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Revision 6 . . January 29, 2004 5:22 am by Darius Sokolov
  

Difference (from prior major revision) (author diff)

Changed: 96c96,98
expected utility in any period is then eu = 1/3 + 1/3 (1+u) + 1/3 p + 1/3 (1-p) DEATH
expected utility in any period is then eu = eu = 1/3 + 1/3 (1+u) + 1/3 p + 1/3 (1-p) DEATH

(or eu = 2/3 + 1/3 p + 1/3 (1-p) DEATH if you give away surplus)

Added: 141a144,172



sharing

To start with - Imagine a small, closed network (stereotypical ye olde village) where everyone knows what everyone else does.

simplifying idea 1 - agents can choose between strategies of being either 'sharing' or 'greedy' every time they get surplus.

sharing agents are known as such, they are upstanding citizens of good reputation. being a sharer is like being a member of a good citizens' insurance club. each period, sharers in surplus will give to fellow-sharers in need.

it is still possible to die. there may be a period where more sharers are in need than get surplus. then needy sharers draw straws. (1-p) above is the probability of this happening and an agent drawing the short straw.

on the other hand, if there is a net surplus amongst sharers, they could have a party with the extra hedons. (can add a term to EU equation - with symmetric distribution of RGC's there is equal chance of party as of death).

if you are not a member of the sharing club, p = 0.

still, it might be preferable to be greedy for an agent who - has little care for the future,

agents will choose sharing if EUs > EUn + u

(note - when is this choice made? perhaps behind a veil of ignorance at some zero period. then formulas need modifying - the immediate pay-off from greed is not u but 1/3 (u + DEATH), but basic idea is the same)

i.e. As eus > An eun + u

i.e. if As/3 (2 + p + (1-p)(DEATH + PARTY) ) > An/3 (2 + u + DEATH) + u

where Ai = ((1 - (1/ (1+d)^Li) / d)) i= share, not share

is the 'annuity factor', and sharers have higher life expectancy Ls > Ln so As > An

Added: 142a174
more likely to choose greed if you are a reckless agent with a great lust for consumption (high u), little care for the future (high d), and no fear of death.

Added: 143a176
there is also a strategic factor - p is higher for a larger pool of sharers (though conversely the chance and value of a 'sharers party' is lower)

Added: 144a178
simplifying idea 2 - alternatively, reputation could be much more short lived. sharing one time only insures you for the next time you are in need (something like tit for tat).

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