It is well known among fund-raisers that many people contribute to charities or organizations only when asked and that large donations are more likely to occur as a fund-raiser increases the time spent soliciting and/or researching a potential donor. As fund-raisers can only spend time with research donors that they are aware of, the relationship (or links) between fund-raisers and donors is quite important. We model a fund-raising game where fund-raisers can only solicit donors whom they are tied to and analyze how this network influences donation requests. We show that if this network is incomplete and if donors experience extreme donor fatigue, then fund-raisers will spend more time soliciting donors that other fund-raisers are also tied to and less time soliciting donors that they are the only fund-raiser tied to. If instead donors experience mild donor fatigue, then fund-raisers prefer donors that they are the only fund-raiser tied to over donors that are shared with other fund-raisers. If donors are potential givers with no donor fatigue, then multiple equilibria may exist. Stochastic stability is used to refine the number of equilibria in this case, and conditions are given under which the unique stochastically stable equilibrium is efficient. 1. Introduction In 2005, seventy percent of all US households gave to charity donations totalling over $200 billion; see Andreoni [1]. In Canada, private donations to charity represent approximately two percent of GDP (this figure includes volunteer time; private monetary donations to charity represent approximately one percent of GDP.); see Hall et al. [2]. This high charitable contribution rate is due in part to the “power of the ask” as most people contribute to charities or organizations only when asked; see Y？rük [3], Y？rük [4], Andreoni [5], Andreoni and Payne [6], and Keegan [7]. Large donations are more likely to occur as a fund-raiser increases the time spent with the potential donor and/or increases the time spent researching the potential donor. (For instance, Dellavigna et al. [8] compare donation rates from a door to door fund-raising drive to donations received via the mail or the Internet. They find that the mail and Internet donation rate is around 0.0001 percent while the face to face donation rate is over 6 percent. Thus, fund-raisers can greatly increase donations by using the more time consuming face to face solicitation technique.) However, a fund-raiser can only research or solicit a donor that he is aware of or has some sort of tie to; for instance, a fund-raiser may research or
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