# Chases and Escapes: The Mathematics of Pursuit and Evasion

By Paul J. Nahin | Go to book overview

Appendix I
Solution to the Challenge
Problem of Section 4.4

If B and R use probability distributions (p, 1 − p) and (q, 1 − q), respectively, then from the pay-off matrix of figure 4.4.6 the average game value can be written as either

V(p,q) = p[4 ·q +1 ·(1 −q)] +(1 − p)[3 ·q +4 ·(1 −q)],

or

V(p,q) = q[4 · p +3· (1 − p)] +(1 −q)[1 · p +4 ·(1 − p)],

with both expressions reducing to

V(p,q) = 4-3pq +4pq.

Figure I clearly shows a minimax point, which can be determined from

and

-222-

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