Solving Cooperative Reliability Games

Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the reliability extension, each agent only "survives" with a certain probability, and a coalition's value is the probability that its surviving members would be a winning coalition in the base game. We study prominent solution concepts in such games, showing how to approximate the Shapley value and how to compute the core in games with few agent types. We also show that applying the reliability extension may stabilize the game, making the core non-empty even when the base game has an empty core.

[1]  Sanjeev Goyal,et al.  Network Formation with Heterogeneous Players , 2002, Games Econ. Behav..

[2]  J. Scott Provan,et al.  The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..

[3]  Jörg Rothe,et al.  The Cost of Stability in Coalitional Games , 2009, SAGT.

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

[5]  Evangelos Markakis,et al.  Approximating power indices: theoretical and empirical analysis , 2010, Autonomous Agents and Multi-Agent Systems.

[6]  Jeffrey S. Rosenschein,et al.  The Cost of Stability in Network Flow Games , 2009, MFCS.

[7]  Xiaotie Deng,et al.  On the Complexity of Cooperative Solution Concepts , 1994, Math. Oper. Res..

[8]  Rahul Savani,et al.  Power Indices in Spanning Connectivity Games , 2009, AAIM.

[9]  Jeffrey S. Rosenschein,et al.  Power in threshold network flow games , 2009, Autonomous Agents and Multi-Agent Systems.

[10]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[11]  Vincent Conitzer,et al.  Computing Shapley Values, Manipulating Value Division Schemes, and Checking Core Membership in Multi-Issue Domains , 2004, AAAI.

[12]  L. Shapley.  Cores of convex games , 1971 .

[13]  Ely Porat,et al.  Power and stability in connectivity games , 2008, AAMAS.

[14]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[15]  J. M. Bilbao,et al.  Cooperative Games on Combinatorial Structures , 2000 .

[16]  Vincent Conitzer,et al.  Complexity of determining nonemptiness of the core , 2003, EC '03.

[17]  A. Rubinstein,et al.  A Course in Game Theory , 1995 .

[18]  Matthias Thimm,et al.  Measuring Inconsistency in Probabilistic Knowledge Bases , 2009, UAI.

[19]  Nicholas R. Jennings,et al.  A randomized method for the shapley value for the voting game , 2007, AAMAS '07.

[20]  Vincent Conitzer,et al.  Prediction Markets, Mechanism Design, and Cooperative Game Theory , 2009, UAI.

[21]  Judith Timmer,et al.  On three Shapley-like solutions for cooperative games with random payoffs , 2004, Int. J. Game Theory.