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28
Resource selection games with unknown number of players
, 2006
"... In the context of preBayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the c ..."
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Cited by 28 (9 self)
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In the context of preBayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the common ignorance about the number of players. In order to perform the analysis we define safetylevel equilibrium for preBayesian games, and prove that it exists in a compactcontinuousconcave setup; in particular it exists in a finite setup. 1
Effective solutions for realworld Stackelberg games: When agents must deal with human uncertainties
 in Proc. of the 8th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS ’09). IFAAMAS
, 2009
"... How do we build multiagent algorithms for agent interactions with human adversaries? Stackelberg games are natural models for many important applications that involve human interaction, such as oligopolistic markets and security domains. In Stackelberg games, one player, the leader, commits to a str ..."
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Cited by 22 (13 self)
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How do we build multiagent algorithms for agent interactions with human adversaries? Stackelberg games are natural models for many important applications that involve human interaction, such as oligopolistic markets and security domains. In Stackelberg games, one player, the leader, commits to a strategy and the follower makes their decision with knowledge of the leader’s commitment. Existing algorithms for Stackelberg games efficiently find optimal solutions (leader strategy), but they critically assume that the follower plays optimally. Unfortunately, in realworld applications, agents face human followers (adversaries) who — because of their bounded rationality and limited observation of the leader strategy — may deviate from their expected optimal response. Not taking into account these likely deviations when dealing with human adversaries can cause an unacceptable degradation in the leader’s reward,
Approximation methods for infinite bayesian Stackelberg games: modeling distributional uncertainty
 In AAMAS
, 2011
"... Game theory is fast becoming a vital tool for reasoning about complex realworld security problems, including critical infrastructure protection. The game models for these applications are constructed using expert analysis and historical data to estimate the values of key parameters, including the p ..."
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Cited by 16 (10 self)
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Game theory is fast becoming a vital tool for reasoning about complex realworld security problems, including critical infrastructure protection. The game models for these applications are constructed using expert analysis and historical data to estimate the values of key parameters, including the preferences and capabilities of terrorists. In many cases, it would be natural to represent uncertainty over these parameters using continuous distributions (such as uniform intervals or Gaussians). However, existing solution algorithms are limited to considering a small, finite number of possible attacker types with different payoffs. We introduce a general model of infinite Bayesian Stackelberg security games that allows payoffs to be represented using continuous payoff distributions. We then develop several techniques for finding approximate solutions for this class of games, and show empirically that our methods offer dramatic improvements over the current state of the art, providing new ways to improve the robustness of security game models.
Robust Solutions to Stackelberg Games: Addressing Bounded Rationality and Limited Observations in Human
"... How do we build algorithms for agent interactions with human adversaries? Stackelberg games are natural models for many important applications that involve human interaction, such as oligopolistic markets and security domains. In Stackelberg games, one player, the leader, commits to a strategy and t ..."
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Cited by 14 (13 self)
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How do we build algorithms for agent interactions with human adversaries? Stackelberg games are natural models for many important applications that involve human interaction, such as oligopolistic markets and security domains. In Stackelberg games, one player, the leader, commits to a strategy and the follower makes her decision with knowledge of the leader’s commitment. Existing algorithms for Stackelberg games efficiently find optimal solutions (leader strategy), but they critically assume that the follower plays optimally. Unfortunately, in many applications, agents face human followers (adversaries) who — because of their bounded rationality and limited observation of the leader strategy — may deviate from their expected optimal response. In other words, human adversaries ’ decisions are biased due to their bounded rationality and limited observations. Not taking into account these likely deviations when dealing with human adversaries may cause an unacceptable degradation in the leader’s reward, particularly in security applications where these algorithms have seen deployment. The objective
Riskaverse strategies for security games with execution and observational uncertainty
 In AAAI
, 2011
"... Attackerdefender Stackelberg games have become a popular gametheoretic approach for security with deployments for LAX Police, the FAMS and the TSA. Unfortunately, most of the existing solution approaches do not model two key uncertainties of the realworld: there may be noise in the defender’s exe ..."
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Cited by 12 (11 self)
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Attackerdefender Stackelberg games have become a popular gametheoretic approach for security with deployments for LAX Police, the FAMS and the TSA. Unfortunately, most of the existing solution approaches do not model two key uncertainties of the realworld: there may be noise in the defender’s execution of the suggested mixed strategy and/or the observations made by an attacker can be noisy. In this paper, we provide a framework to model these uncertainties, and demonstrate that previous strategies perform poorly in such uncertain settings. We also provide RECON, a novel algorithm that computes strategies for the defender that are robust to such uncertainties, and provide heuristics that further improve RECON’s efficiency.
Iterated Regret Minimization: A New Solution Concept
"... For some wellknown games, such as the Traveler’s Dilemma or the Centipede Game, traditional gametheoretic solution concepts—most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret minimization, which ex ..."
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Cited by 10 (1 self)
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For some wellknown games, such as the Traveler’s Dilemma or the Centipede Game, traditional gametheoretic solution concepts—most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret minimization, which exhibits the same qualitative behavior as that observed in experiments in many games of interest, including Traveler’s Dilemma, the Centipede Game, Nash bargaining, and Bertrand competition. As the name suggests, iterated regret minimization involves the iterated deletion of strategies that do not minimize regret. 1
Mediators in Position Auctions ∗
, 2008
"... A mediator is a reliable entity which plays on behalf of the players who give her the right of play. The mediator is guaranteed to behave in a prespecified way based on messages received from the agents. However, a mediator cannot enforce behavior; that is, agents can play in the game directly with ..."
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Cited by 10 (3 self)
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A mediator is a reliable entity which plays on behalf of the players who give her the right of play. The mediator is guaranteed to behave in a prespecified way based on messages received from the agents. However, a mediator cannot enforce behavior; that is, agents can play in the game directly without the mediator’s help. A mediator generates a new game for the players, the mediated game. The outcome in the original game of an equilibrium in the mediated game is called a mediated equilibrium. Monderer and Tennenholtz introduced a theory of mediators for games with complete information. We extend the theory of mediators to games with incomplete information, and use the new theory to study position auctions, a central topic in practical and theoretical electronic commerce. We provide a minimal set of conditions on position auctions, which is sufficient to guarantee that the VCG outcome function is a mediated equilibrium in these auctions.
Wardrop equilibria with riskaverse users
 Transportation Science
, 2010
"... Network games can be used to model competitive situations in which agents select routes to minimize their cost. Common applications include traffic, telecommunication, and distribution networks. Although traditional network models have assumed that realized costs only depend on congestion, in most a ..."
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Cited by 5 (0 self)
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Network games can be used to model competitive situations in which agents select routes to minimize their cost. Common applications include traffic, telecommunication, and distribution networks. Although traditional network models have assumed that realized costs only depend on congestion, in most applications they also have an uncertain component. We extend the traffic assignment problem first proposed by Wardrop in 1952 by adding random deviations, which are independent of the flow, to the cost functions that model congestion in each arc. We map these uncertainties into a Wardrop equilibrium model with nonadditive path costs. The cost on a path is given by the sum of the congestion on its arcs plus a constant safety margin that represents the agents ’ risk aversion. First, we prove that an equilibrium for this game always exists and is essentially unique. Then, we introduce three specific equilibrium models that fall within this framework: the percentile equilibrium where agents select paths that minimize a specified percentile of the uncertain cost; the addedvariability equilibrium where agents add a multiple of the variability of the cost of each arc to the expected cost; and the robust equilibrium where agents select paths by solving a robust optimization problem that imposes a limit on the number of arcs that can deviate from the mean. The percentile equilibrium is difficult to compute because minimizing a percentile among all paths is computationally hard. Instead, the addedvariability and robust Wardrop equilibria can be computed efficiently in practice: The former reduces to a standard Wardrop
ROBUST WARDROP EQUILIBRIUM
"... Abstract. Network games can be used to model competitive situations in which players select routes to maximize their utility. Common applications include traffic, telecommunication and distribution networks. Although traditional network models have assumed that utilities only depend on congestion, i ..."
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Cited by 4 (0 self)
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Abstract. Network games can be used to model competitive situations in which players select routes to maximize their utility. Common applications include traffic, telecommunication and distribution networks. Although traditional network models have assumed that utilities only depend on congestion, in most applications they also have an uncertain component. In this work, we extend Wardrop’s network game (1952) by explicitly incorporating uncertainty in the utility functions. Players are utility maximizers and select their route by solving a robust optimization problem, which takes the uncertainty into account. We define a robust Wardrop equilibrium as a solution under which all players are assigned to an optimal solution to their robust problems. Such a solution always exists and can be computed through efficient column generation methods. We show through a computational study that a robust Wardrop equilibrium tends to be more fair than the classic Wardrop equilibrium which ignores the uncertainty. Hence, a robust Wardrop equilibrium is more stable than the nominal counterpart as it reduces the regret that players experience after the uncertainty is revealed. 1.
TwoTerminal Routing Games with Unknown Active Players
 Artificial Intelligence Journal
"... Abstract. We analyze 2terminal routing games with linear cost functions and with unknown number of active players. We deal with both splittable and unsplittable models. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in many cases every play ..."
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Cited by 4 (2 self)
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Abstract. We analyze 2terminal routing games with linear cost functions and with unknown number of active players. We deal with both splittable and unsplittable models. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in many cases every player benefits from the common ignorance about the number of players. Furthermore, we prove new theorems on existence and uniqueness of equilibrium in 2terminal convex routing games with complete information. 1