. Author manuscript; available in PMC: 2016 Jun 1.

Published in final edited form as: J Am Stat Assoc. 2014 Jun 27;110(510):711–722. doi: 10.1080/01621459.2014.926815

Table 1.

True expected utilities in Scenario 4 assuming that θ^true is known. q₁(d₁, θ^true) = the true expected total utility. Entries under d₂ in columns 4–8 are the true expected cycle 2 utilities, q₂(d₂, θ^true). Expected utilities in grey are those for d₂ violating the no-escalation-after- Y₁ = 1 rule. Expected utilities in italics are those for unacceptable d₂ based on the utility-based criterion.

d ₁	q₁(d₁, θ^true)	(Y₁,Z₁)						$d_{2}^{o p t}$
d ₁	q₁(d₁, θ^true)	(Y₁,Z₁)	1	2	3	4	5	$d_{2}^{o p t}$
1	66.19	(0,0)	37.32	41.40	41.85	38.54	29.66	3
		(0,1)	48.18	55.07	56.80	54.00	45.04	3
		(1,0)	30.60	33.58	33.07	29.57	23.27	NT
		(1,1)	41.20	47.16	47.96	44.80	38.23	NT
2	73.38	(0,0)	36.53	40.33	40.66	37.30	28.38	3
		(0,1)	45.06	51.39	52.92	50.08	41.15	3
		(1,0)	30.13	32.88	32.26	28.70	22.28	NT
		(1,1)	38.36	43.71	44.31	41.12	34.54	1
3	80.61	(0,0)	35.98	39.49	39.70	36.30	27.17	3
		(0,1)	43.31	49.20	50.62	47.73	38.69	3
		(1,0)	30.29	32.82	32.12	28.43	21.53	NT
		(1,1)	37.34	42.27	42.75	39.46	32.48	2
4	69.71	(0,0)	37.17	40.90	41.40	38.19	28.65	3
		(0,1)	44.37	50.46	52.14	49.47	40.09	3
		(1,0)	32.13	34.89	34.39	30.68	22.91	NT
		(1,1)	39.17	44.32	45.02	41.74	33.91	3
5	68.16	(0,0)	38.08	42.02	42.80	39.83	30.06	3
		(0,1)	45.26	51.52	53.46	51.04	41.51	3
		(1,0)	33.00	35.88	35.52	31.85	23.69	2
		(1,1)	40.05	45.32	46.16	42.95	34.75	3