scholarly journals Coordination Games on Weighted Directed Graphs

2021 ◽  
Author(s):  
Krzysztof R. Apt ◽  
Sunil Simon ◽  
Dominik Wojtczak
Keyword(s):  
Nash Equilibrium ◽  
Directed Graphs ◽  
Local Area ◽  
Coordination Games ◽  
Strong Equilibrium ◽  
Polymatrix Games ◽  
Token Ring ◽  
Network Topologies ◽  
Ring Protection ◽  
Natural Classes

We study strategic games on weighted directed graphs, where each player’s payoff is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed nonnegative integer bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. We identify natural classes of graphs for which finite improvement or coalition-improvement paths of polynomial length always exist, and consequently a (pure) Nash equilibrium or a strong equilibrium can be found in polynomial time. The considered classes of graphs are typical in network topologies: simple cycles correspond to the token ring local area networks, whereas open chains of simple cycles correspond to multiple independent rings topology from the recommendation G.8032v2 on Ethernet ring protection switching. For simple cycles, these results are optimal in the sense that without the imposed conditions on the weights and bonuses, a Nash equilibrium may not even exist. Finally, we prove that determining the existence of a Nash equilibrium or of a strong equilibrium is NP-complete already for unweighted graphs, with no bonuses assumed. This implies that the same problems for polymatrix games are strongly NP-hard.

Self-testing the 16-Mbps adapter chip for the IBM token-ring local area network

1990 ◽  
Vol 34 (2.3) ◽  
pp. 416-427
Author(s):  
S. F. Oakland ◽  
J. L. Corr ◽  
J. D. Blair ◽  
R. D. Norman ◽  
W. J. DeGuise
Keyword(s):  
Local Area Network ◽  
Local Area ◽  
Area Network ◽  
Self Testing ◽  
Token Ring

scholarly journals HeNCE: A Heterogeneous Network Computing Environment

1994 ◽  
Vol 3 (1) ◽  
pp. 49-60 ◽  
Author(s):  
Adam Beguelin ◽  
Jack J. Dongarra ◽  
George Al Geist ◽  
Robert Manchek ◽  
Keith Moore
Keyword(s):  
Heterogeneous Network ◽  
Local Area Network ◽  
Directed Graphs ◽  
Local Area ◽  
Control Flow ◽  
Future Research ◽  
Area Network ◽  
Network Computing ◽  
Computing Environment ◽  
Data Dependencies

Network computing seeks to utilize the aggregate resources of many networked computers to solve a single problem. In so doing it is often possible to obtain supercomputer performance from an inexpensive local area network. The drawback is that network computing is complicated and error prone when done by hand, especially if the computers have different operating systems and data formats and are thus heterogeneous. The heterogeneous network computing environment (HeNCE) is an integrated graphical environment for creating and running parallel programs over a heterogeneous collection of computers. It is built on a lower level package called parallel virtual machine (PVM). The HeNCE philosophy of parallel programming is to have the programmer graphically specify the parallelism of a computation and to automate, as much as possible, the tasks of writing, compiling, executing, debugging, and tracing the network computation. Key to HeNCE is a graphical language based on directed graphs that describe the parallelism and data dependencies of an application. Nodes in the graphs represent conventional Fortran or C subroutines and the arcs represent data and control flow. This article describes the present state of HeNCE, its capabilities, limitations, and areas of future research.

Simple token ring local area network

1984 ◽  
Vol 8 (4) ◽  
pp. 171-176 ◽  
Author(s):  
David Hutchison ◽  
David Coffield
Keyword(s):  
Local Area Network ◽  
Local Area ◽  
Area Network ◽  
Token Ring

scholarly journals On Sparse Discretization for Graphical Games

2020 ◽  
Vol 69 ◽  
pp. 67-84
Author(s):  
Luis Ortiz
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Sufficient Conditions ◽  
Research Note ◽  
Graphical Games ◽  
Approximate Nash Equilibrium ◽  
Approximate Nash Equilibria ◽  
Polymatrix Games ◽  
The Impact ◽  
Game Representation

Graphical games are one of the earliest examples of the impact that the general field of graphical models have had in other areas, and in this particular case, in classical mathematical models in game theory. Graphical multi-hypermatrix games, a concept formally introduced in this research note, generalize graphical games while allowing the possibility of further space savings in model representation to that of standard graphical games. The main focus of this research note is discretization schemes for computing approximate Nash equilibria, with emphasis on graphical games, but also briefly touching on normal-form and polymatrix games. The main technical contribution is a theorem that establishes sufficient conditions for a discretization of the players’ space of mixed strategies to contain an approximate Nash equilibrium. The result is actually stronger because every exact Nash equilibrium has a nearby approximate Nash equilibrium on the grid induced by the discretization. The sufficient conditions are weaker than those of previous results. In particular, a uniform discretization of size linear in the inverse of the approximation error and in the natural game-representation parameters suffices. The theorem holds for a generalization of graphical games, introduced here. The result has already been useful in the design and analysis of tractable algorithms for graphical games with parametric payoff functions and certain game-graph structures. For standard graphical games, under natural conditions, the discretization is logarithmic in the game-representation size, a substantial improvement over the linear dependency previously required. Combining the improved discretization result with old results on constraint networks in AI simplifies the derivation and analysis of algorithms for computing approximate Nash equilibria in graphical games.

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