Papers and Reports

Quantum Game Theory and Coordination in the Intellectual Property

View Paper
By Ted Sichelman

The inventive and creative works protected by intellectual property laws are essentially public goods. As in the case of ordinary public goods, it is usually difficult for inventors and creators to erect non-legal barriers to prevent the use of their works (non-excludability), and any such use does not deplete their works (non-rivalry). Thus, scholars have long used classical game theoretic models of public goods to describe the strategies of players in intellectual property (IP) games. These models contain two seemingly common-sense assumptions: one, that if there are a finite number of decisions a player can make for any single move, the player must make exactly one decision; and two, that if a player engages only in a single game, the player will break a pre-game commitment with another player to follow a mutually beneficial strategy if it is in that player’s self-interest.

Recent extensions to classical game theory using the theory of quantum mechanics – known as quantum game theory (QGT) – have dispensed with these two assumptions, yielding radical new results for many types of games. For instance, in the classical version of the prisoner’s dilemma, two prisoners will fail to cooperate even though it is in their mutual interest to do so. However, in the quantum version, the prisoners’ decisions are often “entangled” in a mutually beneficial way that overcomes the ostensible barriers of classical self-interest, leading the players to cooperate. In this regard, quantum game theorists have suggested that if some exogenous quantum mechanical mechanism – like a quantum computer – could be used to entangle players in a public-goods game, doing so would diminish or eliminate sub-optimal free riding.

This paper contends that there are endogenous effects – specifically, quantum game theoretic phenomena present in the absence of external quantum computers – in certain types of IP games that may act to reduce classically predicted free riding, duplicated development costs, and deadweight losses. In particular, instead of modeling underlying IP rights as classical entities, this paper follows the suggestions of several earlier scholars that legal rights are probabilistic and, at least metaphorically, quantum in nature. In so doing, it shows that rights, including IP rights, exhibit an inherent quantum structure that allows players to avoid making a single classical choice for each move. By allowing the government – as a mechanism designer – to engage in quantum strategies, ordinary players can coordinate their strategies in non-classical ways, exhibiting forms of seemingly altruistic behavior and cooperation that are absent in classical models. The paper concludes by commenting briefly on how QGT might be applied more broadly to other areas of the law.

The Web of Law

View Paper
By Thomas A. Smith

Scientists and mathematicians in recent years have become intensely interested in the structure of networks. Networks turn out to be crucial to understanding everything from physics and biology, to economics and sociology. This article proposes that the science of networks has important contributions to make to the study of law as well. The network of American case law closely resembles the Web in structure and can be studied using techniques that are now being used to describe many other networks, some found in nature, and others created by human action. Studying the legal network can shed light on how the legal system evolves, and many other questions.

I present in this article the preliminary results of a significant citation study of nearly four million American legal precedents, which was undertaken at my request by the LexisNexis corporation using the Shepard's citation service. This study demonstrates that the American case law network has the overall structure that network theory predicts it would. It is a highly skewed, scale-free, or similar network. The remarkably great degree of skew is significant. Precedential authority is concentrated in a small number of cases. The vast majority of cases are rarely or never cited. In that it consists largely of dead cases, the Web of Law closely resembles scientific paper citation networks, which consist mostly of dead papers.

This article has three parts. First, I introduce some basic concepts of network science, including such important ideas as nodes, links, random graphs, evolving networks, scale-free networks, small worlds, the rich get richer dynamic, node fitness, and clusters. In Part II, I show that both over all and by particular jurisdiction, the Web of Law is a scale-free or similarly highly skewed network. In Part III, I describe some insights that appear from this application and suggest areas for future research.


Center for Computation, Mathematics, and the Law
Guadalupe Hall, Room 105
Phone: (619) 260-7512