Warrior Warfare

8/6/2019 Warrior Warfare

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An Economic Analysis of Warrior Warfare

Shawn Humphrey and Robert Rider

University of Mary Washington and California State University, San Marcos

November 17, 2006

Abstract

Our popular image of combat, which includes the headlong collision

of opposing conbatants, is inconsistent with reality. A fundamental chal-

lenge that all human societies have had to confront in their conduct of

combat has been the strong tendency of their combatants not to ght

but to take ight. Using a disaggregated contest success function in ratio

form, we identify the source of this challenge; namely, a team production

problem exists on the battleeld. Whenever a combatant ghts, he pro-

duces a positive externality for the rest of the team. Minus a hierarchical

command-and-control structure to internalize this externality, shirking is

endemic. If both parties to the contest are unorganized, collisions are

precluded. Indeed, you have what we call warrior warfare. We test the

models conclusions using the documentary evidence concerning the con-

duct of ritual battles among the Grand Valley and Ilaga Valley Dani. The

forces of both pre-state communities, which reside in the New Guinea

Highlands, are only rudimentarily organized. The empirical evidence is

supportive of the models conclusions.

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1 Introduction

Consider the following images. Two masses of armed combatants oppose each

other across an open eld. Screaming, gesticulating and clanging their weapons

against their armored, merely clothed or painted naked bodies, they impatiently

await battle. Impassioned by the inspirational words of their leaders, with the

raise of a sword and a bellowing roar, they charge forward at top speed to meet

their opponents. The moment of contact is magnicent. Men and beasts alike

collide as they hurl themselves, with careless abandon, into each other. The

masses mix. Each and every combatant, previously wrapped in the safety ofthe surrounding presence of his comrades, nds his back and sides exposed. A

deadly strike can come at any moment from any direction. In the face of this

danger, ghting becomes reckless. This depiction of combat is Hollywood at

its blockbuster best think of Braveheart and Lord of the Rings. It makes for

great drama. However, the reality of warfare is quite dierent.

Ardant du Picq (1921), writing in the middle of the nineteenth cen-

tury, argued against this very same dramatization of combat by painters and

poets. His analysis of documentary evidence concerning primitive and an-

cient combat, in conjunction with his personal experience as a colonel in the

French army, led him to conclude that there is no shock action in combat -

armed masses of men never collide.1 At the heart of his conclusion lies a com-

batants motivation to ght. He is ready and willing to ght, du Picq argues,

when the expected harm and risks to him are low (for example, when his op-

ponent is relatively weak or defenseless); yet, when the conditions are not so

favorable, he is eager to ee. His behavior in combat, in other words, is guided

by an "instinct of self-preservation."2 He is what we call a warrior. One of the

purposes of organization - a hierarchical command and control structure that

1 du Picq (1921) page 48.2 du Picq (1921) page 31.

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imposes sanctions and leads by example - is to suppress the ight instinct. 3 A

hierarchical organization can transform a warrior into a soldier. Soldiers are

motivated to ght even when the conditions are not so favorable - because it

is too costly not to ght.4 They are disciplined. Discipline, however, is imper-

manent. Even in the presence of organization, it can break down, either on the

approach to or during actual combat. It can break down on either one side or

both sides to a conict. However, whenever and to whichever side it happens

once it does combat (for that side or both sides) becomes unorganized. Soldiers,

once again, becomes warriors and their motivation to ght evaporates. Indeed,

a dening characteristic of modern warfare is organization. Yet, evidence is

overwhelming that during combat soldiers have the tendencies to give into their

instincts, ignore their military training, and not ght. For example, in studies

of ring rates among soldiers among U.S. soldiers in World War II, Marshall

(1947) documented in post-combat interviews, that only one in four American

soldiers actually red their guns.5 Without discipline, collisions in combat are

precluded because ight on the part of one or the other. . . is often seized."6

In this paper, we model unorganized combat, what we call warrior war-

fare.7 We will demonstrate that unorganized combatants do not collide en masse

and provide a more complete characterization of an individual combatants mo-

tivation to ght in this setting. This paper makes a valuable contribution in

both areas. First, borrowing from the economics of conict literature, we de-

velop a disaggregated contest success function so as to better understand the

3 ibid. page 53.4 du Picq (1921) page 54 and 59. The cost of not ghting takes two forms - the sanctions

imposed by the military organization and the imminent death, at the hands of the enemy,that results due to turning ones back and eeing combat.

5 Marshall (1947) page 50. Please note that evidence has arisen that has called into questionMarshalls ratio, but not his message.

6 du Picq (1921) page 21.7 This explains our use of "Braveheart" and "Lord of the Rings" as motivating examples. In

both instances command and control on the part of one or both sides is limited at best. Futureresearch will be dedicated to modeling combat bewteen opposing forces that are organized.

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team production problem of combat.8 Second, excepting du Picq, we know

of only one other social scientist who has explored an individuals motivation

to ght while participating in unorganized combat (Gat (1999)).9 We proceed

with a model of warrior warfare, where two groups of unorganized combatants

are engaged in a contest over a prize. In this model, any fraction of the prize

secured by the group is shared among its warriors. Using a general sharing

rule, we conclude that warrior warfare is inecient; that is, the equilibrium

level of eort supplied by the group fails to maximize the dierence between

the size of the prize secured and the total cost of eort. This is due to the fact

that when a warrior ghts he produces a positive externality for the group as

a whole. Inecient warrior warfare, we argue, would manifest itself as the ab-

sence of opposing masses colliding. With a particular sharing rule that reects a

warriors contribution to the prize, we provide an example of inecient warrior

warfare. This inescapable conclusion is due to the presence of a positive exter-

nality. This enables us to examine more closely the incentives that an individual

warrior confronts on the battleeld. For example, when combat conditions are

such that neither side enjoys an advantage in terms of the number of warriors it

elds, military technology, or innate ghting ability (that is, under symmetrical

conditions), and when a warriors private marginal cost of ghting is high or the

value of the prize is low, he not only has an incentive to free-ride on the eort

of his fellow warriors that is to shirk he also has the incentive to retreat

whenever his opponent allocates additional eort toward ghting. Beyond some

critical level of eort exerted by the opposing group, he and his teammates also

have an incentive to ee the battleeld; thus, initiating a rout.

Our primeval practice of open-eld warfare, termed ritual battles by

anthropologists, closely approximates the unorganized combat that we model.

8 Hirshleifer (2001).9 Gat (1999) extends du Picqs analysis by suggesting an evolutionary logic.

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Indeed, a detailed description of ritual battles, as practiced by the Dugum Dani

and Ilaga Dani in the New Guinea Highlands, is consistent with the models

conclusions. In the open eld, when opponents were evenly matched, battle

deteriorated into what we characterize as broad-based warrior shirking. Indi-

vidual warriors chose who and when to ght. They also chose when to rest and

retreat. Coordinated action was largely, if not completely absent. There were

no concerted maneuvers. There were no volleys. Most importantly, there was no

massive clash of bodies. Instead, opposing warriors arrayed against each other

in open-order parallel lines took turns feigning attack and then retreating. Yet,

there were occasions, albeit infrequent, when a ritual battle turned into a rout.

Warriors from one side or the other would break ranks and ee the ght ground.

It was the inability of either side to coordinate the various ghting eorts of

their warriors, we argue, that explains the absence of shock action in ritual

battles.

2 A Model of Warrior Warfare

2.1 The warrior

Suppose that there is a prize, X, over which two groups of warriors (A and

B) are contending. This prize can be very general. It might include territory,

resources, or status. X is assumed to be exogenous and divisible. Band A has

nA warriors and band B has nB warriors. For band A, each warrior is indexed

by i = 1;:::;nA . (Band Bs warriors are indexed by j = 1; :::;nB.) We will

assume that is preference function is given by

XAi(i) CAi(i) (1)

XAirepresents is share of the prize from military action (spoils of war, tro-

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phies, status, etc.) This is assumed to be quasi-concave, strictly monotone

increasing and dierentiable.

CAi(i) is is private cost from military action. This will include not only

the opportunity cost of ones eort and costs of providing for ones own equip-

ment, but also may include fear of battle. This function is assumed to be con-

vex, strictly monotone increasing and dierentiable with CAi(0) = 0: i is the

amount of military eort expended by i, 0 i ai, where ai is is maximum

level of eort that is possible.

(Similar assumptions hold for band Bs members, where j represents js

eort and bj is the maximum level of eort for player j.)

Warrior is problem is the following:

max XAi(i) CAi(i)

s:t:0 i ai (2)

Warrior j has a similar problem.

2.2 The contest

Given the eorts of the warriors of band A and band B, the amount of the prize

secured by band A is given by

XA =1

1 +PmBjPmAi

X (3)

(Note that one can also interpret this in terms of the probability of winningthe entire prize (i.e. expected value).) This function represents a standard con-

test success function from the economics of conict literature. The parameters,

mA, mB, are the "mass eect parameters" for band A and band B, respectively.

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Note that for non-negative mass eect parameter values less than or equal to

one, XA is strictly concave and monotone increasing in i. For non-negative

mass eect parameter values greater than one, the contest success function is

quasi-concave. (See Hirshleifer (1989) for details.) The contests outcome is de-

termined by the relative degrees of military eort of each band. In this model,

the team production is joint military eort of the band in a contest over a prize.

Similarly, band Bs share of the prize is given by

XB =1

1 +

PmAi

PmBj

X (4)

We will assume that XA and XB are both equal to zero whenP

mAi =PmBj = 0. If none of the combatants engages in the contest, none of the

bands receives any of the prize. Note that

XA + XB X (5)

This latter condition is a "global" balancing condition. The distribution of

the spoils of war can never exceed the aggregate spoils of war. This condition

is satised given our assumptions.

2.3 Warrior is share of the prize

After the contest is decided there is a distribution of the spoils, i.e. a distribution

of the prize secured by each band among its warriors. Let warrior is share of

the contest prize be given by

XAi = SAi XA (6)

A similar share function applies for warrior j from band B. There can be

many sharing rules for apportioning the prize secured by the band in the contest.

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A plausible assumption for the share of the prize for warrior i in band A is

XAi = SAi XA =mAiP

mAi XA =

mAiPmAi +

PmBj

X (7)

Warrior is share is a function of his relative contribution to the contest.

This assumption will be used below as a special case. A similar function holds

for warrior j in band B. In addition, for the remainder of this paper we will

assume that mA = mB = 1.

In addition, we require that the shares of the prize that are distributed

among the bands warriors be "locally" balanced, i.e. for band A

XSAi XA XA (8)

For band B, we have the analogous condition,

XSBj XB XB (9)

Note that these conditions are satised given our assumption of the special-

ized sharing rule. We will assume that SAi and SBj are both equal to zero whenPmAi =

PmBj = 0.

2.4 First-order condition (interior solution)

Examining the interior solution for warrior is problem yields the following:

dSAi

di XA + SAi

dXA

di=

dCAi

di(10)

This condition has an intuitive interpretation. The right-hand side is the

warriors private marginal cost for military eort. The left-hand side has two

factors, both of which aect the warriors share of the prize acquired by the band.

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The rst is the marginal change in the warriors share of the prize due solely

to a change in his fraction of any given prize the band has secured. Increases

in his military eort, ceteris paribus, may increase the fraction received. This

is a private benet; only the individual warrior realizes this change. For the

special case (above) this derivative is positive. The second term is the marginal

change in the prize secured by the band due solely to his contribution to the

bands military eort. Warrior is increased eort, ceteris paribus, increases the

prize obtained by the band. This is shared with the entire band, and thus has

a public benet component. It is a positive externality; others in the band can

not be excluded from this benet. As we will demonstrate It is this externality

that leads to the ineciency of warrior warfare.

2.5 Warrior is reaction function - special case

Solving for warrior is problem for the case where his share is based on his eort

relative to the bands eort, we obtain the following reaction function (interior

solution) for warrior i in band A

Ri =

s(P

h2Ari +P

j) XdCAidi

X

j X

h2Ari (11)

(The notation Ari refers to the set of all warriors in band A except warrior

i.) We also assume that CAi is linear. Similarly, for warrior j in band B we

have the following

Rj =

vuut

(P

k2Brj +P

i) XdCBjdj

X

i X

k2Brj (12)

(The notation Brj refers to the set of all warriors in band B except warrior

j.) These reaction functions exhibit a number of properties. First, warrior

is military eort is inversely related to his private marginal cost of ghting.

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Second, warrior is military eort is positively related to the value of the prize.

The greater is the stake in the contest, ceteris paribus, the greater will be the

military eort by any warrior.

Third, the relationship between warrior is marginal military eort and the

marginal military eort expended by the other warriors in band A may be

of either sign. On the one hand, as the aggregate military eort of band A

increases, ceteris paribus, warrior is proportion of any prize may decrease unless

he increases his eort in proportion to his fellow warriors eorts. On the other

hand, the greater is the aggregate military eort, ceteris paribus, the larger

is the prize secured by the band and the larger will be is share without any

increase in is eort. If the latter condition dominates, then warrior i free rides

on the eorts of his fellow warriors. A plausible reaction function for warrior i

as a function of his fellow warriors aggregate military eort that exhibits both

properties is depicted in Figure 1.10 At low levels of aggregate eort, increases

by his fellow warriors lead warrior i to respond in kind. Beyond some critical

value, though, warrior i reduces his eort and begins to free ride, with complete

free riding (i = 0) for aggregate eort levels in excess of :99 (approx.). There

is a small window for coordinated military eort.

To see this more formally, note that warrior i will reduce his military eort

when aggregate military eort of band A increases,11 i.e.

@Ri@(P

h2Ari) 0 (13)

if and only if the following is true: either warrior is marginal private cost

of ghting is bounded below or the prize is bounded above,

10 The assumptions for this gure are that the enemys military eort is low (.01) and theprivate marginal cost of ghting and the value of the prize are both equal to 1.

11 Note that we are treating the aggregate military eort of band A (excluding warrior i) asa single variable.

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Figure 1: Fight or free ride

XdCAidi

(X

h2Ari +X

j) 4 (14)

This condition characterizes the battle as uncoordinated and unorganized;

free riding is endemic. If his fellow warriors increase their military eort, warrior

i will decrease his eort. Warrior i has an incentive to shirk on his duties. (Of

course, if the above inequalities are reversed then warrior i will respond in kind

to any increase in aggregate military eort by his fellow warriors.) A necessary

condition for ecient warfare is that there is coordination and no free riding.

Fourth, similar to the conditions above, the warriors response to increases

in the enemys military eort also can be of any sign. Warrior i will reduce his

military eort if the enemy increases its eort,12 i.e.

@Ri@(P

j) 0 (15)

if and only if the following is true

XdCAidi

(X

h2Ari +X

j) 4 (16)

12 Again note that we are treating the aggregate military eort by band B as a single variable.

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Beyond some critical value in the enemys eort, warrior i has an incentive

to ee the battleeld. If all warriors i are identical then the entire band runs

away, which can be characterized as a rout. This is true if and only if the

marginal private cost to ghting is large enough or the prize is small enough. In

the special case with slight dierences in the values for XdCAidi

and XdCBjdj

, there

exist equilibria with the property that warrior j will choose to ght (j > 0)

while warrior is ghting eort will approach zero (but never equal zero). All

of the warriors in band A show up for battle but once the ght begins, all of

them run away. (For example, when XdCAidi

= 1 < XdCBjdj

= 1 + k; (for k small)

and nA = 5 < nB = 10, the equilibria are (

i ;

j ) = (0; 0) and (

i ;

j) =

(1:08609 1017; :1).) Dierences in the size of the bands do not lead to a

rout in our model. It is only relative dierences in the value of the prize or

the private marginal cost that produce routs. To the extent that increases in

the size of the band relative to the enemy reduce the private marginal cost of

ghting ("safety in numbers"), though, then dierences in relative band size

may produce routs.13

2.6 Warrior warfare as a Nash equilibrium - special case

with symmetry

Suppose that the two bands are symmetric with the share functions from the

special case. Each warrior, regardless to which band he belongs, is the same in

terms of skill and what weapons technology he possesses. In addition, suppose

that the bands are the same size (nA = nB = n). Given the assumption that

the private cost of ghting is linear, let dCAidi

= dCBjdj

= > 0 . It is assumed

to be the same for each warrior. In this case the equilibrium military eort for

warrior i is

13 In our model we have assumed the private marginal cost is independent of the size of theband to maintain tractability.

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i =(2 n 1)

4 n2 X

(17)

By the symmetry assumption all warriors exert the same military eort. It

follows from the balancing conditions that XA = XB =X2

, and XAi = XBj =

X2n

. Note that i is decreasing in n. As the band becomes larger the warrior

will reduce his military eort; more free riding should be expected as the band

becomes larger.

2.7 The ineciency of warrior warfare

i constitutes a Nash equilibrium only if the following holds true

XAi(

i ;

h2Ari; j) CAi(

i ) XAi(i;

h2Ari; j ) CAi(i) (18)

i = 1;:::;nA, and 8i. An analogous condition must be true for

j . The

Pareto optimal amount of warfare for band A requires that the vector of military

eort,

= f

i ;:::;

nAg, satises the following condition

= arg maxfXA(

) X

CAi()g (19)

This condition states that band A achieves optimal military performance

from its warriors. An analogous eciency condition also holds for band B. Does

an ecient Nash equilibrium exist? We will examine the dierentiable case.14

By dierentiating the condition for a warriors best response and examining the

two cases where 0

i ai, we obtain the following

dSAi

diXA + SAi

dXA

di

dCAi

di 0; i = 1;:::;nA (20)

14 The analysis that follows is based on Holmstrom (1982).

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By dierentiating the Pareto optimality condition for warfare, we obtain

dXA

di

dCAi

di 0; i = 1;:::;nA (21)

These two conditions can be satised for interior solutions only if the follow-

ing holds:

(1 SAi) dXA

di=

dSAi

di XA (22)

In order for warrior i to choose a Pareto optimal amount of military eort

in the Nash equilibrium, his marginal contribution to the military eort that

accrues to others (the public benet of his eort) must equal his marginal con-

tribution to the military eort that he receives in the form of a larger fraction of

any prize obtained (the private benet of his eort). But this is impossible for

any band of size greater than one (nA > 1) given the local balancing conditions

(8). Dierentiating (8) yields

dXA

d

i

=X( dSAid

i

XA + SA dXA

d

i

) (23)

For the special case, a necessary condition for an ecient Nash equilibrium

is given by

XdCAidi

(X

i +X

j) 1

XB(24)

Band Bs take of the prize is bounded above and decreases in the size of the

prize. There must be enough of the prize left over after Bs take for it to be

worthwhile to engage in ecient military eort. This bound increases in the

marginal cost of ghting and in the overall level of conict, measured as the

total sum of resources allocated to the contest (P

i +P

j). For the special

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Figure 2: Warrior warfare

case, the symmetric equilibrium satises this condition.

Combining the condition (24) with the converse of the condition for free

riding (14) in the special case, establishes the regions for ecient and inecient

Nash equilibria. Ecient Nash equilibria require that the prize be large and that

band Bs take of the prize be small. For the special case, the Nash equilibria are

inecient. Suppose that nA = nB = 10, each warrior has a marginal cost equal

to 1 and X = 1. The Nash equilibrium values for (i ;

j ) = (:0475; :0475).15

XA = XB = 12 , and XAi = XBj = :05. See Figure 2. Free riding occurs for

all X values left of (14) in the gure. Nash equilibria can only exist below

the hyperbola (24) and below the 45 degree line (the dashed line). The Nash

equilibrium in the special symmetric case lies at the coordinates (1; :5). As

band B gains advantage over band A because of relative dierences in the value

of the prize or the private marginal cost of ghting, the set of possible equilibria

(ray from the origin) rotates upward, approaching the 45 degree line, with the

routing equilibrium lying on it.

15 In the special case there is also another pure strategy equilibrium at the origin, which isbeing ignored here.

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3 Evidence

The model provides an answer to the following question: how would two oppos-

ing and unorganized collectives of rational self-interested individuals engage in

combat? In the heat of an engagement, we expect cooperation to be dicult or

simply impossible to sustain on both sides. The incentives during combat are

such that when your opponents rush forward (allocate eort towards ghting)

you have a tendency to fall back. At the same time, however, your opponents

have a tendency to free-ride on each others eort; that is, your opponents

realized moment of cooperation should be short lived. As their momentum

evaporates, your side may nd it worthwhile to counter with a forward rush

of your own; however, once again, if you rush forward (allocate eort towards

ghting), beyond some point, your teammates will nd it worthwhile to free

ride and let you take the lead (which is not to imply that you would not do it as

well). Indeed, your recognition of their free-riding may even lead you to reduce

your own eort. Your sides moment of cooperation is short-lived as well. With

these incentives common to both sides, we do not expect unorganized opposing

forces to collide en mass. Yet, it is possible that under certain circumstances

your tendency to fall back in the face of a concerted rush from you opponents

may turn into a full-blown retreat from the eld of combat. While this may

embolden your opponents to press forward, your ight, once again, precludes a

collision from occurring.

The models validity, of course, hinges upon whether or not combat between

unorganized collectives of rational self-interested agents actually conforms to

the aforementioned predictions. Our challenge, necessarily, was to compile a

body of evidence with which to test the model; that is, compile instances of

combat between opposing forces that could be characterized as relatively unor-

ganized. That body of evidence those instances of combat - were found in the

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anthropology of war literature, specically, its analysis of pre-state warfare.

3.1 Pre-state warfare among the Dani

Our description of ghting among pre-state societies will be drawn from the

works of Karl Heider (1997), who studied the Grand Valley Dani of the New

Guinea Highlands, and Gordon Larson (1987)who lived among the Dani of the

Ilaga Valley. Both were eye-witnesses to pre-state warfare. Indeed, Gardner, et

al. (1964) captured one aspect of Dani warfare in the 1963 documentary lm

Dead Birds. Moreover, Larson (1987) recorded seventeen instances of open-eld

warfare among the Dani, three occurrences of which he observed in person.16

Consequently, their eldwork, since it is not based solely on informants recol-

lections of warfare, can be considered more reliable.

The Dani are simple horticulturists.17 They engage primarily in two eco-

nomic activities: gardening and pig husbandry. Politically, they are organized

into territorial alliances and confederations. Each alliance and its constituent

confederations are led by one or more Big Men. Their leadership, founded

upon inuence and not coercive power, is neither hereditary nor formal. Thereare twelve alliances, consisting of around ve thousand individuals each, in the

Grand Valley. Each alliance is separated by a no-mans land dotted on each side

with manned watchtowers. In the smaller Ilaga Valley, there are three alliances

with around two thousand individuals each. Wars, in both valleys, are fought

between alliances and not confederations.18

Dani warfare is a cycle composed of two interrelated and recurrent phases:

ritual and secular warfare.19 Ritual warfare includes raids and ritual battles.

16 Larson (1987) page 22.17 Anthropologists employ the convention of talking in the ethnographic present, where thepresent is dened as the time at which the community was observed. We will follow thatconvention here.

18 Heider (1997) page 68 and Larson (1987) page 245.19 Heider (1997) page 103, Shankman (1991) page 308 and Larson (1987) page 166.

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Raids are small-scale surprise attacks on one community by a dozen or fewer

warriors from another.20

Raiding parties, having penetrated enemy territory,

lie in ambush and wait for unsuspecting and isolated targets to appear before

attacking. Ritual battles, captured in the documentary lm Dead Birds, involve

hundreds of warriors on each side. Fighting is scheduled and battleelds are

pre-selected. Opposing warriors gather each morning within bow-shot of each

other. Fighting is individualistic and can continue uninterrupted for days, weeks

or even months and still result in few if any deaths. Secular warfare, on the

other hand, has been described as the "violent" or "explosive" phase.21 It is

during this phase that routs occur. Routs consist of invading an opponents set-

tlements and burning houses, destroying property, deling burial grounds, and

killing indiscriminately. All community members - men, women, children, the

aged, inrmed, or disable are legitimate targets. Routs are brief in duration

and infrequent; however, they are the source of signicant casualties and have

widespread consequences: entire communities are expelled from the valley, al-

liances erupt and are re-congured, territory changes hands, and new no-mans

lands appear.22 Routs can arise as outcomes of large-scale pre-dawn surprise

attacks or during the course of ritual battles.

Most wars arise out of interpersonal disputes.23 Larson (1987) collected

data on one hundred and seventy nine such disputes. One hundred and twenty

six were resolved peacefully either through persuasion, avoidance, withdrawal,

mediation, or compensatory payment for damages caused.24 Yet, when peaceful

measures fail a dispute may turn violent. Either one of the two parties to a

dispute may summon friends and family members to aid them in an armed

20

Shankman (1991) page 301.21 Heider (1970) page 121.22 Heider (1997) page 103, Shankman (1991) pages 301, 308 and Larson (1987) page 295.23 Heider (1972) pages 2-20 and Larson (1987) page 166.24 Larson (1987) page 166.

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threat or attack on the other.25 Disputes are now settled through violence

escalating violence. It begins with stick and then stone ghts, escalates to

feuding with bows and arrows, and may escalate further to include ambushes,

revenge killings and incessant raiding.26 Fifty three disputes in Larsons data

set resulted in some form of violence. Of these, seventeen grew to include the

entire alliance common to both parties and culminated in the call for ritual

battle. And, on two occasions, ritual battle escalated to a rout.

Ritual battles are organized, in both valleys, to prevent these disputes from

escalating that far.27 They arise when the confederations of one alliance combine

to challenge the confederations of an opposing alliance. They are pre-arranged.

There is no surprise. Opposing "owners of the war" (war leaders), through dis-

cussion and consultation with allied leaders throughout the valley, rally warriors

to their cause.28 The operative term here is "rally" since no leader has the

power to coerce a man to participate.29 The "owners of" the war are the parties

to the last dispute that culminates in the call for ritual battle. If allies accede,

then the owner of the war challenges his enemy. If accepted, and it usually is,

the challenged war leader replies in kind and a day and place are agreed upon

for battle. In the Grand Valley then erupts as the jokoik or war whoop is passed

from watch tower to watch tower informing allies near and far of the coming

battle.30

The battleeld selected is usually half way between the two warring alliances.

At the agreed upon location, gathering forces, directed by their respective war

leaders, oppose each other in open-order parallel lines. Warriors are equipped

with bow and arrows, possibly multiple throwing spears, and a jabbing spear (a

25

Heider (1972) pages 2-21.26 Larson (1987) page 166.27 Larson (1987) pages 166, 169, 246. Shankman (1991) page 313.28 Larson (1987) page 255.29 Heider (1997) page 101 and Larson (1987) page 249.30 Heider (1997) page 101.

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very small number of warriors carry shields). Jabbing spears play only a minor

role. With a limited eective range, they are more of a close-quarter combat

weapon. Opposing warriors would have to close the distance between them to

be employed. We have yet to come across any account in which opposing forces

engage each other spear-to-spear in the open eld. Ritual battles are principally

conducted with missile weapons bows and arrows. Moreover, in an attempt to

appear more ferocious, individual warriors and especially war leaders embellish

their standard military attire faces and torsos smeared with pig grease, soot

or dark clay - with plumes, shells and other ornaments. These trappings of war

are reserved for ritual battles, when display is paramount.

Battle begins with a mutual display of ferocity. Warriors, at opposite ends of

the battleeld, perform mock-battle maneuvers, brandish their weapons, scream

high-pitched war cries, and, in the case of the Ilaga Dani, at the top of their

frenzy scale local fences and trample nearby gardens.31 Their war leaders and

other non-combatants who have come to observe and provide vocal support,

cheer them on and hurl insults at the enemy.32 The transition from display to

actual ghting occurs when both sides converge in the middle of the battleeld

each daring the other to make the rst move to start the rst skirmish.

The rst skirmish - like each subsequent skirmish - unfolds with braver warriors

(the spearmen) hesitantly advancing to within 15-20 yards of each other. They

seek out specic enemy warriors to engage in a duel. 33 All the while, they are

supported by archers who release uncoordinated masses of arrows. The Dani

"never shot arrows in volleys."34 To defend themselves warriors must remain

vigilant - constantly dodging enemy arrows.35 With opposing warriors shooting,

dodging, advancing and falling back as one side or the other mounts a charge31 Larson (1987) page 257.32 Larson (1987) page 260.33 Larson (1987) page 259.34 Heider (1997) page 104.35 Heider (1997) page 103. Larson (1987) page 259.

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the two extended lines continually undulate but never come to grips with each

other.36

These braver warriors and the archers who accompany them make up the

rst of four battle lines. Behind them is a line of warriors armed with spears

and sometimes a shield. They are held back just in case ritual battle escalates

into a rout. Next there is a reserve force of resting warriors. Throughout the

engagement, warriors who are tired or have expended their full complement of

arrows will retire to the rear to replenish both. By doing so, they form the

reserve force. Yet, the decision to retire to the rear is an individual one. Whole

ranks do not retire en masse. This is indicative of ritual battles in general. For

the most part, battle is an individual aair in which warrior is pitted against

warrior. There are no "concerted maneuvers" on the ght ground.37 Throngs

of cheering spectators, leaders and advisors make up the nal and fourth battle

line.

Throughout the skirmish, leadership, while not completely absent, is limited.

The command and control of Big Men (who are also not war leaders) is restricted

to helping older men maintain the ow of arrows to the skirmishing warriors,

reecting and deliberating, with the war leaders, on the course of the battle

(specically the number of casualties - a balance which can preclude a rout).

Both Big Men and war leaders, from their vantage point in the rear, can bolster

weak points in the front line by directing warriors from their reserve forces to

concentrate their eort at particular points. Heider (1997) notes that "It was

easy to imagine that they were something like battleeld commanders, directing

their troops," however, he continues, "these men were hardly commanding, and

whenever they tried, no one was obeying."38

Larson records that each skirmish, which lasts between 30 to 45 minutes,

36 Heider (1997) page 104.37 Heider (1997) page 116.38 Heider (1997) page 104.

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is followed by a period of resting - usually another twenty minutes. 39 This lull

in ghting is used to take note of and announce casualties and coach warriors,

who huddle around their respective war leaders in groups of 20 to 30. During

this time, war shamans attempt to inspire greater eort "by circle dancing with

drawn bow" around them.40 Having received their instructions for the next

round of skirmishing, they take o running along the ridges of the battleeld.

Screaming war cries and engaging in mock battle maneuvers, they once again

attempt to impress their opponents with another display of ferocity before con-

verging on the middle of the battleeld to begin the next round of skirmishing.

Fighting can last from dawn to dusk, excluding the possibility for rain, and

include as many as 300 warriors on each side.41 It is in the failing light of dusk,

when ones accuracy with the bow begins to falter and arrow dodging is more

dicult, that both sides agree to bring this days battle to a close.

This pattern will continue uninterrupted for as many days as it takes to reach

a balance in battleeld deaths "normally" no more than three months.42 In-

deed ritual battles may results in "hundreds" being wounded, battleeld deaths

are rather limited. In the Ilaga Valley, the average number of deaths was limited

to 23 ranging from 7 to 48.43 One reason for this is that a tactical objective

shared by both is to turn the enemys ank and unleash a deadly crossre of

arrows. This objective, however, is common knowledge and to achieve it war-

riors must operate outside the boundaries of the battleeld, which is proscribed.

Another reason is that their arrows are not etched. Inevitably, released arrows

quickly lose velocity and accuracy in ight - giving their intended targets ample

time with which to dodge and evade them. Therefore the danger that attends

ones participation stems primarily from the number of arrows simultaneously39 Larson (1987) page 260.40 Larson (1987) page 253.41 Larson (1987) page 260.42 Larson (1987) page 246.43 Larson (1987) page 262.

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discharged - which once again is uncoordinated and therefore of limited danger.

Due to the absence of leaders with coercive power, individualism pervades the

battleeld and "limits the eectiveness of groups in combat."44

Ritual battles, consequently, have been interpreted as a device through which

competing communities can mutually agree upon a de-escalation of hostilities. 45

The battleeld, however, is also a testing ground - each battle a "test of enemy

strength."46 In this context, where neither side enjoys a technological advantage,

military strength translates into the number of warriors that a community can

eld each and every day of battle. Indeed, ritual battles have been referred to as

"man-power testing."47 Allies play a pivotal role in ritual battles. In the Ilaga

Valley, the communities of the third alliance purposively split themselves evenly

between the two owners of the conict.48 The common reason given for this

behavior was to "equalize the size of each ghting force" and thereby prevent the

conict from escalating to a rout.49 As mentioned earlier, whenever a balance

in casualties is realized, a rout can be forestalled. This is true. Nonetheless,

those communities that are owners of the war should suer more losses than

their allies. And, among their allies, those coming from the same alliance as the

owner of the war should suer more losses than those allies that arrived from

another alliance that is not a party to the dispute.50 In want of a balance of

losses or a distribution of losses that fall in with the above expectations, allies

may exit the ght ground or even switch sides during the course of a battle.

If so, a rout commences. It begins with those warriors enjoying a numerical

advantage charging forward. Outnumbered, their opponents break ranks and

ee the ght ground. Retreating warriors rush back to their hamlets to gather

44

Heider (1997) page 116.45 Rappaport (1984) p. 122.46 Larson (1987) p. 257.47 Shankman (1991) p. 310.48 Larson (1987) p. 250.49 Larson (1987) p. 286.50 Larson (1987) pp. 262-3.

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loved ones and seek refuge with allies. All the while, they are being pursued

by spearmen. The scope of acceptable tactics widens. In the eld, no combat-

ant is given quarter and all who can be are hunted down, killed and routinely

mutilated. At the hamlets, women and children are legitimate targets, arson is

employed, and property damage is intentionally maximized.

Larson (1987) reports that out of seventeen documented cases of ritual bat-

tles, on seven occasions, one side was routed from the eld of battle yet was able

to rally support from allies in another part of the valley. With the help of ad-

ditional warriors, they matched the numbers of their opponents and continued

ritual warfare at a later date. However, on two occasions (the 10th and 14th

wars) the losing side, unable to rally supports from allies, could not continue

ritual warfare and restore a balance in casualties. In both instances, the losing

side was pushed out of the valley (200 individuals in the 10th war and 2000

individuals in the 14th).

The conduct of ritual battle, among the Dani, closely resembles the unorga-

nized combat that we model. Yes, the Dani do have in place a command-and-

control structure, which the model does not allow for, however, it is rudimentary

at best and for the most part ineective at inuencing the behavior of their war-

riors. Indeed, the conduct of their ritual battles is consistent with the models

overarching predictions. There is no mass collision of opposing forces. While

convergence in the middle of the ght ground is indicative of some degree of

cooperation among the members of opposing forces, its hesitancy and the fact

that those forces maintain a distance of 15-20 yards inform us that cooperation

at some point falters. There exists a window of cooperation, like the model pre-

dicts; but, it closes rapidly. The pattern of skirmishing - rushing forward and

then retreating - provides additional support. As modeled, each warrior con-

fronts a tension namely, the incentive to ght in order to establish some level

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of personal exclusivity over the prize and the incentive to free-ride and share in

the exclusivity established by others. At the same time, they have an incentive

to ee when opponents increase their eort. We argue that two opposing lines

continually undulating but never coming spear-to-spear is consistent with these

predictions. Individual warriors may traverse this distance and make contact

with an opponent. Others may provide them with indirect support by ring

arrows. The duel-like characterization of these interactions, however, provides

additional support for free-riding. These braver warriors are on their own.

The general conclusion of the model is that warrior warfare is simply un-

coordinated. The absence of concerted maneuvers and volleys, the confused

falling back and resting of warriors and the preferred choice of weapon (the bow

and arrow as opposed to the spear) all lend support for this conclusion. Ritual

battles are battles between individuals fought, for the most part, at a distance.

Barring, that is, the rare occasion in which a rout occurs. Routs enjoy a higher

degree of cooperation among participants. This is consistent with the model as

well. It is during a rout that one side or the other has turned their backs and

run. These circumstances reduce the expected marginal cost of ghting and as

the model predicts we should observe more ghting. It is simply more reward-

ing. The only other aspect of ritual battle that is coordinated is the gathering

of opposing forces at a particular time and place of battle. Ritual battles, we

conclude, are warrior warfare.

4 Conclusion

Warrior warfare is inecient and fails to consummate in a collision. At the

heart of this conclusion lies the warriors choice calculus. In general, when

choosing to allocate a unit of eort toward ghting, a warrior bears the entire

marginal cost of this action; yet, enjoys only a share of the marginal benets.

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Our warrior confers a positive externality on other members of the team of

combatants. Understandably, this fact reduces his incentive to ght. More

specically, when the special case sharing rule and symmetrical conditions on

the battleeld hold, an individual warrior not only has the incentive to shirk

when fellow warriors increase their eort but to retreat when his foes increase

their eort as well. Indeed, at some point during hostilities, every member of

the team of combatants has an incentive to shirk and retreat. And, beyond some

critical level of eort exerted by their opponents, every member of the team of

combatants has an incentive to ee the ght the battleeld completely. The

pattern observed by anthropologists in the Highlands of two opposing parallel

lines continually undulating yet never closing is consistent with these underlying

incentives. Our simple model of unorganized combat gives us insights into the

underlying causes of this pattern as well as routs.

While this papers empirical focus has been limited to communities in the

New Guinea Highlands, the incentive to shirk and retreat was a pervasive prob-

lem for all pre-state societies. Whether hunters and gatherers or, like the

Dani, simple horticulturists, this pattern of face-to-face combat has been de-

scribed independently by anthropologists in numerous communities, including

the Eskimo, Great Plains Indians, Northwest Coast Indians, and Aboriginal

Australians.51 Indeed, as suggested in the introduction, the challenge of coordi-

nating the ghting eorts of friendly combatants has been a problem throughout

all of human warfare. Our capacity for collective violence was and is fundamen-

tally constrained by the simple fact that whenever a combatant exerts eort

during combat he confers a positive externality on other friendly combatants.

This challenge manifests itself in varying degrees, depending largely on the ex-

tent to which combatants are organized and remain organized on the approach

to and during combat. For the Dani, war leaders, Big Men and Shamans could

51 Gat (1999).

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endeavor to inspire more eort on the ght ground; however, no amount of

peer-pressure, cajoling, or circle-dancing could fully internalize this externality.

Tightening the link between a warriors share of the prize and his battleeld

performance would have to await an organizational innovation; namely, the

command and control of a hierarchical military organization.52 Until that time,

our primeval practice of ritual battles would necessarily be warrior warfare; that

is, inecient and inconclusive.

References

[1] Gat, Azar (1999) "The Pattern of Fighting in Simple Small Scale, Prestate

Societies," Journal of Anthropological Research, Vol. 55: 563-83.

[2] Gardner Robert G., Karl G. Heider, and Jan Broekhuyse. (1964) Dead

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[3] Heider, Karl G. (1970) The Dugum Dani: A Papuan Culture in the High-

lands of West New Guinea Chicago: Aldine Publishing Company.

[4] Hirshleifer, Jack (1989) "Conict and Rent-seeking Success Functions: Ra-

tio vs. Dierence Models of relative Success," Public Choice, Vol. 63: 101-

112.

[5] Hirshleifer, Jack (2001) The Dark Side of the Force: Economic Foundations

of Conict Theory, Cambridge, UK: Cambridge University Press.

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[7] Heider, Karl G. (1997) Grand Valley Dani: Peaceful Warriors 3rd ed. Fort

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[8] Holmstrom, Bengt (1982) "Moral Hazard in Teams," Bell Journal of Eco-

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[9] Larson, Gordon (1987) The Structure and Demography of the Cycle of

Warfare among the Ilaga Dani of Irian Jaya. PhD diss., University of

Michigan.

[10] Marshall, S.L.A. (1947) Men Against Fire: The Problem of Battle Com-

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[11] du Picq, Ardant (1921) Battle Studies: Ancient and Modern Battle, New

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[12] Rappaport, Roy A. (1984) Pigs for the Ancestors: Ritual in the Ecology of

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[13] Shankman, Paul. Culture Contact, Cultural Ecology, and Dani Warfare.

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