Chih Chang

A non-cooperative interpretation of the f-just rules of bankruptcy problems

First, we propose an axiomatic characterization of the f-just rules. Second, based on the result, a game is designed and a non-cooperative interpretation of the f-just rules is provided.

Reduced game and converse consistency

Abstract The initiating points of the current paper are the axiomatic characterizations, in terms of consistency, of the equal allocation of nonseparable cost value (by Moulin), the Shapley value (by Hart and Mas-Colell), and the prenucleolus (by Orshan). The basic axioms are the same, but three different reduced games can be used to distinguish these three solutions. The main purpose of the paper is to illustrate that besides the definitions of reduced games are different, the axiom converse consistency also plays an important role to distinguish these three solutions.

The Harsanyi-Shapley solution and independence of irrelevant expansions

We characterize the Harsanyi-Shapley solution/value on essential and smooth games. An axiom – independence of irrelevant expansions of NTU games is introduced.

Closedness under Hart-Mas Colell reduction

Abstract. We will find 3 maximal subclasses with respect to essential, superadditive and convex games, respectively such that a game is in one subclass, so are its reduced games.

Bisection property of the kernel

Maschler, Peleg and Shapley make use of the bisection property of the kernel to provide an interpretation of the kernel for n-person game with grand coalition. We develop the similar results for any n-person game with coalition structure.

On the coincidence property

The collection of the coalitions b is balanced if the Shapley value of the simple game [chi]b is 0. This observation makes us able to derive a class of simple games with the coincidence property, that is, the Shapley value and the nucleolus coincide. And then we use such a class of simple games as generators to construct coincidence regions, convex cones consisting of games with the coincidence property. We will first propose the SP region. Two sets of games satisfying the coincidence property are introduced. Both are SP regions. In fact, the SP regions do not cover all games satisfying the coincidence property even for 3-person case. To enlarge the class of games with the coincidence property, the ST regions are proposed. All 3-person games with the coincidence property can be classified into 4 ST regions.

A non-cooperative interpretation of the kernel

The purpose of the paper is to propose a bargaining game to interpret the kernel non-cooperatively. Based on the idea of the Davis-Maschler reduced game, a bilateral bargaining procedure is provided in our game model. We show that the set of all subgame perfect equilibrium outcomes of our non-cooperative game coincides with the kernel for transferable utility games.

A Note on the von Neumann-Morgenstern Solution [Cooperative Games with Coalition Structures]

Aumann and Dreze claimed that the von Neumann-Morgenstern solution has the reduced game property. In this note, we will give a counterexample that the von Neumann-Morgenstern solution does not have the property.

Some results related to the Harsanyi-Shapley solution

Abstract. The main result of the paper is to characterize the Harsanyi-Shapley solution on a specific class of NTU games by reduced game property.

The kernel, the bargaining set and the reduced game

We present an example showing that forxεK(N, v, B) the section ofK(N, v, B) atx|N-Bk may be a proper subset ofK(Bk, vx, Xk). Further we prove that under appropriate conditions these two sets coincide. For the bargaining set we prove a similar result.