Abstract
In an information graph situation, a finite set of agents and a source are the set of nodes of an undirected graph with the property that two adjacent nodes can share information at no cost. The source has some information (or technology), and agents in the same component as the source can reach this information for free. In other components, some agent must pay a unitary cost to obtain the information. We prove that the core of the derived information graph game is a von Neumann-Morgenstern stable set if and only if the information graph is cycle-complete, or equivalently if the game is concave. Otherwise, whether there always exists a stable set is an open question. If the information graph consists of a ring that contains the source, a stable set always exists and it is the core of a related situation where one edge has been deleted.
Highlights
In an information graph game, there is a finite set of agents that need to make use of information or some technology
This paper shows a characterization of the stability of the core of information graph games and when the graph is has a ring structure that contains the source of information, provides a stable set for this game that coincides with the core of a related information graph where one edge has been deleted
This fact resembles the situation of assignment games where some stable sets are obtained as the union of the cores of some subgames (Nunez and Rafels, 2013) and of patent licensing games in which some stable sets coincide with the core of some suitable defined reduced game (Hirai and Watanabe, 2018)
Summary
In an information graph game, there is a finite set of agents that need to make use of information or some technology. Let us assume there is another saturated information graph situation E that defines a cost game (N, C ) such that C(S) = C (S) for all S ⊆ N This implies that, for all k ∈ N , 0k ∈ E if and only if 0k ∈ E. No core allocation can dominate x because nodes in A are paying their minimal core payoff (or less, case of agent 1) and the others either cannot connect to the source at cost zero without them (nodes 5, 8 and 9) or cannot find it profitable to reach node 3 (node 4) We can generalize this idea to all cycle-complete saturated information graph games. The stable set A is the core of the information graph situation where edge 23 has been deleted and the stable set B is the core of the information graph situation where edge 13 has been deleted
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