I've been reading an interesting paper, "Referendum, Response and Consequences for Sudan: The Game between Juba and Khartoum" by Ibrahim Elbadawi, Gary Milante and Costantino Pischedda, part of the Development Research Group at the World Bank. I'll call the authors EMP for short from now on.
EMP start by using a simple model of strategic interaction to model the likely unfolding of actions after the referendum. Juba (representing the elite of the SPLM, the "deciders" of how the South should vote) first decides whether to secede. If they secede, then Khartoum (representing the NCP regime) decides on war or peace. Obviously the payoffs are crucial here. EMP assume that "under unity the expected payoff to Khartoum is tax revenue plus oil less military expenditures ... and the expected payoff to Juba is tax revenue plus oil less military expenditures ... In the event of partition and peaceful response from Khartoum, the expected payoff is simply tax revenues for Khartoum less military expenditures ... and tax and oil revenues for Juba less military expenditures..." In the event Khartoum goes to war, captures some of the oil revenue, and both sides bear losses proportional to their pre-referndum investments in military capacity.
Oddly, EMP don't model the game as explicitly starting with military investment, which temporally occus before the referendum. They refer to those investments as talking place in a "pre-game" period. (EMP report various estimates of military expenditures and suggest that these were on the order of $1 billion for the north and $500 million of the south, in 2007; the north's army, SAF, is on the order of 100,000 troops, while the army of the south, the SPLA, is about 30,000 troops, and both sides have alliances with informal and rebel fighting groups of sizes difficult to estimate.)
The analysis of the game is largely common-sense: both sides will invest heavily in the military pre-referendum, and the outcome of the referendum then depends on Juba's assessment of its military capacity relative to Khartoum. We did not need a model to understand that.
EMP then move to some asymmetric information scenario, and reasonably conclude that more information (census, resolution of Abyei boundary dispute, oil revenue transparency, etc.) would reduce the likelihood of conflict because if conflict is valued less than partition then they will be less likely to go to war. Of course, the analysis compares moving from lack of information to complete information, whereas in reality the extra information means moving from a situation of lots of asymmetric information to one with less asymmetric information, and where information that is revealed updates prior probabilities about the world. If priors suggested that war would be unwinnable, and more information revealed that war was more likely to be winnable, then the greater information could paradoxically increase the chances of war. But EMP do not consider this possibility.
The more interesting part of the paper comes next, when they take issue with the Collier et al proposition that elections are bad for peace in transitions from conflict and repression to greater political openness. EMP argue that it is likely that the planned 2009 elections (now scheduled for 2010) can lend legitimact to Khartoum, enabling it to credibly commit to lower military expenditures and hence a peaceful outcome from the referendum, possibly even unity. EMP note that the marginal effects on well-being outcomes are likely to be high if military spending is diverted to anti-poverty programs.
The paper concludes with a wish list of lots of good things that could make things better (more northern opposition party involvement and deal-making to give NCP a soft-landing to encourage democratization, a third referendum option of confederation, more efforts to increase integration between north and south, etc.), and reads more like one of those "people of good will" documents than "analysis".
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