The goal is to distribute the total donated amount among the various targets in a way that respects the donors' preferences.
As an example, consider a town with three recreational facilities that require funding: theater, chess club, and basketball field.
Since the donations are voluntary, it is important that the coordination algorithm ensures that each voter weakly gains from participating in the algorithm, i.e., the amount contributed to projects he approves of is weakly higher when he participates than when he does not.
Donor coordination has been studied in several settings, which can be broadly categorized into divisible and indivisible: Donor coordination with divisible targets is similar to the problem of fractional social choice, except that in the latter, the "budget" is fixed in advance (e.g. time, probability, or government funds), and not donated voluntarily by the agents.
Brandl, Brandt, Peters and Stricker[1] study donor coordination with additive binary (dichotomous) preferences, represented by approval ballots.
They prove that the Nash product rule incentivizes donors to contribute their entire budget, even when attractive outside options are available.
On the down side, it is not strategyproof, and violates simple monotonicity conditions (even in the binary case).
They prove that there always exists a unique pure Nash equilibrium, and it can be found efficiently using convex programming, by maximizing the Nash social welfare (a sum of logarithms of agents' utilities, weighted by their donations).
With binary-Leontief utilities, EDR is also egalitarian for projects and for agents (subject to decomposability), can be found efficiently using linear programming, and attained at the limit of a best-response sequence.
Buterin, Hitzig and Weyl[4] present a mechanism in which donors invest money to create public goods.
They assume that agents have quasilinear utilities, so without coordination, there will be under-provision of public goods due to the free-rider problem.
They show that, in the standard model (selfish, independent, private values, quasilinear utilities), this mechanism yields the utilitarian-optimal provision of public goods.
Other ways to encourage public goods provision are: They present variations and extensions of QF.
Each agent approves a subset of the projects, and provides an upper bound on the amount of money he can donate.
The utility of each agent equals the amount of money spent on projects he approves (i.e., cost-satisfaction).
Note that, because the projects are indivisible, probably most donors will pay less than their upper bound.
They also conduct experiments for studying the price of fairness - how much fairness properties effect the social welfare - in instances that model two real-life donor coordination scenarios: share-house setting, and crowdfunding setting.
Aziz, Gujar, Padala, Suzuki and Vollen[6][7] extend the above study to agents with cardinal ballots and quasilinear utilities.
Their aim is to guarantee that rich donors do not use their donations to have an unfairly large influence on the total budget.
They also study two computational problems related to this setting: In the Paris Declaration of 2005, donor countries agreed to coordinate their donations in order to eliminate duplication of efforts and better align foreign aid flows with priorities of the recipient countries.
However, Nunnenkamp, Ohler and Thiele[9] show that these ideas were not implemented in practice, and the donor coordination even declined.
Leiderer[10] presents specific evidence for this from aid to the health and education sectors in Zambia.