# SimulationResults

*ThoughtStorms Wiki*

The best way to understand the StrategicVotingModel and some of its conclusions is by plugging in example distributions F(C).

- Excel SpreadSheet for this model : http://www.nooranch.com/synaesmedia/optimaes/spreadsheets/strategic_voting.xls

Agents’ cost values are identically and independently distributed with distribution function F(c). The probability that any randomly selected agent i will contribute in equilibrium is then:

Prob (ci =< c’*) = F(c’*)

So the probability that exactly n^{-1} out of N-1 agents will contribute is a binomial probability with sample size N-1 and parameter F(c’*).

p (F, c’*) = Wn ^{-1} (N-1, F(c’*))

(I don't know how to write the binomial formula out in wiki.)

So the equilibrium condition is:

c’* = p (F, c’*)

c’* = Wn ^{-1} (N-1, F(c’*))

For F (c) use eg. a normal distribution.

To look at equilibria, then, set up chart with cost on x axis and probability on y axis. Graph the function p (c') and a 45 degree line where p = c. Equilibria occur where the two lines meet.

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