Contributions to Game Theory and Management
We investigate the prenucleolus, the anti-prenucleolus and the SM-nucleolus in glove market games and weighted majority games. This kind of games looks desirable for considering solution concepts taking into account the blocking power of a coalition S with different weights. Analytical formulae for calculating the solutions are presented for glove market game. Influence of the blocking power on players' payoffs is discussed and the examples which demonstrate similarities and differences comparing with other solution concepts are given
Supposing that Player 1’s computational power is higher than that of Player 2, we give three examples of different kinds of public signal about the state of a two-person zero-sum game with symmetric incom- plete information on both sides (both players do not know the state of the game) where Player 1 due to his computational power learns the state of the game meanwhile it is impossible for Player 2. That is, the game with incomplete information on both sides becomes a game with incomplete information on the side of Player 2. Thus we demonstrate that information about the state of a game may appear not only due to a private signal but as a result of a public signal and asymmetric computational resources of players.