Charity auctions on social networks

Charitable giving is influenced by many social, psychological, and economic factors. One common way to encourage individuals to donate to charities is by offering to match their contribution (often by their employer or by the government). Conitzer and Sandholm introduced the idea of using auctions to allow individuals to offer to match the contribution of others. We explore this idea in a social network setting, where individuals care about the contribution of their neighbors, and are allowed to specify contributions that are conditional on the contribution of their neighbors. We give a mechanism for this setting that raises the largest individually rational contributions given the conditional bids, and analyze the equilibria of this mechanism in the case of linear utilities. We show that if the social network is strongly connected, the mechanism always has an equilibrium that raises the maximum total contribution (which is the contribution computed according to the true utilities); in other words, the price of stability of the game defined by this mechanism is one. Interestingly, although the mechanism is not dominant strategy truthful (and in fact, truthful reporting need not even be a Nash equilibrium of this game), this result shows that the mechanism always has a full-information equilibrium which achieves the same outcome as in the truthful scenario. Of course, there exist cases where the maximum total contribution even with true utilities is zero: we show that the existence of non-zero equilibria can be characterized exactly in terms of the largest eigenvalue of the utility matrix associated with the social network.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  Arthur C. Brooks,et al.  Why do People Give? , 2005 .

[3]  Adriaan R. Soetevent,et al.  Anonymity in Giving in a Natural Context : A Field Experiment in 30 Churches , 2005 .

[4]  Dean S. Karlan,et al.  Does Price Matter in Charitable Giving? Evidence from a Large-Scale Natural Field Experiment , 2006 .

[5]  K. Carman,et al.  Social Influences and the Private Provision of Public Goods: Evidence from Charitable Contributions in the Workplace , 2003 .

[6]  Jen Shang,et al.  A Field Experiment in Charitable Contribution: The Impact of Social Information on the Voluntary Provision of Public Goods , 2009 .

[7]  J. Andreoni,et al.  Public goods experiments without confidentiality: a glimpse into fund-raising , 2004 .

[8]  J. Guttman,et al.  Understanding Collective Action: Matching Behavior , 1978 .

[9]  Paul R. Milgrom,et al.  Monotone Comparative Statics , 1994 .

[10]  Catherine C. Eckel,et al.  Rebates Versus Matching: Does How We Subsidize Charitable Contributions Matter? , 2003 .

[11]  Kjetil Telle,et al.  The impact of social approval and framing on cooperation in public good situations , 2004 .

[12]  Barton L. Lipman,et al.  Provision of Public Goods: Fully Implementing the Core through Private Contributions , 1989 .

[13]  Robert McClelland,et al.  SEQUENTIAL CONTRIBUTIONS TO PUBLIC GOODS , 2007 .

[14]  Rachel Croson,et al.  Field experiments in charitable contribution: The impact of social influence on the voluntary provision of public goods , 2006 .

[15]  Hal R. Varian,et al.  A SOLUTION TO THE PROBLEM OF EXTERNALITIES AND PUBLIC GOODS WHEN AGENTS ARE WELL-INFORMED , 1990 .

[16]  Vincent Conitzer,et al.  Expressive negotiation over donations to charities , 2004, EC '04.

[17]  James Andreoni,et al.  Leadership giving in charitable fund-raising , 2006 .