Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-27T13:38:37.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Combatant Fragmentation and the Dynamics of Civil Wars

Published online by Cambridge University Press:  24 April 2012

Michael Findley  and
Peter Rudloff
Get access Rights & Permissions [Opens in a new window]

Abstract

Civil war dynamics and outcomes are shaped by processes of change largely unaccounted for in current studies. This examination explores how the fragmentation of combatants, especially the weaker actors, affects the duration and outcomes of civil wars. Some results of a computational modelling analysis are consistent with the article's expectations, several of them are counterintuitive. They show that when combatants fragment, the duration of war does not always increase and such wars often end in negotiated agreements, contrasting with the expectations of literatures on spoilers, moderates and extremists. Empirical cases, such as Iraq, Congo, Chechnya and the Sudan, illustrate the importance of fragmentation. This study demonstrates the value of accounting for diverse changes in actors and circumstances when studying the dynamics of war.

Type
Articles
Information
British Journal of Political Science , Volume 42 , Issue 4 , October 2012 , pp. 879 - 901
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Department of Political Science, Brigham Young University (email: [email protected]); and Department of Political Science, Oklahoma State University (email: [email protected]), respectively. The authors wish to thank Eric Dickson, Paul Diehl, Stephen Haptonstahl, Patrick James, James Kuklinski, Sarah Mitchell, Glenn Palmer, Toby Rider, Scott Wolford and the Political Science Research Seminar at Oklahoma State University for helpful comments. Special thanks to Wills Hickman, Adam Harris, Ken Noyes and Jon Walton for valuable research assistance. Findley acknowledges support from National Science Foundation Grant No. 0904883 and Rudloff thanks the College of Arts and Sciences at Oklahoma State University for research and travel support through an Arts and Sciences Summer Research grant. Computer code and raw results are available upon request from the authors. The Appendix may be viewed at http://www.journals.cambridge.org/jps.

References

1 Hafez, Mohammed M., Suicide Bombers in Iraq: The Strategy and Ideology of Martyrdom (Washington, D.C.: United States Institute of Peace Press, 2007), pp. 243–249Google Scholar

2 Uppsala Conflict Data Program, Uppsala Conflict Database, see www.pcr.uu.se/database. Uppsala University (accessed May 2010).

3 Fearon, James D., ‘Rationalist Explanations for War’, International Organization, 49 (1995), 379–414CrossRefGoogle Scholar

4 Reiter, Dan, ‘Exploring the Bargaining Model of War’, Perspectives on Politics, 1 (2003), 27–43CrossRefGoogle Scholar

5 E.g., Robert Powell, ‘War as a Commitment Problem’, International Organization, 60 (2006), 169–203Google Scholar

6 E.g., Darren Filson and Suzanne Werner, ‘A Bargaining Model of War and Peace: Anticipating the Onset, Duration, and Outcome of War’, American Journal of Political Science, 46 (2002), 819–837CrossRefGoogle Scholar

Slantchev, Branislav, ‘The Principle of Convergence in Wartime Negotiations’, American Political Science Review, 97 (2003), 621–632CrossRefGoogle Scholar

7 E.g., Alastair Smith and Allan C.Stam, ‘Mediation and Peacekeeping in a Random Walk Model of War’, International Studies Perspective, 5 (2003), 115–136Google Scholar

Fearon, James D., ‘Why Do Some Civil Wars Last so Much Longer than Others?’, Journal of Peace Research, 41 (2004), 275–301CrossRefGoogle Scholar

Cunningham, David, ‘Veto Players and Civil War Duration’, American Journal of Political Science, 50 (2006), 875–892CrossRefGoogle Scholar

Thyne, Clayton, ‘Cheap Signals with Costly Consequences: The Effect of Interstate Relations on Civil War, 1945–1999’, Journal of Conflict Resolution, 50 (2006) 937–961CrossRefGoogle Scholar

8 E.g., David Lake, ‘International Relations Theory and Internal Conflict: Insights from the Interstices’, International Studies Review, 5 (2003), 81–90CrossRefGoogle Scholar

Hegre, Håvard, ‘The Duration and Termination of Civil War’, Journal of Peace Research, 41 (2004), 243–252CrossRefGoogle Scholar

9 Regan, Patrick, ‘Third-party Interventions and the Duration of Intrastate Conflicts’, Journal of Conflict Resolution, 46 (2002), 55–73CrossRefGoogle Scholar

Dylan Balch-Lindsay, Andrew Enterline and Kyle Joyce ‘Third-Party Intervention and the Civil War Process’, Journal of Peace Resesarch, 45 (2009), 345–363Google Scholar

10 Bapat, Navin A., ‘Insurgency and the Opening of Peace Processes’, Journal of Peace Research, 42 (2005), 699–717CrossRefGoogle Scholar

11 Kalyvas, Stathis, ‘The Ontology of “Political Violence”: Action and Identity in Civil Wars’, Perspectives on Politics, 3 (2003), 475–494CrossRefGoogle Scholar

12 Uppsala Conflict Data Program, Uppsala Conflict Database, http://www.pcr.uu.se/database, Uppsala University (accessed 2008).

13 Harrison, Neil E.ed., Complexity in World Politics: Concepts and Methods of a New Paradigm (Albany: State University of New York Press, 2006)CrossRefGoogle Scholar

James, Patrick and Goetze, Davideds, Evolutionary Theory and Ethnic Conflict (Westport, Conn.: Praeger, 2001)Google Scholar

Lake, David A. and Powell, Roberteds, Strategic Choice and International Relations (Princeton, N.J.: Princeton University Press, 2001)Google Scholar

14 Axelrod, Robert M., The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration (Princeton, N.J.: Princeton University Press, 1997)CrossRefGoogle Scholar

15 Scott de Marchi, Computational and Mathematical Modeling in the Social Sciences (Cambridge: Cambridge University Press, 2005)Google Scholar

16 Powell, Robert, ‘Bargaining and Learning while Fighting’, American Journal of Political Science, 48 (2004), p. 345CrossRefGoogle Scholar

17 Stedman, Stephen, ‘Spoiler Problems in Peace Processes’, International Security, 22 (1997), 5–53CrossRefGoogle Scholar

Kydd, Andrew and Walter, Barbara, ‘Sabotaging the Peace: The Politics of Extremist Violence’, International Organization, 56 (2002), 263–296CrossRefGoogle Scholar

Alex Mintz and Bruce Russett, eds, New Directions for International Relations (Lexington, Mass.: Lexington Books, 2005)Google Scholar

18 Cunningham, ‘Veto Players and Civil War Duration’.

19 Wittman, Donald, ‘How a War Ends: A Rational Model Approach’, Journal of Conflict Resolution, 23 (1979), 743–763CrossRefGoogle Scholar

Mason, David T. and Fett, Patrick, ‘How Civil Wars End: A Rational Choice Approach’, Journal of Conflict Resolution, 40 (1996), 546–568CrossRefGoogle Scholar

20 Wagner, R. Harrison, ‘Bargaining and War’, American Journal of Political Science, 44 (2000), 469–484CrossRefGoogle Scholar

21 E.g., Smith and Stam, ‘Mediation and Peacekeeping in a Random Walk Model of War’; Fearon, ‘Why Do Some Civil Wars Last So Much Longer than Others?’; Cunningham, ‘Veto Players and Civil War Duration’; Thyne, ‘Cheap Signals with Costly Consequences’.

22 Carl von Clausewitz, On War, ed. and trans. by Michael Howard and Peter Paret (Princeton, N.J.: Princeton University Press, 1984), p. 140.

23 E.g., Fred Iklé, Every War Must End (New York: Columbia University Press, 1971)Google Scholar

Jack Levy (see ‘Learning in Foreign Policy: Sweeping a Conceptual Minefield’, International Organization, 48 (1994), 279–312)CrossRefGoogle Scholar

24 Filson and Werner, ‘A Bargaining Model of War and Peace’.

25 Goemans, Hein, War and Punishment: The Causes of War Termination and the First World War (Princeton, N.J.: Princeton University Press, 2000)CrossRefGoogle Scholar

Smith, Alastair and Stam, Allan C., ‘Bargaining and the Nature of War’, Journal of Conflict Resolution, 48 (2004), 783–813CrossRefGoogle Scholar

Filson, Darren and Werner, Suzanne, ‘The Dynamics of Bargaining and War’, International Interactions, 33 (2007), 31–50CrossRefGoogle Scholar

26 Fearon, ‘Rationalist Explanations for War’.

27 Clausewitz, On War, p. 140.

28 Slantchev, ‘The Principle of Convergence in Wartime Negotiations’; Smith and Stam, ‘Bargaining and the Nature of War’.

29 Pillar, Paul, Negotiating Peace: War Termination as a Bargaining Process (Princeton, N.J.: Princeton University Press, 1983)CrossRefGoogle Scholar

Slantchev, c.f., ‘The Principle of Convergence in Wartime Negotiations’, p. 621CrossRefGoogle Scholar

30 Robert E. Bohrer and Caroline A. Hartzell, ‘After the Shooting Stops: Civil War Settlements and the Postwar Environment’ (paper presented at the Annual Meeting of the International Studies Association, Honolulu, 2005).

31 E.g., Smith and Stam, ‘Mediation and Peacekeeping in a Random Walk Model of War’; Cunningham, ‘Veto Players and Civil War Duration’.

32 Kalyvas, ‘The Ontology of “Political Violence”’.

33 Cunningham, ‘Veto Players and Civil War Duration’.

34 Walter, Barbara F., ‘Bargaining Failures and Civil War’, Annual Review of Political Science, 12 (2009), 243–261CrossRefGoogle Scholar

35 Stedman, ‘Spoiler Problems in Peace Processes’; Kydd and Walter, ‘Sabotaging the Peace’.

36 Bremer, Stuart and Cusack, Thomas, The Process of War: Advancing the Scientific Study of War (Amsterdam: Gordon and Breach, 1995)Google Scholar

37 James and Goetze, Evolutionary Theory and Ethnic Conflict.

38 E.g., Paul F. Diehl, ‘Just a Phase? Integrating Conflict Dynamics over Time’, Conflict Management and Peace Science, 23 (2006), 199–210CrossRefGoogle Scholar

39 E.g., Barbara F. Walter, Committing to Peace: The Successful Settlement of Civil Wars (Princeton, N.J.: Princeton University Press, 2002)Google Scholar

Slantchev, Branislav, ‘How Initiators End Their Wars: The Duration of Warfare and the Terms of Peace’, American Journal of Political Science, 48 (2004), 813–829CrossRefGoogle Scholar

Ramsay, Kristopher, ‘Settling It on the Field: Battlefield Events and War Termination’, Journal of Conflict Resolution, 52 (2008), 850–879CrossRefGoogle Scholar

40 See, for example, the special issue of the Journal of Conflict Resolution 42:3 (1998) that examines the internal dynamics of wars.

41 Bennett, D. Scott and Stam, Alan, ‘The Duration of Interstate Wars, 1816–1985’, American Political Science Review, 90 (1996), 239–257CrossRefGoogle Scholar

42 Bremer, Stuart, ‘Dangerous Dyads: Conditions Affecting the Likelihood of Interstate War, 1816–1965’, Journal of Conflict Resolution, 36 (1992), 309–341CrossRefGoogle Scholar

43 Croco, Sarah and Teo, Tze Kwang, ‘Assessing the Dyadic Approach to Interstate Conflict Processes: A.k.a. “Dangerous” Dyad-Years’, Conflict Management and Peace Science, 22 (2005), 5–18CrossRefGoogle Scholar

44 E.g., James D. Fearon and David Laitin, ‘Ethnicity, Insurgency, and Civil War’, American Political Science Review, 97 (2003), 75–90CrossRefGoogle Scholar

45 E.g., David E. Cunningham, Kristian Skrede Gleditsch and Idean Salehyan, ‘It Takes Two: A Dyadic Analysis of Civil War Duration and Outcome’, Journal of Conflict Resolution, 53 (2009), 570–597CrossRefGoogle Scholar

46 E.g., Stephen Gent, ‘Strange Bedfellows: The Strategic Dynamics of Major Power Interventions’, Journal of Politics, 69 (2007), 1089–1102CrossRefGoogle Scholar

47 Nilsson, Desirée, ‘Partial Peace: Rebel Groups Inside and Outside of Civil War Settlements’, Journal of Peace Research, 45 (2008), 479–495CrossRefGoogle Scholar

48 Shellman, Stephen, ‘Coding Disaggregated Intrastate Conflict: Machine Processing the Behavior of Substate Actors over Time and Space’, Political Analysis, 16 (2008), 464–477CrossRefGoogle Scholar

49 De Marchi, Computational and Mathematical Modeling in the Social Sciences, p. 127.

50 Cederman, Lars-Erik, ‘Endogenizing Geopolitical Boundaries with Agent-Based Modeling’, Proceedings of the National Academy of the Sciences, 99 (2002), 7296–7303CrossRefGoogle ScholarPubMed

Holland, John H. and Miller, John, ‘Artificial Adaptive Agents in Economic Theory’, American Economic Review Papers and Proceedings, 81 (1991), 365–370Google Scholar

Miller, John H. and Page, Scott E., Complex Adaptive Systems: An Introduction to Computational Models of Social Life (Princeton, N.J.: Princeton University Press, 2007)Google Scholar

51 De Marchi, Computational and Mathematical Modeling in the Social Sciences.

52 Bennett, D. Scott, ‘Governments, Civilians, and the Evolution of Insurgency: Modeling the Early Dynamics of Insurgencies’, Journal of Artificial Societies and Social Simulation, 11 (2008)Google Scholar

Bhavani, Ravi and Backer, David, ‘Localized Ethnic Conflict and Genocide: Accounting for Differences in Rwanda and Burundi’, Journal of Conflict Resolution, 44 (2000), 283–307CrossRefGoogle Scholar

Bhavnani, Ravi and Ross, Michael, ‘Announcement, Credibility, and Turnout in Popular Rebellions’, Journal of Conflict Resolution, 47 (2003), 340–366CrossRefGoogle Scholar

Bhavnani, Ravi, ‘Ethnic Norms and Interethnic Violence: Accounting for Mass Participation in the Rwandan Genocide’, Journal of Peace Research, 43 (2006), 651–669CrossRefGoogle Scholar

Kalyvas, Stathis, Shapiro, Ian and Masoud, Tarekeds, Order, Conflict and Violence (Cambridge: Cambridge University Press, 2008)CrossRefGoogle Scholar

Epstein, Joshua, ‘Modeling Civil Violence: An Agent-based Computation Approach’, Proceedings of the National Academy of the Sciences, 99 (2002), 7243–7250CrossRefGoogle Scholar

53 Filson and Werner, ‘A Bargaining Model of War and Peace’; Filson and Werner, ‘The Dynamics of Bargaining and War’; Slantchev, ‘The Principle of Convergence in Wartime Negotiations’.

54 A more detailed description of parameters can be found in the Appendix on the Journal website.

55 To prevent the unlikely event of an agent randomly drawing zero capability, we round the random draw of each agent's initial capability to the next highest positive integer.

56 E.g., Fearon, ‘Rationalist Explanations for War’, pp. 390–401Google Scholar

57 E.g., Slantchev, ‘The Principle of Convergence in Wartime Negotiations’, p. 624Google Scholar

58 Fudenberg, Drew and Tirole, Jean, Game Theory (Cambridge, Mass.: MIT Press, 1991)Google Scholar

Filson and Werner, ‘A Bargaining Model of War and Peace’, p. 822.)Google Scholar

59 Ward, Hugh, ‘A Behavioural Model of Bargaining’, British Journal of Political Science, 9 (1979), 201–218CrossRefGoogle Scholar

Rubinstein, Ariel, Modeling Bounded Rationality (Cambridge, Mass.: MIT Press, 1998)CrossRefGoogle Scholar

Arthur, Brian W., ‘Inductive Reasoning and Bounded Rationality’, American Economic Review: Papers and Proceedings, 84 (1994) 406–411Google Scholar

60 Arthur, Brian W., Durlauf, Steven and Lane, Davideds, The Economy as an Evolving Complex System II (Reading, Mass.: Perseus, 1997)Google Scholar

61 Lane and Maxfield, ‘Foresight, Complexity, and Strategy’.

62 Laver, Michael, ‘Policy and the Dynamics of Political Competition’, American Political Science Review, 99 (2005), 263–281CrossRefGoogle Scholar

63 Tesfatsion, Leigh and Judd, Kennetheds, Handbook of Computational Economics, Vol. 2 (Amsterdam: North-Holland, 2006)Google Scholar

64 Smith and Stam, ‘Bargaining and the Nature of War’, p. 790–791Google Scholar

65 In other words, ι determines the range of possible values of β s for an agent, indicating uncertainty over the other agent's capability (κ). Rather than assuming that an agent calculates an expected value of β based on an underlying probability distribution, an agent's β is determined through a random draw from the distribution (${{ u}_v} $). In other words, we do not impose a method of calculation that assumes all agents arrive at β in a similar manner.

66 Fearon, ‘Rationalist Explanations for War’.

67 Filson and Werner, ‘A Bargaining Model of War and Peace.

68 Russett, Bruce M.ed., Peace, War, and Numbers (Thousand Oaks, Calif.: Sage Publishers, 1972)Google Scholar

69 Simon, Herbert, Models of Bounded Rationality (Cambridge, Mass.: MIT Press, 1982)Google Scholar

70 E.g., Axelrod, The Complexity of Cooperation.

71 Slantchev, ‘The Principle of Convergence in Wartime Negotiations’.

72 In the two-agent case, the strongest agent makes an offer that it always accepts. Assuming that χ = 1, if the weaker agent adds 1 to β every time the stronger agent accepts its own offer, then it may quickly begin to lower its belief about the capability of the stronger agent. This is similar to the weaker agent assuming that when the stronger agent makes an offer to itself that seems high, it is an indication that the stronger agent is stronger than the weaker agent believes. It could be the case, however, that the weaker agent believes the stronger agent is the one that is overestimating its capability, or that the stronger agent is bluffing (see Fearon, ‘Rationalist Explanations for War’). To reflect the different conclusions that can be drawn about the stronger agent, the weaker agent alternates between adding 1 to α and 1 to β at the end of each negotiation phase.

73 By using the term ‘experiment’, we are not suggesting that the model in any way provides an empirical ‘test’ similar to a laboratory or field experiment. Rather, we begin with a baseline condition similar to a control group and then incrementally change parameters in such a way that we can compare each successive condition against the baseline. While this is not the same as a randomized experiment, because we can compare against a baseline or control condition, using the term ‘experiment’ is useful.

74 Gartzke, Erik, ‘War is in the Error Term’, International Organization, 53 (2003), 567–587CrossRefGoogle Scholar

75 Slantchev, ‘The Principle of Convergence in Wartime Negotiations’.

76 Although there are five graphs with five points on the x-axis, the midpoint across all of the graphs represents the same experiment in which all parameters are set at their midpoints. It follows that each of the additional four points on the x-axis represents a new experiment (where all other key parameters are held constant at their midpoints), for a total of 21 experiments. (Given that the mid-point of each figure represents the same experiment, the total number of experiments amounts to 21 rather than 25.)

77 Fearon, ‘Rationalist Explanations for War’; Gartzke, ‘War is in the Error Term’.

78 Slantchev, ‘The Principle of Convergence in Wartime Negotiations’.

79 See Slantchev, ‘The Principle of Convergence in Wartime Negotiations’.

80 The small number of victories in certain parameter combinations means that the duration findings are sensitive to a small number of simulations. In subsequent discussion, we exercise caution when interpreting findings on the duration of victories, especially when the number of victories is small.

81 This limit of ten is chosen to simplify the number of agents, such that the analysis of the simulation and resulting plots will be easier to interpret. In the sensitivity analyses reported in the Appendix, we change the maximum number to 15 and 21 and find that the results are qualitatively similar to those reported in the article.

82 Uppsala Conflict Database, 2008.

83 Uppsala Conflict Database, 2008.

84 Like most evolutionary models, we allow mutation with a very small probability. We include mutation to allow the possibility that the strongest agents do not immediately defeat all other agents. Like many wars, as certain combatants become stronger, they can also lose their ability to adapt and can suffer setbacks. In the model, mutation alters one agent's beliefs, typically one of the strongest, about another agent such that the belief becomes less accurate on average. A mutation parameter μ represents the probability that a randomly selected agent will undergo mutation. A new random draw is made (uμ∈[0,1]), and if it is less than the probability of an agent mutating (i.e., if μ < s), then the selected agent (assume m) undergoes mutation in which one of agent m's β's is changed. After randomly determining the other agent, a target, another random draw (ut∈[0,1]) is used to change the mutating agent's β in regards to agent target such that

$$ {{\beta }_{m,target}}\, = \,{{\beta }_{m,target}}\, + \,(({{\beta }_{m,target}}\,\times \,\psi )\,\times \,(1{\rm{ - }}(2\,\times \,{{u}_t}))), $$

where ψ represents the maximum possible percentage change in agent m's β parameter in regards to the target agent.

85 In the sensitivity analysis, we consider the case in which the new agents’ beliefs (i.e., how much they deviate from the true capability ratios) are derived from the parent's beliefs. When doing so, the results are broadly similar as the probability of fragmentation increases, but less conclusive when one considers the effect of increasing the deviation of beliefs from the parent's. See Figures 21 and 22 of the Appendix.

86 Guy Arnold, Wars in the Third World since 1945, 2nd edn (London: Cassell, 1995), p. 194Google Scholar

87 Brogan, Patrick, World Conflicts: A Comprehensive Guide to World Strife since 1945 (Lanham, Md.: Scarecrow, 1998)Google Scholar

88 Stedman, ‘Spoiler Problems in Peace Processes’.

89 One alternative would be to allow both coalitions to fight battles with each other, but this does not match empirical cases very well. In the Democratic Republic of the Congo, for example, fighting often took place on multiple fronts with limited engagement of different groups. Furthermore, this alternative requires strong assumptions about actors’ abilities to update beliefs in extremely complicated circumstances. We nonetheless modelled this possibility and report the results in the Appendix (Figures 15 and 16). Overall, the results are qualitatively similar to those that we find here.

90 We constructed an alternative model in which all agents can observe battles (but not necessarily participate) and still update their beliefs about the battling agents. The results of the model presented in Figures 4 and 5 of this article are similar to the results in this alternative specification (see Appendix, Figures 7 and 8).

91 In the Appendix, we consider how the other baseline results (belief deviation, negotiation updating and battle updating) change, once fragmentation is introduced.

92 Each of the new parameters is set at a midpoint, and then varied using a high, medium-high, medium, medium-low, or low value (see Table 2), resulting in 25 experimental runs. Each of these experiments consisted of 1,000 runs of the simulation, and the results of 25 experiments appear in Figure 4, and 25 more experiments appear in Figure 5. We also ran a different set of experiments for each of the baseline runs where each of the baseline runs varied a single baseline parameter, sweeping each of the parameter ranges, for a final total of 1,134 experiments. Given the large number of experiments conducted, it would be impossible to do justice to each. An Appendix is available on the Journal website and details the results for most of the experiments. We also consider a number of additional sensitivity analyses, such as coalition shifting, coalition battling, increasing the maximum number of agents, among others, which we report in the Appendix.

93 We do this for a number of reasons. First, it seems unlikely that a war will end with a single member of each coalition agreeing to negotiated terms, without regard for the number and relative strength of other agents. The conflict in Darfur continues despite the agreement of the government and one of the SLM factions in the May 2006 peace agreement, for example. Secondly, as one might expect, settlements occur relatively quickly under settlement rules requiring the strongest of each coalition and a majority of each coalition to agree for settlement to take place, because fewer agents must agree to a settlement under these settlement rules.

94 Cunningham, ‘Veto Players and Civil War Duration’.

95 Uppsala Conflict Database, 2008.

96 Crenshaw, MarthaEnds’, ‘How Terrorism, U.S. Institute of Peace Special Report (Washington, D.C.: U.S. Institute of Peace, 1999)Google Scholar

97 Ward, ‘A Behavioural Model of Bargaining’, p. 217Google Scholar

98 Slantchev, ‘The Principle of Convergence in Wartime Negotiations’.

99 Powell, ‘War as a Commitment Problem’, p. 170Google Scholar

100 See Fearon, ‘Rationalist Explanations for War’; Slantchev, ‘The Principle of Convergence in Wartime Negotiations’.

101 Ward, ‘A Behavioural Model of Bargaining’.

Supplementary material: PDF

Findley and Rudloff supplementary material

Appendix

Download Findley and Rudloff supplementary material(PDF)
PDF 2.1 MB