Conservation Law of Utility and Equilibria in Non-Zero Sum Games

This short note demonstrates how one can define a transformation of a non-zero sum game into a zero sum, so that the optimal mixed strategy achieving equilibrium always exists. The transformation is equivalent to introduction of a passive player into a game (a player with a singleton set of pure strategies), whose payoff depends on the actions of the active players, and it is justified by the law of conservation of utility in a game. In a transformed game, each participant plays against all other players, including the passive player. The advantage of this approach is that the transformed game is zero-sum and has an equilibrium solution. The optimal strategy and the value of the new game, however, can be different from strategies that are rational in the original game. We demonstrate the principle using the Prisoner's Dilemma example

Intellectual Property and the Prisoner’s Dilemma: A Game Theory Justification of Copyrights, Patents, and Trade Secrets

In this article, I will offer an argument for the protection of intellectual property based on individual self-interest and prudence. In large part, this argument will parallel considerations that arise in a prisoner’s dilemma game. In brief, allowing content to be unprotected in terms of free access leads to a sub-optimal outcome where creation and innovation are suppressed. Adopting the institutions of copyright, patent, and trade secret is one way to avoid these sub-optimal results

Reinforcement Learning Dynamics in Social Dilemmas

In this paper we replicate and advance Macy and Flache\'s (2002; Proc. Natl. Acad. Sci. USA, 99, 7229–7236) work on the dynamics of reinforcement learning in 2�2 (2-player 2-strategy) social dilemmas. In particular, we provide further insight into the solution concepts that they describe, illustrate some recent analytical results on the dynamics of their model, and discuss the robustness of such results to occasional mistakes made by players in choosing their actions (i.e. trembling hands). It is shown here that the dynamics of their model are strongly dependent on the speed at which players learn. With high learning rates the system quickly reaches its asymptotic behaviour; on the other hand, when learning rates are low, two distinctively different transient regimes can be clearly observed. It is shown that the inclusion of small quantities of randomness in players\' decisions can change the dynamics of the model dramatically.Reinforcement Learning; Replication; Game Theory; Social Dilemmas; Agent-Based; Slow Learning

Fairness Emergence in Reputation Systems

Reputation systems have been used to support users in making decisions under uncertainty or risk that is due to the autonomous behavior of others. Research results support the conclusion that reputation systems can protect against exploitation by unfair users, and that they have an impact on the prices and income of users. This observation leads to another question: can reputation systems be used to assure or increase the fairness of resource distribution? This question has a high relevance in social situations where, due to the absence of established authorities or institutions, agents need to rely on mutual trust relations in order to increase fairness of distribution. This question can be formulated as a hypothesis: in reputation (or trust management) systems, fairness should be an emergent property. The notion of fairness can be precisely defined and investigated based on the theory of equity. In this paper, we investigate the Fairness Emergence hypothesis in reputation systems and prove that , under certain conditions, the hypothesis is valid for open and closed systems, even in unstable system states and in the presence of adversaries. Moreover, we investigate the sensitivity of Fairness Emergence and show that an improvement of the reputation system strengthens the emergence of fairness. Our results are confirmed using a trace-driven simulation from a large Internet auction site.Trust, Simulation, Fairness, Equity, Emergence, Reputation System

On Partially Controlled Multi-Agent Systems

Motivated by the control theoretic distinction between controllable and uncontrollable events, we distinguish between two types of agents within a multi-agent system: controllable agents, which are directly controlled by the system's designer, and uncontrollable agents, which are not under the designer's direct control. We refer to such systems as partially controlled multi-agent systems, and we investigate how one might influence the behavior of the uncontrolled agents through appropriate design of the controlled agents. In particular, we wish to understand which problems are naturally described in these terms, what methods can be applied to influence the uncontrollable agents, the effectiveness of such methods, and whether similar methods work across different domains. Using a game-theoretic framework, this paper studies the design of partially controlled multi-agent systems in two contexts: in one context, the uncontrollable agents are expected utility maximizers, while in the other they are reinforcement learners. We suggest different techniques for controlling agents' behavior in each domain, assess their success, and examine their relationship.Comment: See http://www.jair.org/ for any accompanying file