Harsanyi Solutions in Line-graph Games - René van den Brink; Gerard van der Laan; Valeri Vasil'ev (Tinbergen Institute, 2003)
Recently, applications of cooperative game theory to economicallocation problems have gained popularity. To understandthese applications better, economic theory studies thesimilarities and differences between them. The purpose of thispaper is to investigate a special class of cooperative gamesthat generalizes some recent economic applications with asimilar structure. These are so-called line-graph games beingcooperative TU-games in which the players are linearly ordered.Examples of situations that can be modeled like this aresequencing situations, water distribution situations andpolitical majority voting.The main question in cooperative game models of economicsituations is how to allocate the earnings of coalitions amongthe players. We apply the concept of Harsanyi solution toline-graph games. We define four properties that each selectsa unique Harsanyi solution from the class of all Harsanyisolutions. One of these solutions is the well-known Shapleyvalue which is widely applied in economic models. We applythese solutions to the economic situations mentioned above.
Keywords: C71; 330; TU-game; Harsanyi dividends; Shapley value; sharing system; Harsanyi solution; line-graph game.; Kooperatives Spiel; Transferable Utility Games