Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms

In the context of minimum cost spanning tree problems, we present a bargaining mechanism for connecting all agents to the source and dividing the cost among them. The basic idea is very simple: we ask each agent the part of the cost he is willing to pay for an arc to be constructed. We prove that there exists a unique payoff allocation associated with the subgame perfect Nash equilibria of this bargaining mechanism. Moreover, this payoff allocation coincides with the rule defined in Bergantinos and Vidal-Puga [Bergantinos, G., Vidal-Puga, J.J., 2007a. A fair rule in minimum cost spanning tree problems. Journal of Economic Theory 137, 326-352].

[1]  Gustavo Bergantiños,et al.  Additivity in minimum cost spanning tree problems , 2009 .

[2]  Gustavo Bergantiños,et al.  A fair rule in minimum cost spanning tree problems , 2007, J. Econ. Theory.

[3]  Henk Norde,et al.  The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations , 2003 .

[4]  Gustavo Bergantiños,et al.  Optimal Equilibria in the Non-Cooperative Game Associated with Cost Spanning Tree Problems , 2005, Ann. Oper. Res..

[5]  Shigeo Muto,et al.  Bird's tree allocations revisited , 2000 .

[6]  Gustavo Bergantiños,et al.  An implementation of the Owen value , 2003, Games Econ. Behav..

[7]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[8]  Fioravante Patrone,et al.  Game Practice : Contributions from Applied Game Theory , 2000 .

[9]  David Wettstein,et al.  1 CHOOSING WISELY : A MULTI-BIDDING APPROACH , 2022 .

[10]  Anirban Kar,et al.  Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games , 2002, Games Econ. Behav..

[11]  Gustavo Bergantiños,et al.  Noncooperative cost spanning tree games with budget restrictions , 2008 .

[12]  Vincent Feltkamp,et al.  On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems , 1994 .

[13]  Marco Slikker.  Bidding for surplus in network allocation problems , 2007, J. Econ. Theory.

[14]  Gustavo Bergantiños,et al.  A non-cooperative approach to the cost spanning tree problem , 2004, Math. Methods Oper. Res..

[15]  David Wettstein,et al.  Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value , 2001, J. Econ. Theory.

[16]  Juan José Vidal Puga,et al.  The optimistic TU game in minimum cost spanning tree problems , 2007 .

[17]  Anirban Kar,et al.  Cost monotonicity, consistency and minimum cost spanning tree games , 2004, Games Econ. Behav..

[18]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[19]  Yuan Ju,et al.  Implementing cooperative solution concepts: a generalized bidding approach , 2006 .

[20]  C. G. Bird,et al.  On cost allocation for a spanning tree: A game theoretic approach , 1976, Networks.

[21]  L. Shapley.  A Value for n-person Games , 1988 .

[22]  David Wettstein,et al.  Choosing Wisely: A Multibidding Approach , 2002 .

[23]  Eyal Winter,et al.  Subscription Mechanisms for Network Formation , 2002, J. Econ. Theory.

[24]  J. Nash.  Two-Person Cooperative Games , 1953 .