¥E Å peN – p – (1-p)eN +
(1-p)
–As N ˆ infinity, the first term becomes very large
(positive), the third term very large (negative),
and the other terms are negligible by
comparison.
¥So for Ron to
have the maximum winnings,
he should choose p = 1:
–E Å eN, which will become arbitrarily large as N ˆ infinity, no matter how small e is.