About Display Costs

Costs to fixed strategists: Recall that all individuals playing a fixed cost strategy have "decided" before the contest as to the maximum amount that they will pay out in display costs. If their opponent does not quit at the time that that fixed amount is reached, then they lose the amount equal to their fixed strategy. If their opponent quits first, they lose what their opponent was willing to pay.

Now, we have assumed throughout this discussion that costs are a linear function of time:

eq. 2: m = x = k * t

where m or x have the same units as V (and therefore the constant k has units of V / t).So, as contests get longer (i.e.,neither opponent quits) costs increase. Note that it is quite possible that some other function might determine cost; we use this for simplicity and it certainly occurs in many situations.

Here is a plot of eq. 4 for all costs (m or x ) between 0 and 5 where k = 1:

Note that this graph can be viewed as either:

• the cost that any fix(x) strategist is willing to pay (up to with a maximum duration of 5 )
• or the accumulation of costs (m) for an individual (or for a population of individuals) as it (they) display(s) from t = 0 up to any time t.