Holmström's theorem
Impossibility of efficient incentive systems / From Wikipedia, the free encyclopedia
In economics, Holmström's theorem is an impossibility theorem or trilemma attributed to Bengt R. Holmström proving that no incentive system for a team of agents can make all of the following true:
- Income equals outflow (the budget balances),
- The system has a Nash equilibrium, and
- The system is Pareto efficient.
Thus a Pareto-efficient system with a balanced budget does not have any point at which an agent can not do better by changing their effort level, even if everyone else's effort level stays the same, meaning that the agents can never settle down to a stable strategy; a Pareto-efficient system with a Nash equilibrium does not distribute all revenue, or spends more than it has; and a system with a Nash equilibrium and balanced budget does not maximise the total profit of everybody.
The Gibbard–Satterthwaite theorem in social choice theory is a related impossibility theorem dealing with voting systems.