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Signalling games and giving to charity

In recent work with Amrish Patel we model giving to charity using a signalling game. With this approach a person is assumed to give to charity in order to signal some desirable trait about herself such as generosity or wealth. To many this approach seems quite a cynical one. It seemingly paints a picture of very strategic giving. Do people not give to charity because they want to make the world a better place?
      What I want to try and convince you of here is that a signalling game approach actually paints a nice picture of giving - strategic, but not overly cynical.
      Here is how a simple signalling game works: There are two types of people - generous and not-generous. The generous want to make the world a better place. The not-generous do not care. Society likes generous people. It likes them enough that it is willing to reward them in same way. This could be through esteem, status, or a greater willingness to help them when they need help, etc.
      Notice the 'nice' story being told here. There are generous people who want to give to make the world a better place. And society likes such people and wants to reward them.
      Now for the strategic bit. The not-generous do not deserve any esteem or status. The trouble is society cannot know a-priori who is a generous type and who is a not-generous type. There is, therefore, an incentive for the not-generous to appear generous and get some undeserved esteem. This is where signalling comes in. The generous type somehow needs to signal her generosity. How can she do that? She can give such a large amount to charity that no not-generous type would ever match her. This results in a separating equilibrium. Society can tell who the generous and not-generous types are. The only cynical part of this story is that some not-generous people exist. But, that's clearly true!
      A separating equilibrium is not the only possible outcome. Another possibility is a pooling equilibrium where the generous and not-generous are indistinguishable. In the work I did with Amrish Patel we argue that charities might want to set things up so as to get this outcome. The basic logic goes something like this: With a separating equilibrium the generous type gives more than she would like to signal her generosity and the not-generous types give nothing. In a pooling equilibrium the generous type gives what she wants and the not-generous types gives something. By forcing a pooling equilibrium the charity, therefore, loses out on the generous type but gains on the not-generous type. Overall, the gain will likely offset the loss. I also think there is something nice about the not-generous type being incentivized to give something! 
   

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