Some Reasons for which France will remain alone in Mali
Now that French Army has reached a deserved initial military success in Mali, time has come to look forward and check whether its allies will at last decide to join and support France in its efforts to expel islamists from this country (as far as I could understood it seems to be the final objective).
For fun, I will not make use of a traditional strategic analysis, but I will try to make use of Mr Ben Polak's lectures at Yale, available on the Internet (here). Being an absolute math-, eco- and calculus-phobic I will try my best.
The initial hypothesis is that France is negotiating with its allies their joining in the operation in Mali, which is regarded as a risky business. Intentionally, I get rid of the traditional geopolitical analysis.
Starting point would be that the allies act in accordance with their national interests, which is not surprising. Despite the French public statements, and for the sake of this analysis, I will dare say that France, yes even France, the 'Grande Nation' has national interests and acts in accordance with (all the more that philanthropic wars are rather seldom).
By the way, just one principle of war: if one country wages war, it means that the expected payoff, that is gain through victory, is bigger than the cost of the operations. When the countries act differently it turns to Europe after WWII !
Let us then check the different hypothesis, considering that both sides are cooperative, as they are allies, and want to maximize their return on investment, are they are rational actors (at least I hope so).
As far as France is concerned, it has two options: keep its leadership (UL-for unique leadership) or accept to share it (SL-shared leadership). The allies would have to options: provide a large support (LS) and stand shoulder to shoulder or just provide the strictly needed (SN) assets so they make sure that France does not fail, as it would encourage terrorism and therefore open the gates to a new threat much closer to our borders.
Let us now study the combination of those options:
UL + LS:
providing a maximum of the capital (the military assets) without controlling its use and being even less involved in the major decision is simply a non-sense to the eyes of the allies. In contrary, this would be France preferred option, as the return would be maximized: they would get all the glory and prove the superiority of French leadership, while in case of failure, the allies would anyway lose all their capital invested. Even a philanthropic millionaire wants to be sure that the money he pours in a foundation is properly spent, doesn't he? Therefore this option is definitely to be rejected.
The allies provide a large support to the operation, but France accepts to share the leadership on operations and strategic decisions in proportion to their investment in this joint venture. However, any investor needs a business plan in order to maximize the profit versus a minimized risk. Or at least get a greater payoff if the risk is maximum.
Regrettably France didn't offer up to now a strategic vision of the expected payoff of its operation in Mali. Therefore the allies, which are rational actors cannot assess the risk. Then, they do not invest with a large support and France cannot share leadership.
SL + SN:
Would be highly profitable the allies at an excessive cost for France. In other words, our allies would take profit of the French military efforts and risks, by arriving after the main battle. Furthermore, when you own only a few stocks of a business, it's very easy to get out at a low cost, as if the things go wrong and the loss in your investment is minimal. Who can imagine the main stockowner of a risky business leaving an excessive part of power to a minor holder? Not realistic, can be discarded.
UL + LS:
The allies of France invest a minima, so that they are sure that the risks that France is taking are manageable by providing the most urgently needed assets.
Anyway France is already on the ground and has achieved the most dangerous phase of any operation which is the initial entry. Therefore, there is no rationale for a larger investment in the operation.
Furthermore, being purely cynical, I would say that, due to the poverty of Mali and the lack of natural resources in the area, the main payoff could well be only a decrease or at least a stabilization of terrorist threat.
Therefore, even with a limited investment, or no investment, every country will benefit of French investment in Mali as terrorism is a global threat.
My conclusion is that any country, who has an ally ready to run operations on its own regardless of its own costs, but whose profits are equally shared, should let it do!