long as both players act rationally. However, in reality, people are not always rational. According to game theory, the least probable outcome in the prisoner’s dilemma is for neither inmate to confess. However, as you pointed out, in real life situations, this tends to happen 40% of the time, suggesting that in such situations, reason is not the only acting force. Emotions can come into the picture any time the stakes are high. I think one of the main reasons that this statistic is so high, however, is that each prisoner may presume that the other prisoner will be acting according to their emotions as opposed to their reason. Under the premise of reason, the best decision would be to confess. However, if one inmate feels sure that the other inmate will act according to reason, they can presume that the other inmate will choose to not confess. If the first inmate feels certain that the other will not confess, then the most rational decision is to not confess.
ReplyDeleteWhen applying Game Theory to the Cuban Missile Crisis, then, it is important to consider what state the opponent will be in when making their decision. Whereas it may be appropriate to assume many prisoners do not act according to reason, in a situation such as this, it is pretty safe to assume that either opponent will turn to reason to resolve the problem. Sure, emotions ran high during the Cuban Missile Crisis. The general population lived in constant fear that nuclear war would break out any day. Each side painted the other as evil. Americans were taught to view Russians as evil communists, and the Russian population tended to view Americans with a similar sense of disdain. However, at the end of the day, reason was the only sure thing these leaders had to turn to. They were well aware of the gravity of the situation, and knew that they could not act rashly. Each side took a risk by deciding to withdraw their weapons. However, this was a calculated risk, and logically stood as the best option. In real life, things do not always play out according to reason supported by Game Theory. Game Theory is not meant to be predictive. Instead, it suggests probabilistic outcomes. In that sense, the outcome could be considered lucky fluke, although it seems to be more “likely” than “lucky.”
Jamison,
ReplyDeleteI agree that there is some uncertainty as to whether or not the players are going to act rationally in any given game. Even if a player acts irrationally, however, we can still make claims as to what other rational players might do in reaction to the seemingly irrational player. This is exactly at the heart of any madman scenario. Say you and another person are put in a game of atomic chicken and you have some reason to believe the other player may not act rationally. If you have some previous experience with the person you may be able to estimate on previous experience the likelihood the player will do something that may be detrimental to both players (the cold war example might be one side might nuke Berlin despite having military and economic investments in the city... not to mention the population). I'm not sure what would technically be the best strategy against such a player but one way to play would be to attempt to avoid the risk is to appease the irrational player with the hope they don't go ahead with their threat. Another may be to call their bluff, although the risks are much more significant with such an option.
My issue with the presumption that game theory will always work is the assertion that it implies that the beings involved are rational. Game theory seems to only be effective when dealing with rational people on issues that they will determine the outcome for based on the bias of being a rational thinker. The idea of game theory is likely to work out for most situations, where rationalism is emphasized but in a case where rationalism is replaced by irrational thinking due to indecision brought about by unplanned circumstances, it would seem that game theory has the possibility for unaccounted for outcomes. This is just a thought; I wanted to post something a bit different from what everyone was already posting so I tried a counter argument.
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