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An engagement free-rider incentive: a simple payoff example

If engagement benefits all holders but one investor pays the entire cost, that investor’s private incentive can differ from the combined investors’ incentive.

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State the payoff assumptions

Three fictional investors each hold one-third of a company. Assume a successful engagement adds 90 units of value shared equally among them and costs 45 units in total. For this exercise, success is certain and values are measured at the same date. These assumptions simplify the incentive comparison; they do not estimate the likelihood or value of a real engagement.

Compare a sole payer with non-payers

Each investor receives 30 units of the common benefit. If A pays all 45 units, A’s net result is −15. B and C each receive +30 without paying. The combined net result is +45, yet A’s private result is negative.

Sole-payer payoff
InvestorShare of benefitCost paidNet result
A3045−15
B300+30
C300+30
Combined9045+45

Change the cost-sharing rule

If the three investors share the 45-unit cost equally, each pays 15 and receives 30. Each net result becomes +15; the combined result remains +45. Collaboration changes the distribution of costs in this example. It does not create an extra 45 units of benefit or prove that the same arrangement is feasible in practice.

Add uncertainty explicitly

If the probability of obtaining the 90-unit benefit were 40%, its expected value would be 36 before costs. The combined expected net result would then be −9. Sharing costs could still alter private incentives, but it would not turn that assumed negative combined expectation into a positive one. Success probability and costs must be considered together.

Further references