Exercise 2: Games on graphs with numeric goals [2] Let o = (60, . ..,On) be a strong Nash equilibrium (SNE) if for every coalition of players C C N and every alternative joint strategy profile for C, denoted by o' = (ok, . . ., O'), with {k, . .., m} = C, we have u; (p()) 2 uj(p(6_c, 'c)) for every player j E C. That is, in an SNE no coalition of players, C, prefers a run different from the run p(o) induced by the strategy profile o, and therefore no deviations by coalitions of players are possible; since in a Nash equilibrium only single-player deviations are considered (that is, when [C) = 1), we have that for every game G, it is true that SNE(G) C NE(G), where SNE(G) denotes the set of strong Nash equilibria of a given game G. Using these definitions, your task in this exercise is to design a game on a graph with numeric goals such that the game has a non-empty set of Nash equilibria and an empty set of strong Nash equilibria, that is, a game G satisfying that SNE(G) = 0 and NE(G) # 0. Clearly indicate at least one Nash equilibrium of G which verifies that NE(G) # 0