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Mathematicians' & mechanism design

While Leonid ‘Leo’ Hurwicz gave the theory of incentive compatibility in mechanism design, Eric Stark Maskin and Roger Bruce Myerson extended his work by incorporating implementation theory and monetary aspects of mechanism design respectively

Mathematicians & mechanism design
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The Nobel Prize in Economic Sciences in 2007 was awarded jointly to Leonid Hurwicz, then at University of Minnesota; Eric S Maskin, then at Institute for Advanced Study, Princeton; and Roger B Myerson, then at University of Chicago "for having laid the foundations of mechanism design theory".

Hurwicz graduated from Warsaw University in 1938 with a degree in law, following the footsteps of his father. Here he took some courses in economics and became interested in the subject. He was encouraged to go to London to further pursue economics at the London School of Economics where he studied with Nicholas Kaldor and Hayek, but couldn't stay on because of visa issues. As a result, he went to Switzerland in 1939 and enrolled in the Graduate Institute of International Studies. In 1940, Hurwicz managed to get away to Chicago in the USA. He got a job as the Teaching Assistant of Paul Samuelson at MIT in 1940, but only for one semester. In 1941, he returned to University of Chicago where he worked with Oskar Lange and also taught statistics and got involved with the Institute of Meteorology there. He then did a stint at the Cowles Commission, then at Chicago. He joined the economics faculty at Iowa State College in 1946 and was a visiting professor at the Cowles Commission in 1950-51. In 1951, he moved to the University of Minnesota as Professor of Economics, where he spent most of his career, with stints in various universities in the US and other parts of the world.

Maskin graduated in mathematics from Harvard College in 1972. In 1974, he got his Masters in applied mathematics and, in 1976, finished his PhD in applied mathematics, both from Harvard University. After finishing his Doctorate, Maskin became a research fellow at Jesus College, Cambridge University. He was then a faculty member at MIT from 1977-1984, Harvard from 1985-2000, and the Institute for Advanced Study in Jerusalem from 2000-2011. He re-joined the Harvard faculty in 2012 as a professor of economics and mathematics. Maskin's work has spanned numerous areas such as game theory, mechanism and institutional design and mathematical economics.

Myerson got his BA in mathematics and Masters in science from Harvard University in 1973. He completed his PhD in applied mathematics from Harvard University itself in 1976. From 1976 to 2001, Myerson was a professor of economics at North-western University's Kellogg School of Management, where he did most of the research that got him the Nobel Prize. He became Professor of Economics at University of Chicago in 2001.

In this article, we will review the main works of the three Nobel laureates and see how their work continues to be applied in public policy.

Main works of Hurwicz

Hurwicz was a rather unconventional choice for the Nobel Prize in Economics because not only did he not have any formal training in economics, but also because he did not have a PhD. Hurwicz began his studies for a PhD at LSE in 1938 (His chosen topic was 'The Currency Devaluation with Special Reference to the Experience of the Gold Bloc Countries') but his studies were interrupted by the war in the summer of 1939. Further, Hurwicz was primarily a mathematician, with interests in areas such as meteorology.

In one sense, Hurwicz was injecting real-world factors about decision-making in Adam Smith's world, where the invisible hand of the market ensures efficient allocation of resources. He took into account the fact that there are information asymmetries, decision-making uncertainty and the fact that decisions are taken within firms, by managers, workers and other economic agents.

His earliest work was published in Econometrica in 1944, in which he wrote of economic fluctuations under uncertainty. In the following years, his work on the theory of the firm and economic behaviour was published in different journals. But he is best known for his work on mechanism design, particularly for his theory of incentive compatibility which he proposed in 1960. Put simply, the mechanism design theory addresses the gap in knowledge that exists between buyers and sellers in the face of uncertainty and information asymmetry. According to Hurwicz, this is done through a specialized game in which participants submit messages to a central point and a rule determines the allocation of resources based on those messages. In a sense, Hurwicz was using game theory to model institutions under uncertainty. In the 1960 paper, which he developed further in 1972, Hurwicz laid the foundation for the modern theories of mechanism design and implementation. This work showed how economic models can provide a framework for the analysis of systems in the context of incentives such systems provide to economic actors. This was referred to as the theory of incentive compatibility and gave a tool to analyse various economic models viz. centrally planned versus market economies versus socialist economies.

Hurwicz is also known for the 'Hurwicz criterion' which is a decision-making rule used under uncertainty. In this decision rule, the best and worst possible outcomes are considered by the decision maker and given weights to arrive at a final decision. The weights are determined by a 'coefficient of optimism' which tells us the probability of the best outcome.

Hurwicz also worked with Kenneth Arrow on non-linear programming and edited a book with him titled 'Studies in Resource Allocation Processes' in 1978.

Main works of Eric Maskin

Eric Maskin was primarily a mathematician and had wide-ranging interests from game theory to auctions, social choice, political economy and patents. However, his best-known works are in the application of game theory to mechanism design, patents and political economy.

While Maskin was at Cambridge, he took forward Hurwicz's work on mechanism design. To Hurwicz's work, he added implementation theory which provided for mechanisms that would lead to optimal outcomes for all participants. More specifically, Maskin suggested that mechanism design can be thought of as a reverse cooperative game where the outcome was given and the goal was to find the best way to achieve that outcome. More generally, Maskin wanted to frame a mathematical model, which would design a game that would yield a given social goal.

On patents, Maskin has argued against giving patents if innovation is sequential (one invention follows another) or complementary (each invention takes different paths but complements each other). He argued that such patent protection may hinder innovation since there would be no competition.

In political economy, he wrote a paper in 2004 that proposed a mathematical model wherein public officials could be made accountable by requiring them to get re-elected. He argued that not holding officials accountable through re-election is desirable when voters are poorly informed, acquiring relevant information is costly, the impact of official actions takes a long time to become known, and the majority's preferences are likely to inflict severe costs on a minority. This suggests that highly technical decisions should be left to unelected judges or bureaucrats, but he argues that their discretion should be sharply limited and important general decision-making power should be reserved for elected officials.

In social choice, Maskin co-edited a book with Amartya Sen titled 'The Arrow Impossibility Theorem' in 2014. This book explored the implications of Arrow's theorem, its relevance in today's world and its limitations. The book also had articles and commentaries by Arrow himself and other scholars such as Prasanta K Pattanaik Joseph E Stiglitz, Maskin, Dasgupta, and Amartya Sen.

Maskin's many interests were of course inter-related. He was not too happy with the voting system in the US and thought that this may not be truly democratic. Taking the example of the 2003 US presidential election, George W Bush, Al Gore and Ralph Nader were the contenders. While Bush won the most votes, Maskin suggests, had Nader's name not been on the ballot, there would have been a different outcome. Maskin's solution was: "What you should do is to allow voters to rank candidates, as this would be more likely to lead to a 'true majority winner'." His mechanism design of a reverse game where the outcome was known is a result of such dilemmas, which, in turn, were first raised by Arrow's impossibility theorem.

Main works of Roger Myerson

Like Maskin, Myerson was primarily a mathematician, with a focus on game theory. He also built on Hurwicz's work and contributed to another aspect of mechanism design theory. While Maskin's contribution was to focus on the implementation aspects through a reverse cooperative game (where the outcome is known), Myerson looked at the monetary aspects of mechanism design. More specifically, he looked at economic communication between rational agents with differing information, which was a refinement of Nash equilibrium, where no communication is allowed. This work led to important benchmarks such as the revelation principle and the revenue-equivalence theorem, which are widely used in auctions and bargaining.

The revenue equivalence theorem states that if all bidders are risk-neutral, and all have their own valuation for the auctioned items, then all auctions have the same expected sales price (or seller's revenue). All auctions include the English auction, the Dutch auction, first-price sealed-bid auction, and the second-price sealed-bid auction. On the other hand, it demonstrates mathematically how individuals with information secret from others can extract economic value whenever the allocation of economic resources depends on their information. This has important implications for economic problems involving asymmetric information, such as adverse selection and moral hazard.

Myerson's work has also been applied to various areas of political economy such as efficient regulation and voting procedures. For example, Myerson's work in this area shows how different electoral and voting rules can impact the incentives and behaviour of politicians and political candidates to either increase competition in elections or reinforce corrupt behaviour by established politicians. He also analysed how various constitutional systems of division of power among executive and legislative bodies can determine the effectiveness of political parties and coalitions.

Myerson has authored a number of books, including 'Game Theory: Analysis of Conflict' (1991) and 'Probability Models for Economic Decisions' (2005). He also has published numerous articles in professional journals, including 'Econometrica', 'Journal of Economic Theory', 'Games and Economic Behaviour', 'American Political Science Review', 'Mathematics of Operations Research', and 'International Journal of Game Theory'.

Conclusion

Hurwicz, Maskin and Myerson were primarily mathematicians, who applied game theory to many economic and political problems. One such economic problem for which they were awarded the Nobel Prize was mechanism design. While Hurwicz set the tone and laid out the basics of mechanism design theory, Maskin and Myerson contributed to different aspects of the theory as noted above. In particular, their work helped us understand what the best mechanism for optimal allocation would be.

And how private information and incentives would impact such a design. In a sense, mechanism design allows us to address principal-agent problems, and issues of adverse selection and moral hazard, which arise as a result of asymmetric information.

The writer is an IAS officer, working as Principal Resident Commissioner, Government of West Bengal. Views expressed are personal

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