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GraphicalGames

# GraphicalGames - Graphical Models for Game Theory...

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Graphical Models for Game Theory Undirected graph G capturing  local interactions Each player represented by a vertex N_i(G) = neighbors of i in G (includes i) Assume:  M_i( a ) expressible as M’_i( a’ ) over  only  N_i(G) Graphical game: (G,{M’_i}) Compact  representation of game Exponential in max  degree  (<< # of players) Ex’s: geography, organizational structure, networks Analogy to Bayes nets:  special structure 2 4 3 5 8 7 6 1
An Abstract Tree Algorithm Downstream Pass: Each node V receives  T(v,ui)  from  each Ui V computes T(w,v) and  witness  lists  for each T(w,v) = 1 Upstream Pass: V receives values (w,v) from W  s.t. T(w,v) = 1 V picks witness  u for T(w,v),  passes (v,ui) to Ui U1 U2 U3 W V T(w,v) = 1 <-->  5 an “upstream” Nash                       where V = v  given  W = w

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GraphicalGames - Graphical Models for Game Theory...

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