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#11
05-09-2007, 06:56 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
[ QUOTE ] [ QUOTE ] Not surprising, (although its mildly surprising I agree with Nielsio on something, lol) because the nature of most of our day to day experiences are zero sum. Until John Nash came along some very bright people didnt realize that you could prove that non-zero sum but non-cooperative games could reach an equilibrium, and if there were no such equilibrium there would be no win-win solutions. [/ QUOTE ] Well, I think the question is while the examples given by OP (increased number of billionares, Walmart), while they do not necessarily have to have a "loser", they don't necessarily have to be "win-win", and if you look at people that know what they are talking about criticize these things they don't do it from a zero sum perspective (though I agree you do hear stuff like what the OP referred to a lot) [/ QUOTE ] I think what youre saying is that while every non-cooperative situation has a Nash equilibrium, that equilibrium isnt always reached, which I think is true. Prisoner's dilemma as an example. One of the two criminals eventually is too stupid/gullible to keep his mouth shut. [/ QUOTE ] I'm not sure you fully understand the Nash equilibrium. In the PD, defection is the equilibrium. 
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#12
05-09-2007, 07:15 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] Not surprising, (although its mildly surprising I agree with Nielsio on something, lol) because the nature of most of our day to day experiences are zero sum. Until John Nash came along some very bright people didnt realize that you could prove that non-zero sum but non-cooperative games could reach an equilibrium, and if there were no such equilibrium there would be no win-win solutions. [/ QUOTE ] Well, I think the question is while the examples given by OP (increased number of billionares, Walmart), while they do not necessarily have to have a "loser", they don't necessarily have to be "win-win", and if you look at people that know what they are talking about criticize these things they don't do it from a zero sum perspective (though I agree you do hear stuff like what the OP referred to a lot) [/ QUOTE ] I think what youre saying is that while every non-cooperative situation has a Nash equilibrium, that equilibrium isnt always reached, which I think is true. Prisoner's dilemma as an example. One of the two criminals eventually is too stupid/gullible to keep his mouth shut. [/ QUOTE ] I'm not sure you fully understand the Nash equilibrium. In the PD, defection is the equilibrium. [/ QUOTE ] Actually my understanding of the NE with regard to PD is that there are multiple equilbriums, but I could be wrong. Edit: yup. I was wrong. Cooperation is Pareto-optimal while the single NE of defection is sub-optimal. My bad. Its been ~40 years since game theory.
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#13
05-09-2007, 07:20 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] [ QUOTE ] Not surprising, (although its mildly surprising I agree with Nielsio on something, lol) because the nature of most of our day to day experiences are zero sum. Until John Nash came along some very bright people didnt realize that you could prove that non-zero sum but non-cooperative games could reach an equilibrium, and if there were no such equilibrium there would be no win-win solutions. [/ QUOTE ] Well, I think the question is while the examples given by OP (increased number of billionares, Walmart), while they do not necessarily have to have a "loser", they don't necessarily have to be "win-win", and if you look at people that know what they are talking about criticize these things they don't do it from a zero sum perspective (though I agree you do hear stuff like what the OP referred to a lot) [/ QUOTE ] I think what youre saying is that while every non-cooperative situation has a Nash equilibrium, that equilibrium isnt always reached, which I think is true. Prisoner's dilemma as an example. One of the two criminals eventually is too stupid/gullible to keep his mouth shut. [/ QUOTE ] I'm not sure you fully understand the Nash equilibrium. In the PD, defection is the equilibrium. [/ QUOTE ] Actually my understanding of the NE with regard to PD is that there are multiple equilbriums, but I could be wrong. [/ QUOTE ] In the IPD, the equilibrium is cooperation.
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#14
05-09-2007, 07:22 PM
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Re: Is zero-sum the default economic position?
IPD was in the graduate level course lol
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#15
05-09-2007, 07:29 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
I explained to him that this is not the case, as most of a billionaire's "billions" are not locked away in a savings account, but are invested in productive capital; the actual money is still out there in circulation, and the "money" that the billionaire possesses is producing goods and services for others. [/ QUOTE ] Economics question from an admitted econ noob: If that billionaire's "billions" were instead in the hands of a larger middle class, that money would still be out there in circulation producing goods and services for others, right? I mean everyone I know in the "middle class" has at least a 401k or a Roth IRA.
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#16
05-09-2007, 07:37 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] [ QUOTE ] [ QUOTE ] Not surprising, (although its mildly surprising I agree with Nielsio on something, lol) because the nature of most of our day to day experiences are zero sum. Until John Nash came along some very bright people didnt realize that you could prove that non-zero sum but non-cooperative games could reach an equilibrium, and if there were no such equilibrium there would be no win-win solutions. [/ QUOTE ] Well, I think the question is while the examples given by OP (increased number of billionares, Walmart), while they do not necessarily have to have a "loser", they don't necessarily have to be "win-win", and if you look at people that know what they are talking about criticize these things they don't do it from a zero sum perspective (though I agree you do hear stuff like what the OP referred to a lot) [/ QUOTE ] I think what youre saying is that while every non-cooperative situation has a Nash equilibrium, that equilibrium isnt always reached, which I think is true. Prisoner's dilemma as an example. One of the two criminals eventually is too stupid/gullible to keep his mouth shut. [/ QUOTE ] I'm not sure you fully understand the Nash equilibrium. In the PD, defection is the equilibrium. [/ QUOTE ] Actually my understanding of the NE with regard to PD is that there are multiple equilbriums, but I could be wrong. [/ QUOTE ] In the IPD, the equilibrium is cooperation. [/ QUOTE ] Technically speaking, some versions of the IPD have multiple equilibria. Both players always defecting is always an equilibrium. In cases where the game is infinitely or indefinitely repeated, cooperation becomes an equilibrium.
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#17
05-09-2007, 07:49 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] Not surprising, (although its mildly surprising I agree with Nielsio on something, lol) because the nature of most of our day to day experiences are zero sum. Until John Nash came along some very bright people didnt realize that you could prove that non-zero sum but non-cooperative games could reach an equilibrium, and if there were no such equilibrium there would be no win-win solutions. [/ QUOTE ] Well, I think the question is while the examples given by OP (increased number of billionares, Walmart), while they do not necessarily have to have a "loser", they don't necessarily have to be "win-win", and if you look at people that know what they are talking about criticize these things they don't do it from a zero sum perspective (though I agree you do hear stuff like what the OP referred to a lot) [/ QUOTE ] I think what youre saying is that while every non-cooperative situation has a Nash equilibrium, that equilibrium isnt always reached, which I think is true. Prisoner's dilemma as an example. One of the two criminals eventually is too stupid/gullible to keep his mouth shut. [/ QUOTE ] I'm not sure you fully understand the Nash equilibrium. In the PD, defection is the equilibrium. [/ QUOTE ] Why wouldn't the Nash equilibrium it depend at least a little bit on the relative penalties? If the penalties range from going to bed without supper to life imprisonment, can't a scenario be constructed where the best choice for both is silence? I have never understood why the optimal strategy is stated without such things being taken into account. Haven't read it in a while though. Example, 2 prisoners each 25 years old: Punishment 1: both prisoners remain silent = sent to bed without supper tonight Punishment 2: both prisoners confess = 40 years in prison Punishment 3: one prisoner confesses and testifies against the other = no penalty for himself, but life imprisonment for the silent prisoner In the above scenario, the optimum strategy is clearly to risk the negligible punishment of being sent bed without supper tonight along with the chance of the somewhat worse alternative of life in prison compared to 40 years in prison (release at age 65). There isn't a great deal of difference between spending one's years from 25-65 in prison, versus life in prison; but there is a huge difference between being sent to bed without supper and either of the other alternatives. If the 40 years in prison versus life in prison isn't a convincing comparison then change the example to 80 lashes versus 85 lashes...versus going to bed without supper for one night (or versus one lash). Can anyone explain why the oft-touted "answer" to the non-iterative PD neglects the consideration of the relative severity of outcomes?
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#18
05-09-2007, 07:53 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
[ QUOTE ] I explained to him that this is not the case, as most of a billionaire's "billions" are not locked away in a savings account, but are invested in productive capital; the actual money is still out there in circulation, and the "money" that the billionaire possesses is producing goods and services for others. [/ QUOTE ] Economics question from an admitted econ noob: If that billionaire's "billions" were instead in the hands of a larger middle class, that money would still be out there in circulation producing goods and services for others, right? I mean everyone I know in the "middle class" has at least a 401k or a Roth IRA. [/ QUOTE ] Doesnt it depend on the marginal utility of the additional dollars for the members of the MC? Eg. if the billions, once spread over a hundred million or so middle class, results in $30 per family, that money is more likely to be spent than invested? A lot of IRAs are maxed out, and a lot of 401(k) participants dont take advantage of their full match, so their $30 is going for a bottle of wine, not into the market. Even if they save it, that isnt the same as investing it.
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#19
05-09-2007, 08:01 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
Even if they save it, that isnt the same as investing it. [/ QUOTE ] It is. Increased savings shifts the supply of money in the loanable funds market. Money which will then be borrowed by companies to buy new factories, etc...
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#20
05-09-2007, 08:05 PM
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Re: Is zero-sum the default economic position?
[ QUOTE ]
Technically speaking, some versions of the IPD have multiple equilibria. Both players always defecting is always an equilibrium. In cases where the game is infinitely or indefinitely repeated, cooperation becomes an equilibrium. [/ QUOTE ] When repetition is introduced, defection ceases to be pareto-optimal and cooperation becomes pareto-optimal; it just requires a little more planning than the the usual "one-step," single iteration moves that game theory likes to concern itself with.
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Linear Mode
