  Within the context of games on networks S. Goyal (Goya (2007), pg. 39) posed
the following problem. Under any arbitrary but fixed topology, does there exist
at least one pure Nash equilibrium that exhibits a positive relation between
the cardinality of a player's set of neighbors and its utility payoff? In this
paper we present a class of topologies/games in which pure Nash equilibria with
the above property do not exist.
