1,760 research outputs found
Existence of Multiagent Equilibria with Limited Agents
Multiagent learning is a necessary yet challenging problem as multiagent
systems become more prevalent and environments become more dynamic. Much of the
groundbreaking work in this area draws on notable results from game theory, in
particular, the concept of Nash equilibria. Learners that directly learn an
equilibrium obviously rely on their existence. Learners that instead seek to
play optimally with respect to the other players also depend upon equilibria
since equilibria are fixed points for learning. From another perspective,
agents with limitations are real and common. These may be undesired physical
limitations as well as self-imposed rational limitations, such as abstraction
and approximation techniques, used to make learning tractable. This article
explores the interactions of these two important concepts: equilibria and
limitations in learning. We introduce the question of whether equilibria
continue to exist when agents have limitations. We look at the general effects
limitations can have on agent behavior, and define a natural extension of
equilibria that accounts for these limitations. Using this formalization, we
make three major contributions: (i) a counterexample for the general existence
of equilibria with limitations, (ii) sufficient conditions on limitations that
preserve their existence, (iii) three general classes of games and limitations
that satisfy these conditions. We then present empirical results from a
specific multiagent learning algorithm applied to a specific instance of
limited agents. These results demonstrate that learning with limitations is
feasible, when the conditions outlined by our theoretical analysis hold
Multiagent Maximum Coverage Problems: The Trade-off Between Anarchy and Stability
The price of anarchy and price of stability are three well-studied
performance metrics that seek to characterize the inefficiency of equilibria in
distributed systems. The distinction between these two performance metrics
centers on the equilibria that they focus on: the price of anarchy
characterizes the quality of the worst-performing equilibria, while the price
of stability characterizes the quality of the best-performing equilibria. While
much of the literature focuses on these metrics from an analysis perspective,
in this work we consider these performance metrics from a design perspective.
Specifically, we focus on the setting where a system operator is tasked with
designing local utility functions to optimize these performance metrics in a
class of games termed covering games. Our main result characterizes a
fundamental trade-off between the price of anarchy and price of stability in
the form of a fully explicit Pareto frontier. Within this setup, optimizing the
price of anarchy comes directly at the expense of the price of stability (and
vice versa). Our second results demonstrates how a system-operator could
incorporate an additional piece of system-level information into the design of
the agents' utility functions to breach these limitations and improve the
system's performance. This valuable piece of system-level information pertains
to the performance of worst performing agent in the system.Comment: 14 pages, 4 figure
Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games
We consider repeated multiplayer games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multiagent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are “payoff-based” processes in which, at any stage, players know only their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff-based processes for increasingly general scenarios and prove that, after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network
Computer Science and Game Theory: A Brief Survey
There has been a remarkable increase in work at the interface of computer
science and game theory in the past decade. In this article I survey some of
the main themes of work in the area, with a focus on the work in computer
science. Given the length constraints, I make no attempt at being
comprehensive, especially since other surveys are also available, and a
comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic
- …