John Nash’s Footprint on Procurement

Spend Matters welcomes this guest article by Alan Holland, founder and CEO of Keelvar.

John Nash’s research contributions inspired advances in auction theory that have progressed the fields of e-sourcing and procurement and will continue to influence future developments in sourcing optimization. This piece highlights why his contributions are important to our industry.

John Nash and his wife recently died in a tragic car accident. His contributions to mathematical techniques that underpin strategic analysis in many disciplines such as economics, politics, artificial Intelligence and evolutionary biology are well publicized. This piece takes a look at how his contributions influenced auction theory and, in turn, were fundamental in the development of e-sourcing best practice.

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Most people’s understanding of John Nash’s contributions to science stem from viewing the movie about his life, “A Beautiful Mind.” Understandably, the movie chose not to focus on the details of his scientific contributions and their implications across so many fields. Instead, the story followed the arc of his life that involved the acclaimed discovery of a beautifully simple solution concept for strategic games and then periodic battles with schizophrenia. His mind was a truly tortured one but capable of brilliant insights during interludes of “enforced rationality” as he described it.

Most procurement professionals may be unaware of the significance of John Nash’s contributions for their field. This is understandable given that Nash himself was often surprised to learn of new and interesting applications of his work in diverse fields of research. Nash's most famous research contribution was the concept of an “equilibrium” in a strategic game. If we look at a single example of such a game (see Prisoner’s Dilemma example) it helps us understand the notion of strategy and how a game may be analyzed in advance to understand expected behaviour.

A “Nash Equilibrium” solution to a game is a profile of strategy selections across players so that selfish individuals have no incentive to unilaterally change their choice. This mathematical concept has become a central pillar in economic analysis because economic agents (e.g. buyers or bidders in an auction) are notoriously selfish. In fact, the more selfish the players in a game are, the more accurate this solution concept tends to be. Nash Equilibrium analysis is a powerful solution concept for studying auctions, be they sealed bid RFX or live e-auction events, because bidders are rational, self-interested and strategic in their behaviour.

Prior to John Nash’s seminal research, nobody could predict expected outcomes from various auction designs. Economic arguments in favor of a sealed bid event versus a Dutch auction or English auction were grounded in speculative analysis instead of scientific reasoning. The Nash Equilibrium, however, was a solution concept that finally permitted scientific study of bidder behaviour. Famous results such as the Revenue Equivalence Theorem followed as scientists now had a solution concept for analysing a rich array of unsolved problems such as traffic flow management through to explaining evolutionary biology.

The Nash Equilibrium concept naturally required many refinements and specializations for more complex settings such as Extensive Form games where decisions are taken sequentially or conditioned on previous actions. An example of a more complex game is a multi-round auction. We know from experience that bidders only become aggressive late in the auction, but Nash’s research gave us the tools to understand what would happen if we change the rules of an auction (e.g. activity rules) to incentivize earlier progress.

A powerful twist on Nash’s work was to use equilibria to optimize the design of auction mechanisms. The field of Mechanism Design is akin to Inverse Game Theory whereby you try to design the best auctions such that the outcomes (obeying equilibrium rules) achieve your key objectives. These goals may, for example, seek to minimize cost or maximize social value if you are a government body. This field of Mechanism Design has enjoyed a resurgence in recent years because of the computational advances made in searching for optimal mechanisms. The implementation of such intelligent auction designs has become more practicable by breakthroughs in computer science research.

This is still a very active area of research and the most recent wave of study has addressed one of the most powerful auction designs, the Combinatorial Auction. Most sourcing professionals know this only as “sourcing optimization,” but in fact, this is a rebadging of an auction format that facilitates more expressive communication of bids and business constraints from bidders and purchasers, respectively. It is also one of the most challenging auction protocols from a research perspective because there is no known equilibria for many variants of sourcing optimization processes in common industrial use to date. Empirical evidence clearly indicates the superior performance of sourcing optimization and this is one area of cutting edge research that is challenging computational economists and game theorists at present.

Advances in Auction Theory relied heavily on the seminal contributions of John Nash. His insights have unquestionably had a profound impact on the efficacy and design of modern sourcing tools and will serve to influence designs for modern sourcing optimization tools.

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