Multipotential games

  • Authors:
  • Dov Monderer

  • Affiliations:
  • Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Haifa, Israel

  • Venue:
  • IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
  • Year:
  • 2007

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Abstract

We introduce and analyze q-potential games and q- congestion games, where q is a positive integer. A 1-potential (congestion) game is a potential (congestion) game. We show that a game is a q-potential game if and only if it is (up to an isomorphism) a q-congestion game. As a corollary, we derive the result that every game in strategic form is a q- congestion game for some q. It is further shown that every q-congestion game is isomorphic to a q- network game, where the network environment is defined by a directed graph with one origin and one destination. Finally we discuss our main agenda: The issue of representing q-congestion games with non-negative cost functions by congestion models with non-negative and monotonic facility cost functions. We provide some initial results in this regard.