The name is absent



t = 1,2,3... a battle takes place between the players in which A (resp. B)
expends effort
at (resp. bt). A victory by player A (B) in state i at time
t moves the war to state i 1 (i + 1) at time t + 1. The state in period

t + 1 is therefore j (t + 1) = mA + nBt nAt, where nAt and nBt denote

respectively, the number of battle victories that A and B have accumulated
by the end of period t. This continues as long as the war stays in some
interior state j
Mmt{1,2,..., (m 1)}. The war ends when one of
the players achieves final victory by driving the state to his favored terminal
state, j = 0 and j = m, for player A and B respectively. A prize (for final
victory) of size
Za is awarded to A if the terminal state j = 0 is reached
and, alternatively, a prize of
Zb is awarded to B if the terminal state j = m
is reached. Without loss of generality we assume that
ZaZb. Figure 1
depicts the set of states.


φ states j

01


mA-1   mA   mA+1


m-1   m


Figure 1:

Player A’s (B’s) period t payoff ^A(at,j(t)) (%b(bt,j(t))) is assumed to
equal
Za (Zb) if player A (B) is awarded the prize in that period, and
αt (bt) if t is a period in which effort is expended.6 We assume that
each player maximizes the expected discounted sum of his per-period payoffs.
Throughout we assume that 0 < 
δ < 1 denotes the common, time invariant,
discount factor.7

The assumption that the cost of effort is simply measured by the effort
itself is for notational simplicity only. Since a player’s preference over income
streams is invariant with respect to a positive affine transformation of utility,
if player A (B) has a constant unit cost of effort
ca (cb) we may normalize
utility by dividing by
ca (cb) to obtain a new utility function representing
the same preferences in which the unit cost of effort is 1 but player A (B) has

6Since the per-period payoffs do not depend directly on time, we have dropped a time
index.

7It is straightforward to extend our results to cases in which players have different,
time invariant discount factors
5a and ⅛ .



More intriguing information

1. Une Gestion des ressources humaines à l'interface des organisations : vers une GRH territoriale ?
2. Backpropagation Artificial Neural Network To Detect Hyperthermic Seizures In Rats
3. Stillbirth in a Tertiary Care Referral Hospital in North Bengal - A Review of Causes, Risk Factors and Prevention Strategies
4. Synchronisation and Differentiation: Two Stages of Coordinative Structure
5. Ultrametric Distance in Syntax
6. The name is absent
7. The Prohibition of the Proposed Springer-ProSiebenSat.1-Merger: How much Economics in German Merger Control?
8. Determinants of Household Health Expenditure: Case of Urban Orissa
9. If our brains were simple, we would be too simple to understand them.
10. EXPANDING HIGHER EDUCATION IN THE U.K: FROM ‘SYSTEM SLOWDOWN’ TO ‘SYSTEM ACCELERATION’
11. The name is absent
12. The name is absent
13. An Efficient Secure Multimodal Biometric Fusion Using Palmprint and Face Image
14. The name is absent
15. Enterpreneurship and problems of specialists training in Ukraine
16. School Effectiveness in Developing Countries - A Summary of the Research Evidence
17. MULTIMODAL SEMIOTICS OF SPIRITUAL EXPERIENCES: REPRESENTING BELIEFS, METAPHORS, AND ACTIONS
18. WP 48 - Population ageing in the Netherlands: Demographic and financial arguments for a balanced approach
19. Business Networks and Performance: A Spatial Approach
20. The name is absent