Frames and social games

In this paper, we model socially-embedded games. We use non-cooperative game forms with pure strategy Nash equilibria and embed them through framing structures. These frames alter how players perceive the game, or rule out the choice of some elements of players’ option sets. In this way, we explicitly link the notion of social game to concepts taken from Erving Goffman's theory of interaction. According to Goffman, game theory is flawed because it applies a single-level model to two-leveled situations, ignoring the fact that people form impressions and expectations during or before any strategic game. In this essay, we provide a set-up endowed with these two levels. Firstly, players endogenize a given setting and frame the interaction. This determines what kind of game they will play. Secondly, they select Nash equilibrium strategies. As we shall discuss, it is possible in this way to consider how frames operate and what role they have in determining Nash solutions of non-cooperative games.

► We extend the notion of social game in order to consider embedded strategic interactions. We use partially-ordered sets mathematics and Erving Goffman's theory in order to discuss how different game forms can be socialized by players. We show that the concept of Nash equilibrium can be, in this way, put in frame.