On Mechanism Design

Check, check - check mate. I play the bishop like a Wagner composition. Precise, intentional, and aggressive.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.― John von Neumann

What’s better than deploying a winning strategy in a game? Sex, drugs, big game hunting, closing big deals… Feel free to replace those examples however you see fit. Certainly, your examples probably aren’t as truthful. Let the child in you rip. Dance with your inner flame.

I, like many others, enjoy games. I find it fascinating that games can be designed and played a seemingly infinite amount of times. It takes a true genius to create a timeless game. It turns out that it takes an even greater intellect to understand their mechanics.

Hence we must turn to one of the most brilliant minds of any era - John Von Neumann. Neumann was a powerful mind, often times chaotic, and other times anal. The true embodiment of man. Who doesn’t love a fast driving polymath that loves to make money, blow things up and solve mathematical problems in his spare time? If you are familiar with Richard Feynman, then you’ll do well to study up on Von Neumann.

Few books are as enthralling and confounding as "Theory of Games and Economic Behavior", a highly influential and groundbreaking book that introduced game theory as a new tool for analyzing strategic decision-making.

Authored by John von Neumann and Oskar Morgenstern in 1944, the book has had a profound impact on a wide range of fields, including economics, political science, and computer science.

The book's central idea is the concept of a "game," which refers to any situation where the outcome of one's own choices depends on the choices of others. The authors used mathematical models to describe these games and develop tools for analyzing the optimal strategies for each player. They introduced concepts such as the minimax theorem and the Nash equilibrium, which have become fundamental to game theory.

The book also covers a wide range of topics, including bargaining theory, the theory of auctions, and the modeling of markets. The authors applied their theory to a variety of economic issues, such as monopoly, duopoly, and oligopoly. They also explored the role of information in decision-making and the concept of risk and uncertainty.

The impact of "Theory of Games and Economic Behavior" has been far-reaching. It has led to the development of new models in economics, such as mechanism design theory, which focuses on designing mechanisms that incentivize individuals to behave in certain ways. It has also been applied in political science to study voting systems, and in computer science to develop algorithms for solving complex games.

In summary, "Theory of Games and Economic Behavior" is a seminal work that has had a lasting impact on our understanding of strategic decision-making and its applications in a variety of fields.

An element which stimulates itself will hold a stimulus indefinitely.
― John von Neumann

In Practice

Mechanism design theory has been applied in many practical settings. One example is the design of auctions. In an auction, the goal is to allocate a good or service to the bidder who values it the most. However, bidders may have different information about the value of the good, and can strategically bid less than their true value in order to pay a lower price. Mechanism design theory provides a way to design auctions that incentivize bidders to bid truthfully, so that the auctioneer can maximize revenue while still allocating the good to the bidder who values it the most.

Another example is the allocation of resources in public goods provision. A public good is a good or service that is non-excludable and non-rivalrous, meaning that one person's consumption of the good does not reduce the availability of the good to others. Examples of public goods include clean air, national defense, and scientific research. Mechanism design theory can be used to design mechanisms that incentivize individuals to contribute to the provision of public goods, so that the socially optimal level of provision can be achieved.

Mechanism design theory has also been applied in the design of voting systems. Voting systems can have important implications for the outcomes of elections, and different systems can incentivize different types of behavior from voters and candidates. Mechanism design theory can be used to design voting systems that incentivize voters and candidates to behave in ways that lead to socially desirable outcomes.

Mechanism design theory has many practical applications in a variety of settings, and has led to the development of new institutions and mechanisms that can help to solve important economic and social problems.

Sometimes people don’t want to hear the truth because they don’t want their illusions destroyed. - Nietzsche

Auctions

Mechanism design theory can help to prevent collusion in auctions by designing mechanisms that incentivize bidders to bid truthfully and discourage them from colluding with each other.

Collusion occurs when two or more bidders agree to cooperate in order to maximize their joint payoff. For example, in a standard auction, bidders may agree to bid less than their true value in order to reduce the price of the good and increase their profits. However, if all bidders do this, the auctioneer may not be able to allocate the good to the bidder who values it the most, resulting in a suboptimal outcome.

Mechanism design theory provides a way to design auctions that incentivize bidders to bid truthfully, so that the auctioneer can maximize revenue while still allocating the good to the bidder who values it the most. One way to do this is to use an auction mechanism called the Vickrey auction, also known as a second-price sealed-bid auction. In a Vickrey auction, bidders submit sealed bids, and the highest bidder wins the auction and pays the second-highest bid. This mechanism incentivizes bidders to bid truthfully, because bidding less than their true value may result in losing the auction and paying less than their true value.

Another mechanism that can be used to prevent collusion is randomization. In a randomized auction, the auctioneer randomly selects a bidder to win the auction, rather than selecting the highest bidder. This can prevent collusion by making it difficult for bidders to coordinate their bids in advance.

Mechanism design theory provides a powerful set of tools for designing auctions that can prevent collusion and lead to efficient outcomes. By carefully designing the rules of the auction, mechanism design theorists can help to ensure that auctions result in fair and efficient outcomes, even in settings where collusion might otherwise be a problem.

An important viewpoint in classifying games is this: Is the sum of all payments received by all players (at the end of the game) always zero; or is this not the case? If it is zero, then one can say that the players pay only to each other, and that no production or destruction of goods is involved. All games which are actually played for entertainment are of this type. But the economically significant schemes are most essentially not such. There the sum of all payments, the total social product, will in general not be zero, and not even constant. I.e., it will depend on the behavior of the players—the participants in the social economy. This distinction was already mentioned in 4.2.1., particularly in footnote 2, p. 34. We shall call games of the first-mentioned type zero-sum games, and those of the latter type non-zero-sum games.
― John von Neumann, Theory of Games and Economic Behavior

Other utilities

Mechanism design theory has applications in a wide range of fields beyond auctions and economics. It has been used in political science, computer science, and even biology.

In political science, mechanism design theory has been used to design voting systems that incentivize voters and candidates to behave in ways that lead to socially desirable outcomes. For example, the theory can be used to design voting systems that encourage candidates to reveal their true preferences and discourage strategic voting.

In computer science, mechanism design theory has been used to design algorithms for network routing, resource allocation, and task scheduling. For example, in a network routing problem, the goal is to find a path for data packets that minimizes the total delay. Mechanism design theory can be used to design routing algorithms that incentivize individual routers to forward data packets in a way that leads to an efficient outcome for the network as a whole.

In biology, mechanism design theory has been used to study the evolution of cooperation in social animals. The theory can be used to design mechanisms that incentivize individuals to cooperate with each other, even in situations where there is a temptation to defect.

No, No, Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position. Now, real games,’ he said, ‘are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.
― John von Neumann

In sum, mechanism design theory is a powerful tool that can be applied in a wide range of fields. By carefully designing mechanisms that incentivize individuals to behave in certain ways, mechanism design theorists can help to solve important economic, political, and social problems.

Play games, win games, and create games. For it is lunacy to go through life without ever having rolled the dice and lived to the fullest extent possible.