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DESIGNERS OF THE GAME

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By The winning idea for the 2007 economics Nobel could be used in almost any context - even for modifying the rules of cricket, writes Arijit Sen. The author teaches at the Indian Institute of Management, Calcutta. arijitsen@iimcal.ac.in
  • Published 25.10.07
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When the International Cricket Council tinkers with the format of limited-overs cricket (introducing power-plays, inserting super-subs, and so on) it engages in “game design” — it changes the rules of the game to make one-day cricket more competitive and attractive to viewers. When the Telecom Regulatory Authority of India proposes alternative auction mechanisms for 3G spectrum, its aim is to achieve an efficient allocation of a public resource among private players while ensuring adequate revenue generation. When the Indian government embarks on a decentralization programme, it attempts to structure a game of authority and communication between national, state, and local bureaucracies.

The theory of game design — or ‘mechanism design’ — had its “pivotal moment” in 1972 when Leonid Hurwicz’s article, “On Informationally Decentralized Systems”, was published. From then on, “the issue of incentives surfaced forcefully, as if a pair of blinders had been removed”. Thirty-five years later, the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel has been awarded to Leonid Hurwicz, Eric Maskin, and Roger Myerson “for laying the foundation of mechanism design theory.” While the recipients might not have much to say about how the ICC should modify the rules of cricket, their writings have profound implications for the way the TRAI should conduct its auctions, and the manner in which the Indian government should proceed on its path of decentralization.

John Moore chronicles the amazing acumen in game design shown by residents in ancient Greek city-states. In organizing a public ceremony, the citizens had a simple goal — to ensure that the richest person funds the event. Instead of simply coercing that individual to cough up the money, the citizenry played the following game: “Someone nominated the man who was reputed to be the richest. Let us call him Spyros. Spyros would then have to pay up, or claim, ‘I not the richest, old Timon over there is richer than me.’ Then Timon was faced with a choice. Either he could pay, or he could insist that Spyros exchange all his wealth with him, after which Spyros would have to pay.”

Fast-forwarding to 19th-century India, various artisans’ and traders’ guilds in Gujarat faced a related problem. They needed to collect funds from their members for operating expenses, and to give to charity. To this end, the guilds employed an auction scheme described thus in the 1877 Surat Gazetteer: “The men of craft or trade agree, on a certain day, to shut all their shops but one. The right to keep open this one shop is then put up to auction, and the amount bid is credited to the guild fund.” Here, a guild’s objective was not to make just one member pay, but to achieve equitable taxation. The “holiday auction” was an ingenious mechanism, which ensured that guild members came close to contributing a common fraction of their daily profits to the guild fund.

Recognize that if such an auction were held in Christie’s or Sotheby’s, the guild members would bid by holding up their hands as the auctioneer raised the price. In the end, the most-profitable guild member (one whose monopoly profits were the highest) would win when the second-most profitable member dropped out at the price that equalled his own profit estimate. So, instead of organizing the auction, the guild could simply ask its members: “Tell us your daily monopoly profits. We will allow the member who reports the highest profits to stay open on the holiday, and we will make him pay us the second-highest profit number that is reported.” Under this alternative scheme, all guild members would report their profit estimates truthfully, for the simple reason that the subsequent outcome is precisely what would have happened in the holiday auction.

Herein lay the two central tenets of the mechanism design theory. First, any complicated scheme can be reformulated as a direct mechanism that simply asks the participants to reveal their privately-known information and then promises to implement the outcome that the original scheme would generate under the same information structure. Second, the name of the game is to try and ensure that for each player, being truthful and honest is compatible with her individual incentives.

The first concept is called the revelation principle, and Roger Myerson and Eric Maskin have been pre-eminent in establishing and clarifying this principle in different contexts. Leo Hurwicz introduced the second concept — the principle of incentive compatibility. The two principles assert that when we are able to devise a scheme that achieves our desired objective, our success is because of the scheme’s ability to induce the participants to be truthful and honest. By the same token, whenever we fail to find a mechanism that will deliver what we aim for, the failure can be understood wholly in terms of the inability of any mechanism to make truth and honesty compatible with individual interests in that situation.

Consider, for instance, the topical issue of ‘negotiations’ between a farmer with a plot of land and an industrialist who wants to buy it to set up a factory. The farmer knows his benefit from holding on to his land, and the industrialist knows her gain from acquiring it. Here, can we devise a trading scheme that will ensure that the land changes hands if, and only if, the industrialist’s gain is greater than the farmer’s foregone benefits? The short answer is that we cannot, because, in this scenario, it is impossible to provide incentives to both parties to speak the truth about their private information regarding gains and losses. Given that, mechanism design theory goes on to suggest possible schemes which will succeed in attaining less ambitious goals — for example, ones that will ensure efficient trading when a benevolent government is willing to act as an ‘honest broker’.

When one delves into the mechanism design literature, one is dazzled by the plethora of situations to which the theory has been applied. Maskin and Myerson, along with their co-authors, have explored issues of auction design, pollution control, public utility regulation, privatization, voting rules, and electoral systems. On reflection, this is not surprising as the logic of mechanism design is germane to any context where the central issue is to device the rules of the game for a group of strategic participants — be it the authority structure within an organization, the legal system in a country, or a customs union among a group of countries.

Consequently, the theory enables us to view a large number of economic and political institutions as mechanisms that aim to generate a set of socially desirable outcomes. This has been Leo Hurwicz’s consistent vision over the course of his research. One of his recent papers addresses the issue of how to prevent the “implementers” of various societal mechanisms — the politicians, the bureaucrats, and the police — from exploiting the participants. For the citizens of India today, the theme of the paper — and its title — But Who will Guard the Guardians? — should find a deep resonance.