The name is absent



S  Δ0

(1 S2) ^BA + b

SS⅛-2za  ' SS⅛-2za

1


for
for


b [0,


S∆B0A ]
(1-S2) ]
3'0
sδba


(1-S2)


and


^70-1(^) = S

S    Δ30-1

(1S2) δab    ∣__a

SSm(>o+1)ZB + SSm-(J0+1)ZB


for
for


a [0,


S Δ30
s δab


where


(1-S2


S ∆A0B


(1-S2


b

S   Δ0-1

(1 S2) δab

1


for b [0, 'AB ]

,       , S δA0b 1

for bT-aBt


Δλ = [m-*>Zb - Si°Zλ] and ∆⅛1 = Ao1Z, - δm-l*0~-ZB].


(12)

(13)

(14)

(15)


Note first that this equilibrium candidate has the properties described in
Proposition 1. Players’ continuation values can be stated as functions of the
respective state
j as follows:

(           Zλ           for j<jα - 1

vλ(j) = ^  (⅛'-`    Zλ - r-(70-1)Zb]  for j = jo - 1      (16)

I                0                 for    j jo

and

(       δm- Zb        for   j>jo

vb(j)={ (⅛) Г-0 Zb - ^ Zλ] for j = jo         (17)

I             0              for jjo - 1

These constitute the payoffs stated in the proposition. For 0 < j < jo - 1,
player
A wins the next j battles without any effort. This takes j periods and
explains why the value of the final prize must be discounted to
57Zλ. Also,
B does not expend effort in these j battles and finally loses after j battles.
Hence,
B’s payoff is equal to zero. For mj > jo, players A and B simply
switch roles.

Turn now to the states jo - 1 and jo as in Figure 2. We call these states
"tipping states", because of their pivotal role in determining the outcome
of the contest. Consider
jo - 1. From there, if A wins, the game moves to
jo - 2 with continuation values vλio - 2) = 570-2Zλ and vb(jo - 2) = 0.

13



More intriguing information

1. Une nouvelle vision de l'économie (The knowledge society: a new approach of the economy)
2. Target Acquisition in Multiscale Electronic Worlds
3. WP 36 - Women's Preferences or Delineated Policies? The development or part-time work in the Netherlands, Germany and the United Kingdom
4. Social Balance Theory
5. The name is absent
6. The name is absent
7. The name is absent
8. The name is absent
9. Perceived Market Risks and Strategic Risk Management of Food Manufactures: Empirical Results from the German Brewing Industry
10. Peer Reviewed, Open Access, Free