Abstract
The thesis focuses on cooperative games with transferable utility and incorporates two topics: Solutions for TU-games with restricted coalition formation and the stability of the grand coalition.
Chapters 3 is devoted to a new solution for cooperative games with coalition structures, called the α-egalitarian Owen value, and this coalitional value is characterized by three approaches. Firstly, we provide two axiomatizations by introducing the α-indemnificatory null player axiom, and the (intra) coalitional quasi-balanced contributions axiom. Secondly, we characterize the coalitional value by introducing an α-guarantee potential function. Finally, the coalitional value is implemented by a punishment-reward bidding mechanism.
In Chapter 4, we continue to work with TU-games restricted by coalition structures and propose a coalitional value called the two-step Shapley-solidarity value. A procedural interpretation is provided for this coalitional value, and we introduce a new axiom called the coalitional A-null player axiom to axiomatize the value based on additivity. Moreover, two other axiomatizations on the basis of quasi-balanced contributions for the grand coalition are also provided.
In Chapter 5, we focus on cooperative games with communication structures and provide efficient extensions of the Myerson value (Myerson, 1977). The idea lies in introducing the Shapley payoffs of the underlying game as players' claims to derive a graph-induced bankruptcy problem. Then, two efficient extensions of the Myerson value are achieved through bankruptcy rules, including the CEA rule and the CEL rule (Aumann & Maschler, 1985).
Moreover, corresponding axiomatizations are also provided.
Chapter 6 proceeds with studying the stability of the grand coalition for cost TU-games by addressing an optimization problem to maximize the total shareable cost over what we called the almost core. We analyze the computational complexity of this optimization problem, in relation to the computational complexity of related problems for the core. In particular, we consider a special class of games, i.e., the minimum cost spanning tree games. We show that maximizing the total shareable costs over the (non-negative) almost core is NP-hard for mcst games, and we provide a tight 2-approximation algorithm for this almost core optimization problem with the additional non-negative constraint.
Chapters 3 is devoted to a new solution for cooperative games with coalition structures, called the α-egalitarian Owen value, and this coalitional value is characterized by three approaches. Firstly, we provide two axiomatizations by introducing the α-indemnificatory null player axiom, and the (intra) coalitional quasi-balanced contributions axiom. Secondly, we characterize the coalitional value by introducing an α-guarantee potential function. Finally, the coalitional value is implemented by a punishment-reward bidding mechanism.
In Chapter 4, we continue to work with TU-games restricted by coalition structures and propose a coalitional value called the two-step Shapley-solidarity value. A procedural interpretation is provided for this coalitional value, and we introduce a new axiom called the coalitional A-null player axiom to axiomatize the value based on additivity. Moreover, two other axiomatizations on the basis of quasi-balanced contributions for the grand coalition are also provided.
In Chapter 5, we focus on cooperative games with communication structures and provide efficient extensions of the Myerson value (Myerson, 1977). The idea lies in introducing the Shapley payoffs of the underlying game as players' claims to derive a graph-induced bankruptcy problem. Then, two efficient extensions of the Myerson value are achieved through bankruptcy rules, including the CEA rule and the CEL rule (Aumann & Maschler, 1985).
Moreover, corresponding axiomatizations are also provided.
Chapter 6 proceeds with studying the stability of the grand coalition for cost TU-games by addressing an optimization problem to maximize the total shareable cost over what we called the almost core. We analyze the computational complexity of this optimization problem, in relation to the computational complexity of related problems for the core. In particular, we consider a special class of games, i.e., the minimum cost spanning tree games. We show that maximizing the total shareable costs over the (non-negative) almost core is NP-hard for mcst games, and we provide a tight 2-approximation algorithm for this almost core optimization problem with the additional non-negative constraint.
| Original language | English |
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| Qualification | Doctor of Philosophy |
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| Supervisors/Advisors |
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| Award date | 3 Mar 2023 |
| Place of Publication | Enschede |
| Publisher | |
| Print ISBNs | 978-90-365-5530-2 |
| Electronic ISBNs | 978-90-365-5531-9 |
| DOIs | |
| Publication status | Published - 3 Mar 2023 |