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


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.