Continual Reassessment Designs with Early Termination by O'Quigley J.

By O'Quigley J.

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Proof of Lemma 2 From the text, the objective probability of a match in an excess demand equilibrium is: (1− β) s( ps ) h(π ,β ) = where d(p b ) − βs( p s) ps = βp b + (1− β )p* − m(µ(β ))(1− β)(1− π) p b = πp * + (1− π )b p* = ωb + (1− ω )c. At an excess demand equilibrium, d(p* ) > s( p* ). This implies that: (1− β) s( p* ) / d( p* ) h(1, β ) = <1 1− βs( p* ) / d(p* ) Suppose that β∈[0, 1). As π approaches 0 from above, h(π,β) remains positive so that h(π,β) > π. 1) π = h(π,β) 32 has a solution π[β] in the open interval (0,1).

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Rubinstein, Ariel (1982), “Perfect Equilibrium in a Bargaining Model”, Econometrica, 50, 97-109. ”, Econometrica, 67, 741-82. Weingast, Barry 1993 “Constitutions as Governance Structures: The Political Foundations of Secure Markets,” Journal of Institutional and Theoretical Economics 146, no. 1, 286-311. World Economic Forum (1997), The Global Competitiveness Report 1997 (Geneva: World Economic Forum). 8), note that as µ → µ , m(µ)→ 0 so -µ/m(µ)→∞ . As µ → µ , -µ/m(µ) becomes negative. Given a piecewise continuous probability density function f(µ), -µ/m(µ) is monotonic and continuous in µ.

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