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On the Verification and Computation of Strong Nash Equilibrium
"... Computing equilibria of games is a central task in computer science. A large number of results are known for Nash equilibrium (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form coalitions, NE is inadequate and an appropriate solution concept is st ..."
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Cited by 4 (3 self)
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Computing equilibria of games is a central task in computer science. A large number of results are known for Nash equilibrium (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form coalitions, NE is inadequate and an appropriate solution concept is strong Nash equilibrium (SNE). Few computational results are known about SNE. In this paper, we first study the problem of verifying whether a strategy profile is an SNE, showing that the problem is inP. We then design a spatial branch–and–bound algorithm to find an SNE, and we experimentally evaluate the algorithm.
Equilibria in Load Balancing Games
 Acta Mathematicae Applicatae Sinica(English Series
"... Abstract A Nash equilibrium (NE) in a multiagent game is a strategy profile that is resilient to unilateral deviations. A strong Nash equilibrium (SE) is one that is stable against coordinated deviations of any coalition. We show that, in the load balancing games, NEs approximate SEs in the sense ..."
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Abstract A Nash equilibrium (NE) in a multiagent game is a strategy profile that is resilient to unilateral deviations. A strong Nash equilibrium (SE) is one that is stable against coordinated deviations of any coalition. We show that, in the load balancing games, NEs approximate SEs in the sense that the benefit of each member of any coalition from coordinated deviations is well limited. Furthermore, we show that an easily recognizable special subset of NEs exhibit even better approximation of SEs.
Equilibria for two parallel links: The strong price of anarchy versus the price of anarchy
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"... Abstract Bottleneck congestion games properly model the properties of many realworld network routing applications. They are known to possess strong equilibriaa strengthening of Nash equilibrium to resilience against coalitional deviations. In this paper, we study the computational complexity of pu ..."
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Abstract Bottleneck congestion games properly model the properties of many realworld network routing applications. They are known to possess strong equilibriaa strengthening of Nash equilibrium to resilience against coalitional deviations. In this paper, we study the computational complexity of pure Nash and strong equilibria in these games. We provide a generic centralized algorithm to compute strong equilibria, which has polynomial running time for many interesting classes of games such as, e.g., matroid or singlecommodity bottleneck congestion games. In addition, we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics. Using unilateral improvement dynamics in matroid games pure Nash equilibria can be reached efficiently. In contrast, computing even a single coalitional improvement move in matroid and singlecommodity games is strongly NPhard. In addition, we establish a variety of hardness results and lower bounds regarding the
Approximate Equilibrium and Incentivizing Social Coordination
, 2014
"... We study techniques to incentivize selfinterested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic preferences but they stand to gain if others choose the same ..."
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We study techniques to incentivize selfinterested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic preferences but they stand to gain if others choose the same strategy as them. For nontrivial versions of our game, stable solutions like Nash Equilibrium may not exist, or may be socially inefficient even when they do exist. This motivates us to focus on designing efficient algorithms to compute (almost) stable solutions like Approximate Equilibrium that can be realized if agents are provided some additional incentives. Our results apply in many settings like adoption of new products, project selection, and group formation, where a central authority can direct agents towards a strategy but agents may defect if they have better alternatives. We show that for any given instance, we can either compute a high quality approximate equilibrium or a nearoptimal solution that can be stabilized by providing small payments to some players. We then generalize our model to encompass situations where player relationships may exhibit complementarities and present an algorithm to compute an Approximate Equilibrium whose stability factor is linear in the degree of complementarity. Our results imply that a little influence is necessary in order to ensure that selfish players coordinate and form socially efficient solutions.
Fully Mixed Nash Equilibria for the Load Balancing Games on Uniform Parallel Machines
, 2010
"... In this paper, we consider the load balancing games on uniform parallel machines with speeds s1 = s2 = · · · = sm−1 = 1 and sm = s> 0, discuss the existence of the fully mixed Nash equilibrium. We derive the function of each task’s strategy profile, and show that the fully mixed Nash equilibr ..."
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In this paper, we consider the load balancing games on uniform parallel machines with speeds s1 = s2 = · · · = sm−1 = 1 and sm = s> 0, discuss the existence of the fully mixed Nash equilibrium. We derive the function of each task’s strategy profile, and show that the fully mixed Nash equilibrium is unique if it exists.
Strong Stability of Nash Equilibria in Load Balancing Games
, 2013
"... We study strong stability of Nash equilibria in load balancing games of m (m ≥ 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the workload of the server it chooses. A Nash equilibrium (NE) is a strategy profile that is resilie ..."
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We study strong stability of Nash equilibria in load balancing games of m (m ≥ 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the workload of the server it chooses. A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an NE approximates an SNE. Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the preand postdeviation costs. An NE is said to be a ρapproximate SNE (ρ ≥ 1) if there is no coalition of jobs such that each job of the coalition will have an IR more than ρ from coordinated deviations of the coalition. While it is already known that NEs are the same as SNEs in the 2server load balancing game, we prove that, in the mserver load balancing game for any given m ≥ 3, any NE is a (5/4)approximate SNE, which together with the lower bound already established in the literature yields a tight approximation bound. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in load balancing games. To establish our upper bound, we make a novel use of a graphtheoretic tool.