Skip to main content

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! 
   

Comments

Post a Comment

Popular posts from this blog

Revealed preference, WARP, SARP and GARP

The basic idea behind revealed preference is incredibly simple: we try to infer something useful about a person's preferences by observing the choices they make. The topic, however, confuses many a student and academic alike, particularly when we get on to WARP, SARP and GARP. So, let us see if we can make some sense of it all.           In trying to explain revealed preference I want to draw on a  study  by James Andreoni and John Miller published in Econometrica . They look at people's willingness to share money with another person. Specifically subjects were given questions like:  Q1. Divide 60 tokens: Hold _____ at $1 each and Pass _____ at $1 each.  In this case there were 60 tokens to split and each token was worth $1. So, for example, if they held 40 tokens and passed 20 then they would get $40 and the other person $20. Consider another question: Q2. D...
Post a Comment
Read more

Nash bargaining solution

Following the tragic death of John Nash in May I thought it would be good to explain some of his main contributions to game theory. Where better to start than the Nash bargaining solution. This is surely one of the most beautiful results in game theory and was completely unprecedented. All the more remarkable that Nash came up with the idea at the start of his graduate studies!          The Nash solution is a 'solution' to a two-person bargaining problem . To illustrate, suppose we have Adam and Beth bargaining over how to split some surplus. If they fail to reach agreement they get payoffs €a and €b respectively. The pair (a, b) is called the disagreement point . If they agree then they can achieve any pair of payoffs within some set F of feasible payoff points . I'll give some examples later. For the problem to be interesting we need there to be some point (A, B) in F such that A > a and B > b. In...
Post a Comment
Read more

Prisoners dilemma or stag hunt

Over Christmas I had chance to read The Stag Hunt and the Evolution of Social Structure by Brian Skyrms. A nice read, very interesting and thought provoking. There’s a couple of things in the book that prompt further discussion. The one I want to focus on in this post is the distinction between the stag hunt game and the prisoners dilemma game.    To be sure what we are talking about, here is a specific version of both type of game. Adam and Eve independently need to decide whether to cooperate or defect. The payoff matrix details their payoff for any combination of choices, where the first number is the payoff of Adam and the second number the payoff of Eve. For example, in the Prisoners Dilemma, if Adam cooperates and Eve defects then Adam gets 65 and Eve gets 165. Prisoners Dilemma Eve Cooperate Defect Adam Cooperate 140, 140 65, 165 Defect 165,...
Post a Comment
Read more