Abstract
If there are more than two players in a game, then there is a potential for forming coalitions. The Core is the most prominent solution concept in this case. It assigns payoff vectors to the players. However, the Core of an n-person game can be empty or contain an infinite number of possible outcome vectors. In this chapter, applying the Core to a network game illustrates this problem. As a consequence, alternative solution concepts are briefly discussed: the Stable Set concept, proposed by von Neumannand Morgenstern, as the Solution; Bargaining Sets that are based on objections and (successful) counterobjections; the Kernel and the Nucleolus. Results are confronted with the problem of competition and cooperation in the triad.
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Notes
- 1.
If the game between S and N\S cannot be reduced to a zero-sum game, we differentiate between value \(v_{\upalpha} \left(\text{S} \right)\) that S may secure against resistance of coalition N\S, and value \(v_{\upbeta} \left(\text{S} \right)\) for S that coalition N\S cannot prevent, thus defining the \(\upalpha\)- and \(\upbeta\)-characteristic function.
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- 4.
Anyone wanting to see the details, please turn the book such that (0, 1000, 0) and thereafter (0, 0, 1000) is on top. The parallel restriction lines regarding the fees of communities 2 and 3 are easily recognized.
- 5.
The English translation “The Prince” reduces Machiavelli’s use of “Il Principe” to a certain extent; he calls the institution holding the power in the state “Principe,” irrespective of whether it is a monarchy, a tyranny or a republic. This becomes clear in his second main work: the “Discorsi.” It refers to the Roman Republic. Its subtitle is “Thoughts about Politics and Governing.” However, the following quotations are taken from “Il Principe.”
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Holler, M.J., Klose-Ullmann, B. (2020). More Than Two Players. In: Scissors and Rock. Springer, Cham. https://doi.org/10.1007/978-3-030-44823-3_11
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