Game theory has an elegant way of modeling structural aspects of social games. The predicted outc... more Game theory has an elegant way of modeling structural aspects of social games. The predicted outcome of the social games holds as long as “the rules of the game” are kept. Therefore, a game authority (which enforces the “rules”) is required. We present the first design for such a game authority, where the game authority is a middleware of distributed systems. The middleware restricts the agents to “play by the rules”, and excludes agents that do not obey the (selfish) rules of the game since we consider them as Byzantine. We base our design on a self-stabilizing Byzantine agreement that allows processors to audit each other’s actions. We show that when the agents are restricted to act selfishly resource allocation can become asymptotically optimal (according to our performance criteria, which is: multi-round anarchy cost). Our design also includes services that allow owners to share a collaborative effort for coalition optimization using group-preplay negotiation. Since there are no...
ABSTRACT In this work we present a simple quadratic formulation for the problem of computing Nash... more ABSTRACT In this work we present a simple quadratic formulation for the problem of computing Nash equilibria in symmetric bimatrix games, inspired by the well-known formulation of Mangasarian and Stone [26]. We exploit our formulation to shed light to the approximability of NE points. First we observe that any KKT point of this formulation (and indeed, any quadratic program) is also a stationary point, and vice versa. We then prove that any KKT point of the proposed formulation (is not necessarily itself, but) indicates a ( -\left(NE point, which is polynomially tractable, given as input the KKT point. We continue by proposing an algorithm for constructing an (\frac13+d)-\left(\frac{1}{3}+\delta\right)-NE point for any δ > 0, in time polynomial in the size of the game and quasi-linear in \frac1d\frac{1}{\delta}, exploiting Ye’s algorithm for approximating KKT points of QPs [34]. This is (to our knowledge) the first polynomial time algorithm that constructs ε −NE points for symmetric bimatrix games for any ε close to \frac13\frac{1}{3}. We extend our main result to (asymmetric) win lose games, as well as to games with maximum aggregate payoff either at most 1, or at least \frac53\frac{5}{3}. To achieve this, we use a generalization of the Brown & von Neumann symmetrization technique [6] to the case of non-zero-sum games, which we prove that is approximation preserving. Finally, we present our experimental analysis of the proposed approximation and other quite interesting approximations for NE points in symmetric bimatrix games.
A brief survey on the most recent results concerning the simulation of PRAMs on DMMs is presented... more A brief survey on the most recent results concerning the simulation of PRAMs on DMMs is presented, along with the design of a Shared Memory Simulator (SMS) that is based on a distributed environment provided by many realistic architectures, based on the DMM model. The Shared Memory Simulation Frame (SMS-Frame) will give the opportunity of executing parallel algorithms designed for a variant of PRAM, over a purely distributed working environment, that will be c onsidered to comply with the DMM model. The reason why the models of PRAM and DMM have been chosen, is that t he former has proved to be the most popular cost model i n the parallel algorithms community, while the latter is an abstracted model based on message passing, that is very close to, or is provided through specialized interfaces by the majority of the vendors of parallel machines.
Game theory has an elegant way of modeling structural aspects of social games. The predicted outc... more Game theory has an elegant way of modeling structural aspects of social games. The predicted outcome of the social games holds as long as “the rules of the game” are kept. Therefore, a game authority (which enforces the “rules”) is required. We present the first design for such a game authority, where the game authority is a middleware of distributed systems. The middleware restricts the agents to “play by the rules”, and excludes agents that do not obey the (selfish) rules of the game since we consider them as Byzantine. We base our design on a self-stabilizing Byzantine agreement that allows processors to audit each other’s actions. We show that when the agents are restricted to act selfishly resource allocation can become asymptotically optimal (according to our performance criteria, which is: multi-round anarchy cost). Our design also includes services that allow owners to share a collaborative effort for coalition optimization using group-preplay negotiation. Since there are no...
ABSTRACT In this work we present a simple quadratic formulation for the problem of computing Nash... more ABSTRACT In this work we present a simple quadratic formulation for the problem of computing Nash equilibria in symmetric bimatrix games, inspired by the well-known formulation of Mangasarian and Stone [26]. We exploit our formulation to shed light to the approximability of NE points. First we observe that any KKT point of this formulation (and indeed, any quadratic program) is also a stationary point, and vice versa. We then prove that any KKT point of the proposed formulation (is not necessarily itself, but) indicates a ( -\left(NE point, which is polynomially tractable, given as input the KKT point. We continue by proposing an algorithm for constructing an (\frac13+d)-\left(\frac{1}{3}+\delta\right)-NE point for any δ > 0, in time polynomial in the size of the game and quasi-linear in \frac1d\frac{1}{\delta}, exploiting Ye’s algorithm for approximating KKT points of QPs [34]. This is (to our knowledge) the first polynomial time algorithm that constructs ε −NE points for symmetric bimatrix games for any ε close to \frac13\frac{1}{3}. We extend our main result to (asymmetric) win lose games, as well as to games with maximum aggregate payoff either at most 1, or at least \frac53\frac{5}{3}. To achieve this, we use a generalization of the Brown & von Neumann symmetrization technique [6] to the case of non-zero-sum games, which we prove that is approximation preserving. Finally, we present our experimental analysis of the proposed approximation and other quite interesting approximations for NE points in symmetric bimatrix games.
A brief survey on the most recent results concerning the simulation of PRAMs on DMMs is presented... more A brief survey on the most recent results concerning the simulation of PRAMs on DMMs is presented, along with the design of a Shared Memory Simulator (SMS) that is based on a distributed environment provided by many realistic architectures, based on the DMM model. The Shared Memory Simulation Frame (SMS-Frame) will give the opportunity of executing parallel algorithms designed for a variant of PRAM, over a purely distributed working environment, that will be c onsidered to comply with the DMM model. The reason why the models of PRAM and DMM have been chosen, is that t he former has proved to be the most popular cost model i n the parallel algorithms community, while the latter is an abstracted model based on message passing, that is very close to, or is provided through specialized interfaces by the majority of the vendors of parallel machines.
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