Today’s Eponymy in August is a three-fer, as we will be talking about Holmström’s Theroem.
Holmström’s Theorem states that it is impossible to have a system of economic incentives that satisfies all of the following three conditions:
- the system as a whole is income-neutral (the total income into the system equals the total outflow from it).
- the system has a Nash Equilibrium
- the system is Pareto-efficient
The latter two conditions are worth exploring on their own, given that they are also eponymous to their respective discoverers. Nash equilibria are conditions in game theory where every actor, given perfect knowledge about the system, cannot change strategy to improve their outcome. That is, if I am in the game and employ strategy A and know that the other player employs strategy B, and I know that for any other strategy A’, the other player will change to a strategy B’ that does not increase my outcome, and this is also true for the other player in all possible B’ strategies, then we are in Nash equilibrium. Applied to a system of economic incentives, that means that I won’t be able to devise a way to increase my income any more than I already have, by working harder or smarter or differently.
Pareto made an appearance in last year’s Eponymy in August with the Pareto principle, and its most common manifestation in the 80/20 Rule. Pareto was also known for theories of allocation of goods and optimality — these still being the underpinnings of economics a century later — and his understanding of an economic optimality is what matters here. A Pareto-optimal distribution of goods is one where any change to itself that makes one actor better off will also make at least one other actor worse off. You can imagine this as starting with an arbitrary allocation of goods between actors in the system, and making swaps between actors that make one better off without making the other worse off until you can’t make any more swaps. You now have a Pareto-efficient distribution.
Bengt Holmström is a Finnish-born, Nobel Prize-winning economist who specializes in the economics of contracts. He received his Ph.D. in economics from Stanford in 1978, and started his career at Northwestern before joining MIT in 1994 and continuing there to the present day. His 1982 paper for the Bell Journal of Economics, Moral Hazard in Teams, introduced the conditions of his impossibility theorem by examining the application of it to employees of a company. Because there are many rational agents (the employees) in this setting, providing effort and receiving compensation, the organization must deal with the free rider problem and the role of competition within the team. Competition within the team is worthless if there cannot be any incentive to compete (the balanced budget condition, which in this case means that all money into the system is paid to the employees with fixed sharing rules), and free riders will never be penalized to the extent of their shirking, because the individual penalty will never rise to the level of the savings in effort. Holmström’s argument is that the way to alleviate this impossibility is to do away with the balanced budget and instead have a monitor who decides what portion of the firm’s revenue is allocated to the team, which stimulates competition and alleviates some free riding.
John Nash also won the Nobel Prize for his work in game theory, a branch of economics that deals with the decisions of actors in a system when dealing with other actors making their own decisions. Nash received his Ph.D in mathematics from Princeton in 1950, after gradually transitioning from chemical engineering early in his college career. Though his Ph.D dissertation was based on game theory and included what later was known as the Nash equilibrium, Nash also made important contributions to the pure mathematics, including work in partial differential equations, manifolds, and cryptography. Nash is also remembered for a period between 1959 and 1970 in which his “beautiful” mind was crippled by paranoid schizophrenia. He overcame the delusions via a dedication to rational thinking, but admitted later in life that he felt limited by this method, implying that the same patterns of thought that led to paranoid delusions were also responsible for his better ideas in the sciences. Tragically, Nash was killed in a car crash in 2015 while returning home from receiving the Abel Prize in Norway.