The bargaining power of the potential aggressor increases
dramatically
if she is able to make probabilistic threats, e.
Schwarz - Committments
A Theory of Brinkmanship, Cona?
icts, and Commitments
Michael Schwarzyand Konstantin Soninz December 20, 2004
Abstract
Many cona? icts and negotiations can be viewed as a dynamic game, where parties have no commitment power. In our model, a potential aggressor demands concessions from the weaker party threatening a war. The absence of commitment makes a con- cessions in the form of a continuous stream of transfers a more e? ective appeasement strategy than a lump sum transfer. Based on such strategy, it is possible to construct a self-enforcing peace agreement between risk-neutral parties even if transfers shift the balance of power. However, when parties are risk averse, a self-enforcing peace agree- ment may not be feasible. The bargaining power of the potential aggressor increases dramatically if she is able to make probabilistic threats, e. g. by taking an observable action that leads to a war with positive probability. In particular, the ability to engage in brinkmanship allows a blackmailer to extract a positive stream of payments from the victim even if carrying out the threat is harmful to both parties. Although we use the terminology of international relations, our results are applicable to environ- ments ranging from diplomacy to negotiations within or among O? rms, and are aimed to bring together i? paralleli? investigations in the nature of commitment in economics and political science.
The authors are grateful to Andrei Shleifer, Luigi Zingales, and seminar participants at the Kellogg Business School, Pennsylvania State University and UCSC for valuable comments.
yUniversity of California at Berkeley and NBER; mschwartz@berkeley. edu. Part of this paper was written
while this author was a National Fellow at the Hoover Institution at Stanford. He would like to express his
gratitude to the Hoover Institution for enabling him to spend a productive year at Stanford.
z Institute for Advanced Study, Princeton, NJ, and New Economic School/CEFIR, Moscow;
ksonin@ias. edu.
? 1
1 Introduction
When the ria? e was invented, bows and arrows became obsolete. After the invention of nuclear weapons many observers expected that the conventional weapons would go the way of bows and arrows. For instance, one of the leading columnists of his time, Drew Pearson, declared in the Fall of 1945 that: i`the Navy and huge armies are now obsoletei^. 1 Later it became apparent that nuclear weapons do not give expected political leverage. In 1957, rea? ecting on the time when the US had a nuclear monopoly, Henry Kissinger commented with a measure of surprise that i^We never succeeded in translating our military [nuclear] superiority into a political advantage. i^Today, the verdict of history is clear: conventional arsenal remains important in the nuclear era.
Unfortunately, history is an infallible judge that never writes opinions to explain its ver- dicts. This paper o? ers a framework that deepens our understanding of the role of threats in the environments ranging from international negotiations to negotiations among or within a O? rm. We show that an i`indivisiblei^threat such as such as a nuclear capabilities gives a party far less bargaining power than a threat that is divisible, such as a large arsenal of con- ventional weapons. We also show that a self-enforcing peace agreement between negotiating parties should rely on a sequence of transfers or pre-negotiated concessions (as opposed to one large concession that buys peace). Fearon (1995) argues that indivisibility of the object of bargaining might be a rationalist explanation for cona? icts,2 while Powell (2004) argues that the commitment problem lies in the heart of the i? indivisibility argumenti? : if commitment is possible, a lottery over the indivisible object would be Pareto-superior to any cona? ict. We focus on how the ability to make observable probabilistic or divisible threats a? ects partiesi? bargaining power.
The study of blackmail received little attention from economists. At the O? rst glance, this may seem justiO? ed because relevance of blackmail may appear to be limited to small time crooks and nations with nuclear capabilities. However, in a broader sense many economic relationships involve an element of a blackmail. For instance, a manager induces a worker
1 For a full text of the quote and for analysis of evolution of conventional wisdom about the role of nuclear
weapons in national defence see Besse and Lasswell (1950).
2Early studies of war as a bargaining process are Schelling (1966), Wagner (1982), and Pillar (1983).
Recent models of negotiations in/and wars include Fearon (1995), Filson and Werner (2002), Smith and Stam (2003), Powell (2002, 2004), Slantchev (2003), Wittman (2003), Baliga and Sjostrom (2004).
? 2
to put forth more e? ort by a threat of O? ring, a tenant wants the landlord to do timely maintenance threatening to terminate the lease etc. Legal scholars devoted considerable attention to blackmail. 3 The celebrated Coase theorem (Coase, 1962) was in part an outcome of a decades-long intellectual inquiry of the author in legal questions related to blackmail (Coase, 1988). 4 A deO? ning feature of a successful blackmail is that the threat must be credible (e. g. , Shavell, 1992). Shavell and Spier (2002) analyze blackmail in the absence of binding commitment. In particular, they O? nd that if carrying out a threat is costly, then extracting a payment from a victim is impossible even in an inO? nite horizon setting. The main innovation of our paper relative to Shavell and Spier (2002) is that we introduce brinkmanship into the model. We deO? ne brinkmanship as an ability of the aggressor to undertake an observable action that will lead with positive probability to a war or some other mutually undesirable outcome; i`shooting over the headi^is a metaphor for the kind of brinkmanship we have in mind. We show that being able to engage in this kind of visible brinkmanship may allow the potential aggressor to extract the whole surplus from the victim.
In this paper, we employ the international-relations terminology, though the applications of this idea stretch far beyond the nuclear power politics. For example, in a relationship between a manager and an employee we observe the same pattern: if the only threat available to the manager is to O? re an employee, then manageri? s ability to extract e? ort from the employee may be less than in the case where the manager can make the punishment inO? nitely divisible or probabilistic. Intuitively, if the only options available to a manager are to O? re or to retain a worker, a worker only has to put forth enough e? ort to make the manager indi? erent between O? ring and retaining him. All the bargaining power resides with the worker. If the manager can impose arbitrarily small penalties on the worker he can induce a higher e? ort level (though it might be that in equilibrium penalties are never imposed).
For an economist, the phenomenon of war is in striking contradiction with the so-called i? Coase theoremi? that says that rational agents will always negotiate a Pareto e? cient arrange- ment. 5 At the O? rst glance, it may seem that the weaker party can avoid a cona? ict by trans-
3The fasciation of legal scholars with blackmail dates to at least the O? rst half of the 20th century, as
Campbell (1939) puts it: i^The law of blackmail has something in common with the blackmailer: it allows
its student no peace of mind. i^
4 Other works on economics of blackmail include Ginsburg and Shechtman (1993) and Posner (1993). 5Theories explaining failure of Pareto-e? ciency abound (see, e. g. , very di? erent perspectives in Coase,
1962, Myerson and Satterthwaite, 1983, Acemoglu, 2003). However, neither transaction costs, nor informa-
? 3
ferring resources to the stronger side. 6;7 However, in the absence of external enforcement, no peaceful agreement could ensure that a strong party would not ask for more concessions in the future. Furthermore, the more transfers the strong party receives, the stronger it becomes. One problem is that the commitment power of parties involved in any destructive cona? ict is very limited. 8 Indeed, a binding agreement that calls for a lump sum wealth transfer from one nation to the other in exchange for a promise of peace, can make both parties better o? . However, this type of agreement is not self-enforcing, except for an unlikely scenario, where the pay-o? to the potential aggressor from starting a war decreases substantially as a result of receiving a transfer. 9 Consequently, due to the lack of commitment power, a lump sum transfer in exchange for peace is unlikely to be viable. 10 Rajan and Zingales (2000) formalize this point and show that the lack of commitment power leads to ine? cient outcomes rang- ing from wars to wasteful political cona? icts in organizations. Acemoglu (2003) emphasizes that i^parties holding political power cannot make commitments to bind their future actions because there is no outside agency with the coercive capacity to enforce such arrangements. i^
This paper builds on Rajan and Zingales (2000). We show that their results need not hold
in dynamic setting where a continuos stream of transfers is feasible. Proposition 2 establishes
that resource transfers can form a basis for lasting peace. Unavailability of external contract
enforcement can be mitigated by spreading transfers over time. For example, a potential
aggressor, who receives a transfer every period, would O? nd it proO? table to refrain from
tional asymmetry can fully explain the phenomenon of war (e. g. , Fearon, 1995).
6Lengi? s (1993) typology of ina? uence strategies refers to such a strategy as appeasing. In Huth (1988)
typology, any policy of concessions is conciliatory. Hensel and Diehl (1994) analyze various non-militarized
responses on an immediate military threat. Wittman (2003) considers appeasement in a static setting and
argues that it should be possible to redraw the map so that peace becomes a self enforcing outcome. 7There is a strand of literature that argues that most wars are wanted from the ex-ante perspectives
(e. g, Blainley, 1988). Still, this case is much harder to make from the Pareto-e? ciency perspective: in rare
circumstances, a war is wanted on both sides.
8Barzel (2002) considers the absence of commitment a major cause for violent cona? icts: i^The problem
of . . . the inability to commit is also the root of theft and some warsi^. Classic work that focused on the problem of commitment is North and Weingast (1989) and Shepsle (1991). Most recently, the problem has become the central element in dynamic models of development suggested by Acemoglu and Robinson (e. g. , Acemoglu, 2003). Powell (2004) discusses commitment problems in various contexts close to ours.
9This is not entirely impossible. According to a legend when Attilla the Hun came to Rome, the citizens
of Rome gave him all the gold of Rome in exchange for peace, thus making conquest of the city less attractive
for him.
10Shavell and Spier (2002) invoke Vikings history to illustrate the importance of succession of payments.
? 4
starting a war as long as the present value of the stream of transfers exceeds the payo? from a war. Similarly, the other side would be willing to make transfer payments if the following two conditions are satisO? ed: (i) Present value of transfers is less than the expected loss from a war. (ii) The i? weaki? side believes that reducing the size of transfers would prompt the war. 11 We identify the conditions under which an appeasement strategy can succeed. We show that if parties have constant marginal utility of consumption then there exists a continuous stream of transfers that supports a sub-game perfect peaceful equilibrium. Constant marginal utility of consumption is mathematically equivalent to risk-neutrality. This assumption insures that any stream of transfers corresponds to a Pareto e? cient outcome.
If agents are risk-averse, then a self enforcing peace agreement may not be viable because concession will shift the balance of powers and increase future expected losses of the weaker party. 12 Risk aversion assumption implies diminishing marginal utility. Consequently, the weaker party may be very averse to being completely wiped out and the stronger party may gain very little from swallowing the weaker side completely. In this case, there may not exist a viable appeasement strategy, since appeasement may lead to a shift in the balance of power that makes the destruction of the weaker party inevitable. This is consistent with Fearon (1995) who argues that preventive wars should be understood as a result of commitment problems. 13 Slantchev (2001) analyzes the functioning of the Concert of Europe during the O? rst half of the 19th century. He concludes that "the pattern of cooperative behavior is seen to result from the commitment to uphold the settlement, which hinged on the credibility of enforcement threats. . . ".
This logic helps us understand many historic events. Every year since 1933, then- European powers, including England, France, and Poland faced a dilemma: either to O? ght Hitler now, or appease him and wait (Taylor, 1961). First concession was postponement of the World War I debt payments, next came tolerance of mobilization in Germany and launching of German air forces, and then re-occupation of Ruhrgebiet. The Munich treaty
11In fact, arrangements of this nature were practiced throughout history. A number of medieval cities bought peace by making annual contributions to their stronger neighbors. Above arguments suggest that a self-enforcing peace agreement may be viable, provided wealth transfers have a su? ciently small ina? uence on the balance of powers.
12Addressing the moral side of the problem, Walzer (1992) draws a parallel between international negotia-
tions and negotiations with kidnappers and extortionists. Our argument might explain the underlying logic
of legal obstacles to the former negotiations.
13Powell (2004) provides a survey of the literature related to the commitment problem.
? 5
of 1938 year, where the (future) allies agreed with occupation of Sudetenland, a part of Czechoslovakia, is probably the most prominent concession (e. g. , Walzer, 1992; for a game- theoretic analysis, see Hirshleifer, 2001). On October 5, 1938 Winston Churchill, the leader of the opposition in the British parliament, said that i`it seems to me that all those countries of Middle Europe, all those Danubian countries, will, one after another, be drawn into this vast system of power politics - not only power military politics but power economic politics n? radiating from Berlin, and I believe this can be achieved quite smoothly and swiftly and will not necessarily entail the O? ring of a single shot. . . . i^In 1940, it became too clear that Germany is already too strong, and England actually entered the World War II out of the fear that Germany would be even stronger in the future. 14 On May 13, Churchill, a prime-minister for O? ve days, said: i`What is our aim? I can answer in one word: Victory - victory - at all costs, victory, . . . however long and hard the road may be; for without victory, there is no survival.
The bargaining power of the potential aggressor increases dramatically if she is able to make probabilistic threats, e. g. by taking an observable action that leads to a war with positive probability. In particular, the ability to engage in brinkmanship allows a blackmailer to extract a positive stream of payments from the victim even if carrying out the threat is harmful to both parties. Although we use the terminology of international relations, our results are applicable to environ- ments ranging from diplomacy to negotiations within or among O? rms, and are aimed to bring together i? paralleli? investigations in the nature of commitment in economics and political science.
The authors are grateful to Andrei Shleifer, Luigi Zingales, and seminar participants at the Kellogg Business School, Pennsylvania State University and UCSC for valuable comments.
yUniversity of California at Berkeley and NBER; mschwartz@berkeley. edu. Part of this paper was written
while this author was a National Fellow at the Hoover Institution at Stanford. He would like to express his
gratitude to the Hoover Institution for enabling him to spend a productive year at Stanford.
z Institute for Advanced Study, Princeton, NJ, and New Economic School/CEFIR, Moscow;
ksonin@ias. edu.
? 1
1 Introduction
When the ria? e was invented, bows and arrows became obsolete. After the invention of nuclear weapons many observers expected that the conventional weapons would go the way of bows and arrows. For instance, one of the leading columnists of his time, Drew Pearson, declared in the Fall of 1945 that: i`the Navy and huge armies are now obsoletei^. 1 Later it became apparent that nuclear weapons do not give expected political leverage. In 1957, rea? ecting on the time when the US had a nuclear monopoly, Henry Kissinger commented with a measure of surprise that i^We never succeeded in translating our military [nuclear] superiority into a political advantage. i^Today, the verdict of history is clear: conventional arsenal remains important in the nuclear era.
Unfortunately, history is an infallible judge that never writes opinions to explain its ver- dicts. This paper o? ers a framework that deepens our understanding of the role of threats in the environments ranging from international negotiations to negotiations among or within a O? rm. We show that an i`indivisiblei^threat such as such as a nuclear capabilities gives a party far less bargaining power than a threat that is divisible, such as a large arsenal of con- ventional weapons. We also show that a self-enforcing peace agreement between negotiating parties should rely on a sequence of transfers or pre-negotiated concessions (as opposed to one large concession that buys peace). Fearon (1995) argues that indivisibility of the object of bargaining might be a rationalist explanation for cona? icts,2 while Powell (2004) argues that the commitment problem lies in the heart of the i? indivisibility argumenti? : if commitment is possible, a lottery over the indivisible object would be Pareto-superior to any cona? ict. We focus on how the ability to make observable probabilistic or divisible threats a? ects partiesi? bargaining power.
The study of blackmail received little attention from economists. At the O? rst glance, this may seem justiO? ed because relevance of blackmail may appear to be limited to small time crooks and nations with nuclear capabilities. However, in a broader sense many economic relationships involve an element of a blackmail. For instance, a manager induces a worker
1 For a full text of the quote and for analysis of evolution of conventional wisdom about the role of nuclear
weapons in national defence see Besse and Lasswell (1950).
2Early studies of war as a bargaining process are Schelling (1966), Wagner (1982), and Pillar (1983).
Recent models of negotiations in/and wars include Fearon (1995), Filson and Werner (2002), Smith and Stam (2003), Powell (2002, 2004), Slantchev (2003), Wittman (2003), Baliga and Sjostrom (2004).
? 2
to put forth more e? ort by a threat of O? ring, a tenant wants the landlord to do timely maintenance threatening to terminate the lease etc. Legal scholars devoted considerable attention to blackmail. 3 The celebrated Coase theorem (Coase, 1962) was in part an outcome of a decades-long intellectual inquiry of the author in legal questions related to blackmail (Coase, 1988). 4 A deO? ning feature of a successful blackmail is that the threat must be credible (e. g. , Shavell, 1992). Shavell and Spier (2002) analyze blackmail in the absence of binding commitment. In particular, they O? nd that if carrying out a threat is costly, then extracting a payment from a victim is impossible even in an inO? nite horizon setting. The main innovation of our paper relative to Shavell and Spier (2002) is that we introduce brinkmanship into the model. We deO? ne brinkmanship as an ability of the aggressor to undertake an observable action that will lead with positive probability to a war or some other mutually undesirable outcome; i`shooting over the headi^is a metaphor for the kind of brinkmanship we have in mind. We show that being able to engage in this kind of visible brinkmanship may allow the potential aggressor to extract the whole surplus from the victim.
In this paper, we employ the international-relations terminology, though the applications of this idea stretch far beyond the nuclear power politics. For example, in a relationship between a manager and an employee we observe the same pattern: if the only threat available to the manager is to O? re an employee, then manageri? s ability to extract e? ort from the employee may be less than in the case where the manager can make the punishment inO? nitely divisible or probabilistic. Intuitively, if the only options available to a manager are to O? re or to retain a worker, a worker only has to put forth enough e? ort to make the manager indi? erent between O? ring and retaining him. All the bargaining power resides with the worker. If the manager can impose arbitrarily small penalties on the worker he can induce a higher e? ort level (though it might be that in equilibrium penalties are never imposed).
For an economist, the phenomenon of war is in striking contradiction with the so-called i? Coase theoremi? that says that rational agents will always negotiate a Pareto e? cient arrange- ment. 5 At the O? rst glance, it may seem that the weaker party can avoid a cona? ict by trans-
3The fasciation of legal scholars with blackmail dates to at least the O? rst half of the 20th century, as
Campbell (1939) puts it: i^The law of blackmail has something in common with the blackmailer: it allows
its student no peace of mind. i^
4 Other works on economics of blackmail include Ginsburg and Shechtman (1993) and Posner (1993). 5Theories explaining failure of Pareto-e? ciency abound (see, e. g. , very di? erent perspectives in Coase,
1962, Myerson and Satterthwaite, 1983, Acemoglu, 2003). However, neither transaction costs, nor informa-
? 3
ferring resources to the stronger side. 6;7 However, in the absence of external enforcement, no peaceful agreement could ensure that a strong party would not ask for more concessions in the future. Furthermore, the more transfers the strong party receives, the stronger it becomes. One problem is that the commitment power of parties involved in any destructive cona? ict is very limited. 8 Indeed, a binding agreement that calls for a lump sum wealth transfer from one nation to the other in exchange for a promise of peace, can make both parties better o? . However, this type of agreement is not self-enforcing, except for an unlikely scenario, where the pay-o? to the potential aggressor from starting a war decreases substantially as a result of receiving a transfer. 9 Consequently, due to the lack of commitment power, a lump sum transfer in exchange for peace is unlikely to be viable. 10 Rajan and Zingales (2000) formalize this point and show that the lack of commitment power leads to ine? cient outcomes rang- ing from wars to wasteful political cona? icts in organizations. Acemoglu (2003) emphasizes that i^parties holding political power cannot make commitments to bind their future actions because there is no outside agency with the coercive capacity to enforce such arrangements. i^
This paper builds on Rajan and Zingales (2000). We show that their results need not hold
in dynamic setting where a continuos stream of transfers is feasible. Proposition 2 establishes
that resource transfers can form a basis for lasting peace. Unavailability of external contract
enforcement can be mitigated by spreading transfers over time. For example, a potential
aggressor, who receives a transfer every period, would O? nd it proO? table to refrain from
tional asymmetry can fully explain the phenomenon of war (e. g. , Fearon, 1995).
6Lengi? s (1993) typology of ina? uence strategies refers to such a strategy as appeasing. In Huth (1988)
typology, any policy of concessions is conciliatory. Hensel and Diehl (1994) analyze various non-militarized
responses on an immediate military threat. Wittman (2003) considers appeasement in a static setting and
argues that it should be possible to redraw the map so that peace becomes a self enforcing outcome. 7There is a strand of literature that argues that most wars are wanted from the ex-ante perspectives
(e. g, Blainley, 1988). Still, this case is much harder to make from the Pareto-e? ciency perspective: in rare
circumstances, a war is wanted on both sides.
8Barzel (2002) considers the absence of commitment a major cause for violent cona? icts: i^The problem
of . . . the inability to commit is also the root of theft and some warsi^. Classic work that focused on the problem of commitment is North and Weingast (1989) and Shepsle (1991). Most recently, the problem has become the central element in dynamic models of development suggested by Acemoglu and Robinson (e. g. , Acemoglu, 2003). Powell (2004) discusses commitment problems in various contexts close to ours.
9This is not entirely impossible. According to a legend when Attilla the Hun came to Rome, the citizens
of Rome gave him all the gold of Rome in exchange for peace, thus making conquest of the city less attractive
for him.
10Shavell and Spier (2002) invoke Vikings history to illustrate the importance of succession of payments.
? 4
starting a war as long as the present value of the stream of transfers exceeds the payo? from a war. Similarly, the other side would be willing to make transfer payments if the following two conditions are satisO? ed: (i) Present value of transfers is less than the expected loss from a war. (ii) The i? weaki? side believes that reducing the size of transfers would prompt the war. 11 We identify the conditions under which an appeasement strategy can succeed. We show that if parties have constant marginal utility of consumption then there exists a continuous stream of transfers that supports a sub-game perfect peaceful equilibrium. Constant marginal utility of consumption is mathematically equivalent to risk-neutrality. This assumption insures that any stream of transfers corresponds to a Pareto e? cient outcome.
If agents are risk-averse, then a self enforcing peace agreement may not be viable because concession will shift the balance of powers and increase future expected losses of the weaker party. 12 Risk aversion assumption implies diminishing marginal utility. Consequently, the weaker party may be very averse to being completely wiped out and the stronger party may gain very little from swallowing the weaker side completely. In this case, there may not exist a viable appeasement strategy, since appeasement may lead to a shift in the balance of power that makes the destruction of the weaker party inevitable. This is consistent with Fearon (1995) who argues that preventive wars should be understood as a result of commitment problems. 13 Slantchev (2001) analyzes the functioning of the Concert of Europe during the O? rst half of the 19th century. He concludes that "the pattern of cooperative behavior is seen to result from the commitment to uphold the settlement, which hinged on the credibility of enforcement threats. . . ".
This logic helps us understand many historic events. Every year since 1933, then- European powers, including England, France, and Poland faced a dilemma: either to O? ght Hitler now, or appease him and wait (Taylor, 1961). First concession was postponement of the World War I debt payments, next came tolerance of mobilization in Germany and launching of German air forces, and then re-occupation of Ruhrgebiet. The Munich treaty
11In fact, arrangements of this nature were practiced throughout history. A number of medieval cities bought peace by making annual contributions to their stronger neighbors. Above arguments suggest that a self-enforcing peace agreement may be viable, provided wealth transfers have a su? ciently small ina? uence on the balance of powers.
12Addressing the moral side of the problem, Walzer (1992) draws a parallel between international negotia-
tions and negotiations with kidnappers and extortionists. Our argument might explain the underlying logic
of legal obstacles to the former negotiations.
13Powell (2004) provides a survey of the literature related to the commitment problem.
? 5
of 1938 year, where the (future) allies agreed with occupation of Sudetenland, a part of Czechoslovakia, is probably the most prominent concession (e. g. , Walzer, 1992; for a game- theoretic analysis, see Hirshleifer, 2001). On October 5, 1938 Winston Churchill, the leader of the opposition in the British parliament, said that i`it seems to me that all those countries of Middle Europe, all those Danubian countries, will, one after another, be drawn into this vast system of power politics - not only power military politics but power economic politics n? radiating from Berlin, and I believe this can be achieved quite smoothly and swiftly and will not necessarily entail the O? ring of a single shot. . . . i^In 1940, it became too clear that Germany is already too strong, and England actually entered the World War II out of the fear that Germany would be even stronger in the future. 14 On May 13, Churchill, a prime-minister for O? ve days, said: i`What is our aim? I can answer in one word: Victory - victory - at all costs, victory, . . . however long and hard the road may be; for without victory, there is no survival. i^
The same reasoning may explain why rulers often miss opportunities to make concessions to the opposition in the days preceding revolutions. Why would not the Russian czar agree to share power with the elected parliament (where the majority was very far from any leftist movement) in January 1917? Why Louis XVI gambled on counter-revolutionary plots during the O? rst years of French revolution, instead of trying to work out a real political compromise? The answer is that the reluctance of these rulers can be explained by the fear that any concession would have empowered the opposition to ask for even more concessions. Then, they would have a choice between making an escalating sequence of greater and greater concessions or an open struggle under less favorable conditions. Nikolai II of Russia and Louis XVI were the ultimate losers, but there are examples of rulers who ultimately prevailed. 15
In Section 4 we show that the bargaining power of the potential aggressor increases dramatically if she is able to make her threat divisible. For instance she may achieve so by taking observable action that lead to a war with positive probability.
Michael Schwarzyand Konstantin Soninz December 20, 2004
Abstract
Many cona? icts and negotiations can be viewed as a dynamic game, where parties have no commitment power. In our model, a potential aggressor demands concessions from the weaker party threatening a war. The absence of commitment makes a con- cessions in the form of a continuous stream of transfers a more e? ective appeasement strategy than a lump sum transfer. Based on such strategy, it is possible to construct a self-enforcing peace agreement between risk-neutral parties even if transfers shift the balance of power. However, when parties are risk averse, a self-enforcing peace agree- ment may not be feasible. The bargaining power of the potential aggressor increases dramatically if she is able to make probabilistic threats, e. g. by taking an observable action that leads to a war with positive probability. In particular, the ability to engage in brinkmanship allows a blackmailer to extract a positive stream of payments from the victim even if carrying out the threat is harmful to both parties. Although we use the terminology of international relations, our results are applicable to environ- ments ranging from diplomacy to negotiations within or among O? rms, and are aimed to bring together i? paralleli? investigations in the nature of commitment in economics and political science.
The authors are grateful to Andrei Shleifer, Luigi Zingales, and seminar participants at the Kellogg Business School, Pennsylvania State University and UCSC for valuable comments.
yUniversity of California at Berkeley and NBER; mschwartz@berkeley. edu. Part of this paper was written
while this author was a National Fellow at the Hoover Institution at Stanford. He would like to express his
gratitude to the Hoover Institution for enabling him to spend a productive year at Stanford.
z Institute for Advanced Study, Princeton, NJ, and New Economic School/CEFIR, Moscow;
ksonin@ias. edu.
? 1
1 Introduction
When the ria? e was invented, bows and arrows became obsolete. After the invention of nuclear weapons many observers expected that the conventional weapons would go the way of bows and arrows. For instance, one of the leading columnists of his time, Drew Pearson, declared in the Fall of 1945 that: i`the Navy and huge armies are now obsoletei^. 1 Later it became apparent that nuclear weapons do not give expected political leverage. In 1957, rea? ecting on the time when the US had a nuclear monopoly, Henry Kissinger commented with a measure of surprise that i^We never succeeded in translating our military [nuclear] superiority into a political advantage. i^Today, the verdict of history is clear: conventional arsenal remains important in the nuclear era.
Unfortunately, history is an infallible judge that never writes opinions to explain its ver- dicts. This paper o? ers a framework that deepens our understanding of the role of threats in the environments ranging from international negotiations to negotiations among or within a O? rm. We show that an i`indivisiblei^threat such as such as a nuclear capabilities gives a party far less bargaining power than a threat that is divisible, such as a large arsenal of con- ventional weapons. We also show that a self-enforcing peace agreement between negotiating parties should rely on a sequence of transfers or pre-negotiated concessions (as opposed to one large concession that buys peace). Fearon (1995) argues that indivisibility of the object of bargaining might be a rationalist explanation for cona? icts,2 while Powell (2004) argues that the commitment problem lies in the heart of the i? indivisibility argumenti? : if commitment is possible, a lottery over the indivisible object would be Pareto-superior to any cona? ict. We focus on how the ability to make observable probabilistic or divisible threats a? ects partiesi? bargaining power.
The study of blackmail received little attention from economists. At the O? rst glance, this may seem justiO? ed because relevance of blackmail may appear to be limited to small time crooks and nations with nuclear capabilities. However, in a broader sense many economic relationships involve an element of a blackmail. For instance, a manager induces a worker
1 For a full text of the quote and for analysis of evolution of conventional wisdom about the role of nuclear
weapons in national defence see Besse and Lasswell (1950).
2Early studies of war as a bargaining process are Schelling (1966), Wagner (1982), and Pillar (1983).
Recent models of negotiations in/and wars include Fearon (1995), Filson and Werner (2002), Smith and Stam (2003), Powell (2002, 2004), Slantchev (2003), Wittman (2003), Baliga and Sjostrom (2004).
? 2
to put forth more e? ort by a threat of O? ring, a tenant wants the landlord to do timely maintenance threatening to terminate the lease etc. Legal scholars devoted considerable attention to blackmail. 3 The celebrated Coase theorem (Coase, 1962) was in part an outcome of a decades-long intellectual inquiry of the author in legal questions related to blackmail (Coase, 1988). 4 A deO? ning feature of a successful blackmail is that the threat must be credible (e. g. , Shavell, 1992). Shavell and Spier (2002) analyze blackmail in the absence of binding commitment. In particular, they O? nd that if carrying out a threat is costly, then extracting a payment from a victim is impossible even in an inO? nite horizon setting. The main innovation of our paper relative to Shavell and Spier (2002) is that we introduce brinkmanship into the model. We deO? ne brinkmanship as an ability of the aggressor to undertake an observable action that will lead with positive probability to a war or some other mutually undesirable outcome; i`shooting over the headi^is a metaphor for the kind of brinkmanship we have in mind. We show that being able to engage in this kind of visible brinkmanship may allow the potential aggressor to extract the whole surplus from the victim.
In this paper, we employ the international-relations terminology, though the applications of this idea stretch far beyond the nuclear power politics. For example, in a relationship between a manager and an employee we observe the same pattern: if the only threat available to the manager is to O? re an employee, then manageri? s ability to extract e? ort from the employee may be less than in the case where the manager can make the punishment inO? nitely divisible or probabilistic. Intuitively, if the only options available to a manager are to O? re or to retain a worker, a worker only has to put forth enough e? ort to make the manager indi? erent between O? ring and retaining him. All the bargaining power resides with the worker. If the manager can impose arbitrarily small penalties on the worker he can induce a higher e? ort level (though it might be that in equilibrium penalties are never imposed).
For an economist, the phenomenon of war is in striking contradiction with the so-called i? Coase theoremi? that says that rational agents will always negotiate a Pareto e? cient arrange- ment. 5 At the O? rst glance, it may seem that the weaker party can avoid a cona? ict by trans-
3The fasciation of legal scholars with blackmail dates to at least the O? rst half of the 20th century, as
Campbell (1939) puts it: i^The law of blackmail has something in common with the blackmailer: it allows
its student no peace of mind. i^
4 Other works on economics of blackmail include Ginsburg and Shechtman (1993) and Posner (1993). 5Theories explaining failure of Pareto-e? ciency abound (see, e. g. , very di? erent perspectives in Coase,
1962, Myerson and Satterthwaite, 1983, Acemoglu, 2003). However, neither transaction costs, nor informa-
? 3
ferring resources to the stronger side. 6;7 However, in the absence of external enforcement, no peaceful agreement could ensure that a strong party would not ask for more concessions in the future. Furthermore, the more transfers the strong party receives, the stronger it becomes. One problem is that the commitment power of parties involved in any destructive cona? ict is very limited. 8 Indeed, a binding agreement that calls for a lump sum wealth transfer from one nation to the other in exchange for a promise of peace, can make both parties better o? . However, this type of agreement is not self-enforcing, except for an unlikely scenario, where the pay-o? to the potential aggressor from starting a war decreases substantially as a result of receiving a transfer. 9 Consequently, due to the lack of commitment power, a lump sum transfer in exchange for peace is unlikely to be viable. 10 Rajan and Zingales (2000) formalize this point and show that the lack of commitment power leads to ine? cient outcomes rang- ing from wars to wasteful political cona? icts in organizations. Acemoglu (2003) emphasizes that i^parties holding political power cannot make commitments to bind their future actions because there is no outside agency with the coercive capacity to enforce such arrangements. i^
This paper builds on Rajan and Zingales (2000). We show that their results need not hold
in dynamic setting where a continuos stream of transfers is feasible. Proposition 2 establishes
that resource transfers can form a basis for lasting peace. Unavailability of external contract
enforcement can be mitigated by spreading transfers over time. For example, a potential
aggressor, who receives a transfer every period, would O? nd it proO? table to refrain from
tional asymmetry can fully explain the phenomenon of war (e. g. , Fearon, 1995).
6Lengi? s (1993) typology of ina? uence strategies refers to such a strategy as appeasing. In Huth (1988)
typology, any policy of concessions is conciliatory. Hensel and Diehl (1994) analyze various non-militarized
responses on an immediate military threat. Wittman (2003) considers appeasement in a static setting and
argues that it should be possible to redraw the map so that peace becomes a self enforcing outcome. 7There is a strand of literature that argues that most wars are wanted from the ex-ante perspectives
(e. g, Blainley, 1988). Still, this case is much harder to make from the Pareto-e? ciency perspective: in rare
circumstances, a war is wanted on both sides.
8Barzel (2002) considers the absence of commitment a major cause for violent cona? icts: i^The problem
of . . . the inability to commit is also the root of theft and some warsi^. Classic work that focused on the problem of commitment is North and Weingast (1989) and Shepsle (1991). Most recently, the problem has become the central element in dynamic models of development suggested by Acemoglu and Robinson (e. g. , Acemoglu, 2003). Powell (2004) discusses commitment problems in various contexts close to ours.
9This is not entirely impossible. According to a legend when Attilla the Hun came to Rome, the citizens
of Rome gave him all the gold of Rome in exchange for peace, thus making conquest of the city less attractive
for him.
10Shavell and Spier (2002) invoke Vikings history to illustrate the importance of succession of payments.
? 4
starting a war as long as the present value of the stream of transfers exceeds the payo? from a war. Similarly, the other side would be willing to make transfer payments if the following two conditions are satisO? ed: (i) Present value of transfers is less than the expected loss from a war. (ii) The i? weaki? side believes that reducing the size of transfers would prompt the war. 11 We identify the conditions under which an appeasement strategy can succeed. We show that if parties have constant marginal utility of consumption then there exists a continuous stream of transfers that supports a sub-game perfect peaceful equilibrium. Constant marginal utility of consumption is mathematically equivalent to risk-neutrality. This assumption insures that any stream of transfers corresponds to a Pareto e? cient outcome.
If agents are risk-averse, then a self enforcing peace agreement may not be viable because concession will shift the balance of powers and increase future expected losses of the weaker party. 12 Risk aversion assumption implies diminishing marginal utility. Consequently, the weaker party may be very averse to being completely wiped out and the stronger party may gain very little from swallowing the weaker side completely. In this case, there may not exist a viable appeasement strategy, since appeasement may lead to a shift in the balance of power that makes the destruction of the weaker party inevitable. This is consistent with Fearon (1995) who argues that preventive wars should be understood as a result of commitment problems. 13 Slantchev (2001) analyzes the functioning of the Concert of Europe during the O? rst half of the 19th century. He concludes that "the pattern of cooperative behavior is seen to result from the commitment to uphold the settlement, which hinged on the credibility of enforcement threats. . . ".
This logic helps us understand many historic events. Every year since 1933, then- European powers, including England, France, and Poland faced a dilemma: either to O? ght Hitler now, or appease him and wait (Taylor, 1961). First concession was postponement of the World War I debt payments, next came tolerance of mobilization in Germany and launching of German air forces, and then re-occupation of Ruhrgebiet. The Munich treaty
11In fact, arrangements of this nature were practiced throughout history. A number of medieval cities bought peace by making annual contributions to their stronger neighbors. Above arguments suggest that a self-enforcing peace agreement may be viable, provided wealth transfers have a su? ciently small ina? uence on the balance of powers.
12Addressing the moral side of the problem, Walzer (1992) draws a parallel between international negotia-
tions and negotiations with kidnappers and extortionists. Our argument might explain the underlying logic
of legal obstacles to the former negotiations.
13Powell (2004) provides a survey of the literature related to the commitment problem.
? 5
of 1938 year, where the (future) allies agreed with occupation of Sudetenland, a part of Czechoslovakia, is probably the most prominent concession (e. g. , Walzer, 1992; for a game- theoretic analysis, see Hirshleifer, 2001). On October 5, 1938 Winston Churchill, the leader of the opposition in the British parliament, said that i`it seems to me that all those countries of Middle Europe, all those Danubian countries, will, one after another, be drawn into this vast system of power politics - not only power military politics but power economic politics n? radiating from Berlin, and I believe this can be achieved quite smoothly and swiftly and will not necessarily entail the O? ring of a single shot. . . . i^In 1940, it became too clear that Germany is already too strong, and England actually entered the World War II out of the fear that Germany would be even stronger in the future. 14 On May 13, Churchill, a prime-minister for O? ve days, said: i`What is our aim? I can answer in one word: Victory - victory - at all costs, victory, . . . however long and hard the road may be; for without victory, there is no survival.
The bargaining power of the potential aggressor increases dramatically if she is able to make probabilistic threats, e. g. by taking an observable action that leads to a war with positive probability. In particular, the ability to engage in brinkmanship allows a blackmailer to extract a positive stream of payments from the victim even if carrying out the threat is harmful to both parties. Although we use the terminology of international relations, our results are applicable to environ- ments ranging from diplomacy to negotiations within or among O? rms, and are aimed to bring together i? paralleli? investigations in the nature of commitment in economics and political science.
The authors are grateful to Andrei Shleifer, Luigi Zingales, and seminar participants at the Kellogg Business School, Pennsylvania State University and UCSC for valuable comments.
yUniversity of California at Berkeley and NBER; mschwartz@berkeley. edu. Part of this paper was written
while this author was a National Fellow at the Hoover Institution at Stanford. He would like to express his
gratitude to the Hoover Institution for enabling him to spend a productive year at Stanford.
z Institute for Advanced Study, Princeton, NJ, and New Economic School/CEFIR, Moscow;
ksonin@ias. edu.
? 1
1 Introduction
When the ria? e was invented, bows and arrows became obsolete. After the invention of nuclear weapons many observers expected that the conventional weapons would go the way of bows and arrows. For instance, one of the leading columnists of his time, Drew Pearson, declared in the Fall of 1945 that: i`the Navy and huge armies are now obsoletei^. 1 Later it became apparent that nuclear weapons do not give expected political leverage. In 1957, rea? ecting on the time when the US had a nuclear monopoly, Henry Kissinger commented with a measure of surprise that i^We never succeeded in translating our military [nuclear] superiority into a political advantage. i^Today, the verdict of history is clear: conventional arsenal remains important in the nuclear era.
Unfortunately, history is an infallible judge that never writes opinions to explain its ver- dicts. This paper o? ers a framework that deepens our understanding of the role of threats in the environments ranging from international negotiations to negotiations among or within a O? rm. We show that an i`indivisiblei^threat such as such as a nuclear capabilities gives a party far less bargaining power than a threat that is divisible, such as a large arsenal of con- ventional weapons. We also show that a self-enforcing peace agreement between negotiating parties should rely on a sequence of transfers or pre-negotiated concessions (as opposed to one large concession that buys peace). Fearon (1995) argues that indivisibility of the object of bargaining might be a rationalist explanation for cona? icts,2 while Powell (2004) argues that the commitment problem lies in the heart of the i? indivisibility argumenti? : if commitment is possible, a lottery over the indivisible object would be Pareto-superior to any cona? ict. We focus on how the ability to make observable probabilistic or divisible threats a? ects partiesi? bargaining power.
The study of blackmail received little attention from economists. At the O? rst glance, this may seem justiO? ed because relevance of blackmail may appear to be limited to small time crooks and nations with nuclear capabilities. However, in a broader sense many economic relationships involve an element of a blackmail. For instance, a manager induces a worker
1 For a full text of the quote and for analysis of evolution of conventional wisdom about the role of nuclear
weapons in national defence see Besse and Lasswell (1950).
2Early studies of war as a bargaining process are Schelling (1966), Wagner (1982), and Pillar (1983).
Recent models of negotiations in/and wars include Fearon (1995), Filson and Werner (2002), Smith and Stam (2003), Powell (2002, 2004), Slantchev (2003), Wittman (2003), Baliga and Sjostrom (2004).
? 2
to put forth more e? ort by a threat of O? ring, a tenant wants the landlord to do timely maintenance threatening to terminate the lease etc. Legal scholars devoted considerable attention to blackmail. 3 The celebrated Coase theorem (Coase, 1962) was in part an outcome of a decades-long intellectual inquiry of the author in legal questions related to blackmail (Coase, 1988). 4 A deO? ning feature of a successful blackmail is that the threat must be credible (e. g. , Shavell, 1992). Shavell and Spier (2002) analyze blackmail in the absence of binding commitment. In particular, they O? nd that if carrying out a threat is costly, then extracting a payment from a victim is impossible even in an inO? nite horizon setting. The main innovation of our paper relative to Shavell and Spier (2002) is that we introduce brinkmanship into the model. We deO? ne brinkmanship as an ability of the aggressor to undertake an observable action that will lead with positive probability to a war or some other mutually undesirable outcome; i`shooting over the headi^is a metaphor for the kind of brinkmanship we have in mind. We show that being able to engage in this kind of visible brinkmanship may allow the potential aggressor to extract the whole surplus from the victim.
In this paper, we employ the international-relations terminology, though the applications of this idea stretch far beyond the nuclear power politics. For example, in a relationship between a manager and an employee we observe the same pattern: if the only threat available to the manager is to O? re an employee, then manageri? s ability to extract e? ort from the employee may be less than in the case where the manager can make the punishment inO? nitely divisible or probabilistic. Intuitively, if the only options available to a manager are to O? re or to retain a worker, a worker only has to put forth enough e? ort to make the manager indi? erent between O? ring and retaining him. All the bargaining power resides with the worker. If the manager can impose arbitrarily small penalties on the worker he can induce a higher e? ort level (though it might be that in equilibrium penalties are never imposed).
For an economist, the phenomenon of war is in striking contradiction with the so-called i? Coase theoremi? that says that rational agents will always negotiate a Pareto e? cient arrange- ment. 5 At the O? rst glance, it may seem that the weaker party can avoid a cona? ict by trans-
3The fasciation of legal scholars with blackmail dates to at least the O? rst half of the 20th century, as
Campbell (1939) puts it: i^The law of blackmail has something in common with the blackmailer: it allows
its student no peace of mind. i^
4 Other works on economics of blackmail include Ginsburg and Shechtman (1993) and Posner (1993). 5Theories explaining failure of Pareto-e? ciency abound (see, e. g. , very di? erent perspectives in Coase,
1962, Myerson and Satterthwaite, 1983, Acemoglu, 2003). However, neither transaction costs, nor informa-
? 3
ferring resources to the stronger side. 6;7 However, in the absence of external enforcement, no peaceful agreement could ensure that a strong party would not ask for more concessions in the future. Furthermore, the more transfers the strong party receives, the stronger it becomes. One problem is that the commitment power of parties involved in any destructive cona? ict is very limited. 8 Indeed, a binding agreement that calls for a lump sum wealth transfer from one nation to the other in exchange for a promise of peace, can make both parties better o? . However, this type of agreement is not self-enforcing, except for an unlikely scenario, where the pay-o? to the potential aggressor from starting a war decreases substantially as a result of receiving a transfer. 9 Consequently, due to the lack of commitment power, a lump sum transfer in exchange for peace is unlikely to be viable. 10 Rajan and Zingales (2000) formalize this point and show that the lack of commitment power leads to ine? cient outcomes rang- ing from wars to wasteful political cona? icts in organizations. Acemoglu (2003) emphasizes that i^parties holding political power cannot make commitments to bind their future actions because there is no outside agency with the coercive capacity to enforce such arrangements. i^
This paper builds on Rajan and Zingales (2000). We show that their results need not hold
in dynamic setting where a continuos stream of transfers is feasible. Proposition 2 establishes
that resource transfers can form a basis for lasting peace. Unavailability of external contract
enforcement can be mitigated by spreading transfers over time. For example, a potential
aggressor, who receives a transfer every period, would O? nd it proO? table to refrain from
tional asymmetry can fully explain the phenomenon of war (e. g. , Fearon, 1995).
6Lengi? s (1993) typology of ina? uence strategies refers to such a strategy as appeasing. In Huth (1988)
typology, any policy of concessions is conciliatory. Hensel and Diehl (1994) analyze various non-militarized
responses on an immediate military threat. Wittman (2003) considers appeasement in a static setting and
argues that it should be possible to redraw the map so that peace becomes a self enforcing outcome. 7There is a strand of literature that argues that most wars are wanted from the ex-ante perspectives
(e. g, Blainley, 1988). Still, this case is much harder to make from the Pareto-e? ciency perspective: in rare
circumstances, a war is wanted on both sides.
8Barzel (2002) considers the absence of commitment a major cause for violent cona? icts: i^The problem
of . . . the inability to commit is also the root of theft and some warsi^. Classic work that focused on the problem of commitment is North and Weingast (1989) and Shepsle (1991). Most recently, the problem has become the central element in dynamic models of development suggested by Acemoglu and Robinson (e. g. , Acemoglu, 2003). Powell (2004) discusses commitment problems in various contexts close to ours.
9This is not entirely impossible. According to a legend when Attilla the Hun came to Rome, the citizens
of Rome gave him all the gold of Rome in exchange for peace, thus making conquest of the city less attractive
for him.
10Shavell and Spier (2002) invoke Vikings history to illustrate the importance of succession of payments.
? 4
starting a war as long as the present value of the stream of transfers exceeds the payo? from a war. Similarly, the other side would be willing to make transfer payments if the following two conditions are satisO? ed: (i) Present value of transfers is less than the expected loss from a war. (ii) The i? weaki? side believes that reducing the size of transfers would prompt the war. 11 We identify the conditions under which an appeasement strategy can succeed. We show that if parties have constant marginal utility of consumption then there exists a continuous stream of transfers that supports a sub-game perfect peaceful equilibrium. Constant marginal utility of consumption is mathematically equivalent to risk-neutrality. This assumption insures that any stream of transfers corresponds to a Pareto e? cient outcome.
If agents are risk-averse, then a self enforcing peace agreement may not be viable because concession will shift the balance of powers and increase future expected losses of the weaker party. 12 Risk aversion assumption implies diminishing marginal utility. Consequently, the weaker party may be very averse to being completely wiped out and the stronger party may gain very little from swallowing the weaker side completely. In this case, there may not exist a viable appeasement strategy, since appeasement may lead to a shift in the balance of power that makes the destruction of the weaker party inevitable. This is consistent with Fearon (1995) who argues that preventive wars should be understood as a result of commitment problems. 13 Slantchev (2001) analyzes the functioning of the Concert of Europe during the O? rst half of the 19th century. He concludes that "the pattern of cooperative behavior is seen to result from the commitment to uphold the settlement, which hinged on the credibility of enforcement threats. . . ".
This logic helps us understand many historic events. Every year since 1933, then- European powers, including England, France, and Poland faced a dilemma: either to O? ght Hitler now, or appease him and wait (Taylor, 1961). First concession was postponement of the World War I debt payments, next came tolerance of mobilization in Germany and launching of German air forces, and then re-occupation of Ruhrgebiet. The Munich treaty
11In fact, arrangements of this nature were practiced throughout history. A number of medieval cities bought peace by making annual contributions to their stronger neighbors. Above arguments suggest that a self-enforcing peace agreement may be viable, provided wealth transfers have a su? ciently small ina? uence on the balance of powers.
12Addressing the moral side of the problem, Walzer (1992) draws a parallel between international negotia-
tions and negotiations with kidnappers and extortionists. Our argument might explain the underlying logic
of legal obstacles to the former negotiations.
13Powell (2004) provides a survey of the literature related to the commitment problem.
? 5
of 1938 year, where the (future) allies agreed with occupation of Sudetenland, a part of Czechoslovakia, is probably the most prominent concession (e. g. , Walzer, 1992; for a game- theoretic analysis, see Hirshleifer, 2001). On October 5, 1938 Winston Churchill, the leader of the opposition in the British parliament, said that i`it seems to me that all those countries of Middle Europe, all those Danubian countries, will, one after another, be drawn into this vast system of power politics - not only power military politics but power economic politics n? radiating from Berlin, and I believe this can be achieved quite smoothly and swiftly and will not necessarily entail the O? ring of a single shot. . . . i^In 1940, it became too clear that Germany is already too strong, and England actually entered the World War II out of the fear that Germany would be even stronger in the future. 14 On May 13, Churchill, a prime-minister for O? ve days, said: i`What is our aim? I can answer in one word: Victory - victory - at all costs, victory, . . . however long and hard the road may be; for without victory, there is no survival. i^
The same reasoning may explain why rulers often miss opportunities to make concessions to the opposition in the days preceding revolutions. Why would not the Russian czar agree to share power with the elected parliament (where the majority was very far from any leftist movement) in January 1917? Why Louis XVI gambled on counter-revolutionary plots during the O? rst years of French revolution, instead of trying to work out a real political compromise? The answer is that the reluctance of these rulers can be explained by the fear that any concession would have empowered the opposition to ask for even more concessions. Then, they would have a choice between making an escalating sequence of greater and greater concessions or an open struggle under less favorable conditions. Nikolai II of Russia and Louis XVI were the ultimate losers, but there are examples of rulers who ultimately prevailed. 15
In Section 4 we show that the bargaining power of the potential aggressor increases dramatically if she is able to make her threat divisible. For instance she may achieve so by taking observable action that lead to a war with positive probability.
