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Autonomous vehicletarget assignment: a game theoretical formulation
 ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL
, 2007
"... We consider an autonomous vehicletarget assignment problem where a group of vehicles are expected to optimally assign themselves to a set of targets. We introduce a gametheoretical formulation of the problem in which the vehicles are viewed as selfinterested decision makers. Thus, we seek the opt ..."
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Cited by 89 (22 self)
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We consider an autonomous vehicletarget assignment problem where a group of vehicles are expected to optimally assign themselves to a set of targets. We introduce a gametheoretical formulation of the problem in which the vehicles are viewed as selfinterested decision makers. Thus, we seek the optimization of a global utility function through autonomous vehicles that are capable of making individually rational decisions to optimize their own utility functions. The first important aspect of the problem is to choose the utility functions of the vehicles in such a way that the objectives of the vehicles are localized to each vehicle yet aligned with a global utility function. The second important aspect of the problem is to equip the vehicles with an appropriate negotiation mechanism by which each vehicle pursues the optimization of its own utility function. We present several design procedures and accompanying caveats for vehicle utility design. We present two new negotiation mechanisms, namely, “generalized regret monitoring with fading memory and inertia ” and “selective spatial adaptive play, ” and provide accompanying proofs of their convergence. Finally, we present simulations that illustrate how vehicle negotiations can consistently lead to nearoptimal assignments provided that the utilities of the vehicles are designed appropriately.
Joint Strategy Fictitious Play with Inertia for Potential Games
, 2005
"... We consider finite 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 ..."
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Cited by 58 (22 self)
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We consider finite 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. A motivating example is a congestion game in a complex transportation system, in which a large number of vehicles make daily routing decisions to optimize their own objectives in response to their observations. In this setting, observing and responding to the individual actions of all vehicles on a daily basis would be a formidable task for any individual driver. This disqualifies some of the well known decision making models such as “Fictitious Play” (FP) as
CoSIGN: a parallel algorithm for coordinated traffic signal control
 IEEE Transactions on Intelligent Transportation Systems
, 2007
"... Abstract — The problem of finding optimal coordinated signal timing plans for a large number of traffic signals is a challenging problem because of the exponential growth in the number of joint timing plans that need to be explored as the network size grows. In this paper, we employ the gametheoret ..."
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Cited by 11 (6 self)
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Abstract — The problem of finding optimal coordinated signal timing plans for a large number of traffic signals is a challenging problem because of the exponential growth in the number of joint timing plans that need to be explored as the network size grows. In this paper, we employ the gametheoretic paradigm of fictitious play to iteratively search for a coordinated signal timing plan that improves a systemwide performance criterion for a traffic network. The algorithm is robustly scalable to realisticsize networks modelled with high fidelity simulations. We report results of a case study for the the city of Troy, Michigan, where there are 75 signalized intersections. Under normal traffic conditions, savings in average travel time of more than 20 percent are experienced against a static timing plan, and even against an aggressively tuned automatic signal retiming algorithm, savings of more than 10 percent are achieved. The efficiency of the algorithm stems from its parallel nature. With a thousand parallel CPUs available, our algorithm finds the plan above in under 10 minutes, while a version of a hillclimbing algorithm makes virtually no progress in the same amount of wallclock computational time. Index Terms — Coordinated traffic signal control, optimization, area traffic control I.
A Decentralized Approach to Discrete Optimization via Simulation: Application to Network Flow
, 2006
"... We study a new class of decentralized algorithms for discrete optimization via simulation, which is inspired by the fictitious play algorithm applied to games with identical interests. In this approach, each component of the solution vector of the optimization model is artificially assumed to have a ..."
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Cited by 7 (0 self)
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We study a new class of decentralized algorithms for discrete optimization via simulation, which is inspired by the fictitious play algorithm applied to games with identical interests. In this approach, each component of the solution vector of the optimization model is artificially assumed to have a corresponding “player”, and the interaction of these players in simulation allows for exploration of the solution space and, for some problems, ultimately results in the identification of the optimal solution. Our algorithms also allow for correlation in players ’ decision making, a key feature when simulation output is shared by multiple decisionmakers. We first establish convergence under finite sampling to equilibrium solutions. In addition, in the context of discrete network flow models, we prove that if the underlying link cost functions are convex, then our algorithms converge almost surely to an optimal solution. Subject classifications: simulation, optimization, network flows, game theory. 1
Distributed algorithms based on fictitious play for near optimal sequential decision making
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On Similarities between Inference in Game Theory and Machine Learning
"... In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach ..."
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Cited by 4 (0 self)
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In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoffdominant but riskdominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We
Sampled Fictitious Play for Approximate Dynamic Programming
, 2011
"... Sampled Fictitious Play (SFP) is a recently proposed iterative learning mechanism for computing Nash equilibria of noncooperative games. For games of identical interests, every limit point of the sequence of mixed strategies induced by the empirical frequencies of best response actions that players ..."
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Cited by 4 (3 self)
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Sampled Fictitious Play (SFP) is a recently proposed iterative learning mechanism for computing Nash equilibria of noncooperative games. For games of identical interests, every limit point of the sequence of mixed strategies induced by the empirical frequencies of best response actions that players in SFP play is a Nash equilibrium. Because discrete optimization problems can be viewed as games of identical interests wherein Nash equilibria define a type of local optimum, SFP has recently been employed as a heuristic optimization algorithm with promising empirical performance. However there have been no guarantees of convergence to a globally optimal Nash equilibrium established for any of the problem classes considered to date. In this paper, we introduce a variant of SFP and show that it converges almost surely to optimal policies in modelfree, finitehorizon stochastic dynamic programs. The key idea is to view the dynamic programming states as players, whose common interest is to maximize the total multiperiod expected reward starting in a fixed initial state. We also offer empirical results suggesting that our SFP variant is effective in practice for small to moderate sized modelfree problems.
Game Theory and Distributed Control
, 2012
"... Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems fro ..."
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Cited by 3 (1 self)
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Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game theoretic methods in this role as a framework for distributed control in engineered systems.
CoSIGN: A Fictitious Play Algorithm for Coordinated Traffic Signal Control
, 2004
"... The problem of finding efficient coordinated signal timing plans for a large number of traffic signals is a challenging problem because of the exponential growth in the number of joint timing plans that need to be explored as the network size grows. In this paper, we employ the gametheoretic paradi ..."
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Cited by 2 (1 self)
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The problem of finding efficient coordinated signal timing plans for a large number of traffic signals is a challenging problem because of the exponential growth in the number of joint timing plans that need to be explored as the network size grows. In this paper, we employ the gametheoretic paradigm of fictitious play to iteratively converge to a locally optimal coordinated signal timing plan. Since there is only one traffic simulation required per iteration, the resulting algorithm is robustly scalable to realistic size networks modelled with high fidelity simulations. We report the results of a case study for the the city of Troy, Michigan where we experienced delay and throughput savings in excess of 10 percent for a network model of 75 signalized intersections. 1