Coalitional Stability in a Class of Social Interactions Games

In this paper, we define additive dyadic social interactions games (ADG), in which each player cares not only about the selected action, but also about interactions with other players, especially those who choose the same action. This class of games includes alliance formation games, network games, and discrete choice problems with network externalities. While it is known that games in the ADG class admit a pure strategy Nash equilibrium that is a maximizer of the game ís potential, the potential approach does not always apply if all coalitional deviations are allowed. In this paper, we systematically identify both restrictions on possible coalitional deviations to preserve the potential function and types of equilibria that ensures their existence for various subclasses of ADG or its subclasses, extending the approach taken by Le Breton et al. (2021). An additional avenue of our results is the examination of games with outside option which expand the set of alternatives. Although this modification complicates the analysis significantly, positive results are obtained with different class of restrictions.