Volunteering and the Strategic Value of Ignorance



Otherwise, i’s expected payoff from a concession in ti is

Γ (v - t) dΦj (t) + (1

7o


- ^j (ti)) (v - ti - Ci)


= f (V - t) dΦj

Jo


(t) - Γ (v

Jti


+ (1 - φj∙ (T)) (v - ti - <⅛) + (Φj (T) - φj∙ (ti)) (v - ti - ci)

= Λ (v - t) dΦj (t) + (1
Jo

- φj (T)) (v - ti - ci}


I (ti + Ci
Jti


- t) dΦj (t).


(9)


Φj (ti) 1 implies that Φj(T) - Φj(ti) 0 or∕and 1 - Φj(T) > 0. Therefore, for
all
ti (-ci2 + T, T), (9) is strictly smaller than

Γ (v - t) dΦj (t) + (1

Jo


- φ (T)) (v - ci/2 - T)


which is i’s expected payoff for ti = T.

A.2 Proof of Lemma 2

(i) As argued in the main text, the best response to tj = T is ti = T, and qi (T) =
Qj (T) = 1 is an equilibrium. Moreover, since -ci2 + T < 0, Lemma 1 rules out
any further equilibrium because any individual who contributes with strictly positive
probability in
t' [0,T) would strictly prefer a concession in T to a concession in t'.
(ii) The structure of the equilibrium strategies follows from Hendricks et al. (1988)
and the analysis in the main text. We only show that the strategies constitute an
equilibrium. Suppose that
j randomizes according to Fj (t) = Φ (t; c, - ^ + T, 0j,
where
Φ is defined in (2). Then, by Lemma 1, i strictly prefers ti = T to any
ti (-c/2 + T, T). For ti [0, -c/2 + T], i’s payoff is

ʃ (v - x) - exp (-—) dx + exp ^-τθ

(v — ti — c) — v — c,


27



More intriguing information

1. The Integration Order of Vector Autoregressive Processes
2. Self-Help Groups and Income Generation in the Informal Settlements of Nairobi
3. Licensing Schemes in Endogenous Entry
4. The Triangular Relationship between the Commission, NRAs and National Courts Revisited
5. The name is absent
6. The name is absent
7. Output Effects of Agri-environmental Programs of the EU
8. The Structure Performance Hypothesis and The Efficient Structure Performance Hypothesis-Revisited: The Case of Agribusiness Commodity and Food Products Truck Carriers in the South
9. The Role of Land Retirement Programs for Management of Water Resources
10. Notes on an Endogenous Growth Model with two Capital Stocks II: The Stochastic Case