which again is equal to V — (1 — pL) exp (—1/2 + T/c) c. Hence, i is indifferent to all
t E (0, —c/2 + T] U {T}. Any ti E (—c/2 + T, T) leads to a lower payoff.
Now turn to j and suppose that i follows Fi. The equilibrium strategy of jH
follows from Lemma 1. For jL, a concession in t E [0, —c/2 + T] yields an expected
payoff of
I (v — x) —e cl dx + e cl (v — cL — t)
= V — Cl-
Jo cl
Hence, jL is indeed indifferent to all t E [0, —c/2 + T]. For all t > —c/2 + t, jLs
expected payoff is strictly lower. The ex ante expected payoffs in the second row of
(6) and (7) follow directly from these calculations.
A.4 Proof of Lemma 4
By Assumption 1 and Lemma 1, FiH (t) = 0 for all t < T and FiH (t) = 1 otherwise,
i = 1, 2. Thus, for iL, a concession in T is strictly preferred to any t E (—cL/2 + T, T).
Suppose that jL follows FjL. For any ti E [0,t), iL’s payoff is
Pl / (v — x)
Jo
----e cl dx + e cl
PlCl
(v — ti — cL ) = v — cL-
By choosing ti = T, iL gets
Pl
[t (v — x)
Jo
PlCl
cl dx +
cL (v
CL)
Cl + exp
+CL)∙
If
— ^2~ + T < — CL ln(1 — pL) , (13)
c = — ɪ + T, and iL is indifferent between all ti E [0,t) U {T}: (13) implies that
FiL (t) < 1 and iL waits until T with strictly positive probability. If (13) is violated,
30
More intriguing information
1. The Complexity Era in Economics2. Conditions for learning: partnerships for engaging secondary pupils with contemporary art.
3. A Review of Kuhnian and Lakatosian “Explanations” in Economics
4. Magnetic Resonance Imaging in patients with ICDs and Pacemakers
5. The purpose of this paper is to report on the 2008 inaugural Equal Opportunities Conference held at the University of East Anglia, Norwich
6. Economie de l’entrepreneur faits et théories (The economics of entrepreneur facts and theories)
7. The role of statin drugs in combating cardiovascular diseases
8. The name is absent
9. Climate Policy under Sustainable Discounted Utilitarianism
10. The name is absent