On the coalition-proofness of the Pareto frontier of the set of Nash equilibria

This article shows that the Pareto efficient frontier of the Nash equilibri um set of games with strategic substitutes is coalition-proof under the fol lowing conditions: (1) the game has three players, or, alternatively, a pla yer's payoff depends on her own strategy and on the sum (but not on the com position) of other players' strategies; (2) an increase in a player's strat egy either raises all other players' payoffs monotonically or reduces them monotonically; and (3) each prayer's payoff is strictly concave in her own strategy. Under these conditions, the Pareto dominance refinement is equiva lent to the coalition-proof Nash equilibrium refinement. Classification Num ber: C72. (C) 1999 Academic Press.