Do you love Coffee???

I was walking back from school today and started thinking about a simple choice problem. Let me start with the basic set up and assumptions. Assume that we are all part of organization X. The members of the organization are myself, mano, meera, brainwaves, saumya, mindframes and survivor (others are welcome to join and should not change anything, except the division of the pie). Let us assume we have a big boss "M". We are all coffee lovers and at present the office does not have a coffee machine. The machine will cost the firm $ "c". Now "M" being the kind of guy he is, decides that he will buy the machine only if his staff (we) value the machine sufficiently to justify the expense. Not buying the coffee machine will not lead to any loss of productivity is an inherent assumption. Therefore the only decision driver for "M" is that we value the machine sufficiently.

Each one of us have private valuations for the machine. The valuation is not the cost of the machine but what is utility that the coffee machine gives me or you. In other words, if asked to contribute to buying the coffee machine, what is my willingness to pay for the machine. Let each of our potential contributions be "x with a subscript i representing each of us". "M" does not drink coffee and his decision rule is that the coffee maker is worth buying if and only if the sum of all the "x's" is greater than or equal to "c". In other words, if the sum of our individual contributions is greater than the cost of the machine, the machine will be bought. Hence what we think about our valuations is important in the outcome and each one of us prefers an outcome where the machine is bought.

Question: What can "M" do in this situation?

Solution 1: "M" can call each one of us privately to his room and ask us for what is our personal valuation. If the sum of our revealed valuation is greater than the cost, the machine is purhcased! Sounds good but there is a problem.

Remember that though we are asked for our valuations, we do not bear any cost. Therefore, one or all of us can inflate our true valuations, because our objective is to get the coffee machine and since inflating the valuation is not costly, the mechanism achieves the objective. "M" being a smart person himself decides that this is not effective and decides against this.

Solution 2: Suppose "M" decides that each one of us will make a contribution equivalent to our valuations and then if our total contribution exceed the cost, the machine will be purchased. Any excess cash collected can be used to purchase say beans. Is this solution optimal? Again it sounds good but there is a problem.

Let us assume here that we are good friends, but do not want to contribute more than an equal share. Also assume that we cannot collude. Therefore our private valuations are known only to us. Now it is possible that some of us might try to free ride on the others. Therefore there is a possibility of understating our true valuation, because we want the same benefit with a lower contribution, expecting another person to subsidize. Hence, again the situation leads to a failure. Therefore "M" rejects this.

What would be the best strategy that "M" can use to resolve this problem? Any suggestions? Is the problem interesting or would modifications be better?? I'm thinking about building examples which can probably be used for teaching design of management control systems (which is something that I want to teach at some point). I presume that such situations probably do arise in real life when there is a need to buy some goods in an organization which are useful collectively. If yes and you were part of it, please do share your experience on how it was solved.