Results 1  10
of
72
Multiagent Systems: Algorithmic, GameTheoretic, and Logical Foundations
, 2009
"... formatted differently than the book—and in particular has different page numbering—and has not been fully copy edited. Please treat the printed book as the definitive version. You are invited to use this electronic copy without restriction for onscreen viewing, but are requested to print it only un ..."
Abstract

Cited by 106 (11 self)
 Add to MetaCart
formatted differently than the book—and in particular has different page numbering—and has not been fully copy edited. Please treat the printed book as the definitive version. You are invited to use this electronic copy without restriction for onscreen viewing, but are requested to print it only under one of the following circumstances: You live in a place that does not offer you access to the physical book; The cost of the book is prohibitive for you; You need only one or two chapters. Finally, we ask you not to link directly to the PDF or to distribute it electronically. Instead, we invite you to link to
Intrinsic Robustness of the Price of Anarchy
"... The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium ..."
Abstract

Cited by 56 (11 self)
 Add to MetaCart
The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium. This drawback motivates the search for inefficiency bounds that apply more generally to weaker notions of equilibria, such as mixed Nash and correlated equilibria; or to sequences of outcomes generated by natural experimentation strategies, such as successive best responses or simultaneous regretminimization. We prove a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective. First, we identify a “canonical sufficient condition ” for an upper bound of the POA for pure Nash equilibria, which we call a smoothness argument. Second, we show that every bound derived via a smoothness argument extends automatically, with no quantitative degradation in the bound, to mixed Nash equilibria, correlated equilibria, and the average objective function value of regretminimizing players (or “price of total anarchy”). Smoothness arguments also have automatic implications for the inefficiency of approximate and BayesianNash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomiallength bestresponse sequences. We also identify classes of games — most notably, congestion games with cost functions restricted to an arbitrary fixed set — that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worstcase upper bound on the POA, even for the smallest set of interest (pure Nash equilibria). Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with nonpolynomial cost functions, and the first
private communication
"... A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic BreadthFirst Search (LBFS) and Maximum Cardinality Search (M ..."
Abstract

Cited by 56 (4 self)
 Add to MetaCart
A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic BreadthFirst Search (LBFS) and Maximum Cardinality Search (MCS), Corneil and Krueger propose in 2008 the socalled Maximal Neighborhood Search (MNS) and show that one sweep of MNS is enough to recognize chordal graphs. We develop the MNS properties of rigid interval graphs and characterize this graph class in several different ways. This allows us obtain several linear time multisweep MNS algorithms for recognizing rigid interval graphs and unit interval graphs, generalizing a corresponding 3sweep LBFS algorithm for unit interval graph recognition designed by Corneil in 2004. For unit interval graphs, we even present a new linear time 2sweep MNS certifying recognition algorithm. Submitted:
Joint strategy fictitious play with inertia for potential games
 in Proceedings of the 44th IEEE Conference on Decision and Control
, 2005
"... We consider multiplayer repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these “largescale ” games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in lar ..."
Abstract

Cited by 41 (22 self)
 Add to MetaCart
We consider multiplayer repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these “largescale ” games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in largescale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as “Fictitious Play ” (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion. 1
Connections Between Cooperative Control and Potential Games Illustrated on the Consensus Problem
, 2007
"... This paper presents a view of cooperative control using the language of learning in games. We review the game theoretic concepts of potential games and weakly acyclic games and demonstrate how the specific cooperative control problem of consensus can be formulated in these settings. Motivated by th ..."
Abstract

Cited by 35 (15 self)
 Add to MetaCart
This paper presents a view of cooperative control using the language of learning in games. We review the game theoretic concepts of potential games and weakly acyclic games and demonstrate how the specific cooperative control problem of consensus can be formulated in these settings. Motivated by this connection, we build upon game theoretic concepts to better accommodate a broader class of cooperative control problems. In particular, we introduce sometimes weakly acyclic games for timevarying objective functions and action sets, and provide distributed algorithms for convergence to an equilibrium. Finally, we illustrate how to implement these algorithms for the consensus problem in a variety of settings, most notably, in an environment with nonconvex obstructions.
Payoff Based Dynamics for MultiPlayer Weakly Acyclic Games
 SIAM JOURNAL ON CONTROL AND OPTIMIZATION, SPECIAL ISSUE ON CONTROL AND OPTIMIZATION IN COOPERATIVE NETWORKS
, 2007
"... 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 coo ..."
Abstract

Cited by 26 (16 self)
 Add to MetaCart
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 only know 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 socalled 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.
Exact Price of Anarchy for Polynomial Congestion Games
, 2006
"... We show exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions. The given values also hold for weighted and unweighted network congestion games. ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
We show exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions. The given values also hold for weighted and unweighted network congestion games.
Revisiting LogLinear Learning: Asynchrony, Completeness and PayoffBased Implementation
, 2008
"... Loglinear learning is a learning algorithm with equilibrium selection properties. Loglinear learning provides guarantees on the percentage of time that the joint action profile will be at a potential maximizer in potential games. The traditional analysis of loglinear learning has centered around ..."
Abstract

Cited by 25 (9 self)
 Add to MetaCart
Loglinear learning is a learning algorithm with equilibrium selection properties. Loglinear learning provides guarantees on the percentage of time that the joint action profile will be at a potential maximizer in potential games. The traditional analysis of loglinear learning has centered around explicitly computing the stationary distribution. This analysis relied on a highly structured setting: i) players ’ utility functions constitute a potential game, ii) players update their strategies one at a time, which we refer to as asynchrony, iii) at any stage, a player can select any action in the action set, which we refer to as completeness, and iv) each player is endowed with the ability to assess the utility he would have received for any alternative action provided that the actions of all other players remain fixed. Since the appeal of loglinear learning is not solely the explicit form of the stationary distribution, we seek to address to what degree one can relax the structural assumptions while maintaining that only potential function maximizers are the stochastically stable action profiles. In this paper, we introduce slight variants of loglinear learning to include both synchronous updates and incomplete action sets. In both settings, we prove that only potential function maximizers are stochastically stable. Furthermore, we introduce a payoffbased version of loglinear learning, in which players are only aware of the utility they received and the action that they played. Note that loglinear learning in its original form is not a payoffbased learning algorithm. In payoffbased loglinear learning, we also prove that only potential maximizers are stochastically stable. The key enabler for these results is to change the focus of the analysis away from deriving the explicit form of the stationary distribution of the learning process towards characterizing the stochastically stable states. The resulting analysis uses the theory of resistance trees for regular perturbed Markov decision processes, thereby allowing a relaxation of the aforementioned structural assumptions.