Example graph topologies. 

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... the worst case of a complete graph, the size of the graphical game representation equals that of the normal-form representation. In Figure 1, we illustrate four graph topologies (borrowed from Ortiz & Kearns, 2003), capturing different kinds of locality of interaction among the agents. These are also the graph topologies on which we evaluate the performance of our algorithm. ...

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... are also the graph topologies on which we evaluate the performance of our algorithm. Figure 1a is a ring topology in which each agent has exactly two neigh- bors, Figure 1b is a grid topology, Figure 1c is an acyclic graph topology, and Figure 1d is a chordal graph in which a fraction of the edges are chords. Before presenting our PureProp algorithm we show how the locality of interactions in a graphical game reduces the computation required to compute the expected rewards of Equations (1) to (6) as follows. ...

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... are also the graph topologies on which we evaluate the performance of our algorithm. Figure 1a is a ring topology in which each agent has exactly two neigh- bors, Figure 1b is a grid topology, Figure 1c is an acyclic graph topology, and Figure 1d is a chordal graph in which a fraction of the edges are chords. Before presenting our PureProp algorithm we show how the locality of interactions in a graphical game reduces the computation required to compute the expected rewards of Equations (1) to (6) as follows. ...

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... are also the graph topologies on which we evaluate the performance of our algorithm. Figure 1a is a ring topology in which each agent has exactly two neigh- bors, Figure 1b is a grid topology, Figure 1c is an acyclic graph topology, and Figure 1d is a chordal graph in which a fraction of the edges are chords. Before presenting our PureProp algorithm we show how the locality of interactions in a graphical game reduces the computation required to compute the expected rewards of Equations (1) to (6) as follows. ...

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... are also the graph topologies on which we evaluate the performance of our algorithm. Figure 1a is a ring topology in which each agent has exactly two neigh- bors, Figure 1b is a grid topology, Figure 1c is an acyclic graph topology, and Figure 1d is a chordal graph in which a fraction of the edges are chords. Before presenting our PureProp algorithm we show how the locality of interactions in a graphical game reduces the computation required to compute the expected rewards of Equations (1) to (6) as follows. ...

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... used the τ -discretization idea described above to construct an -induced game and then used PureProp to compute approximate equilibria in party games for the fol- lowing neighborhood topologies (shown in Figure 1): (a) ring, (b) grid, (c) acyclic with a branching factor of 2 (i.e. each node has 3 neighbors), (d) chordal in which a tenth of the edges are chords, and chordal in which a fifth of the edges are chords. For each topology, we varied the number of players and measured the effect on the runtime of vari- ous phases of our algorithm. ...