Handbook of Game Theory

3.4.4.5 Conformity and conspicuous effects

Let us consider one last application of the quadratic model, with some modifications. In that model, it is the sum offriends’ activities that impact a player's utility from increasing his or her action [3.3]. This is clearly not always the right model, as it might be some other function of friends’ activities that matters. Patacchini and Zenou (2012) and Liu et al. (2014) alter the model so that it is the average effort level of friends that affects a player's marginal utility of own action.

Let ${\widehat{g}}_{ij}=g_{ij}/d_i(\mathbf{g}),$ and ${\widehat{g}}_{ij}=0$. By construction, $0\le {\widehat{g}}_{ij}\le 1.$

Let ${\overline{a}}_i$ the average effort of individual i's friends: ...