Affective Interactions

In game theory, individuals react to what others do. But oftentimes individuals react to how others are, to their wellbeing. Somewhat surprisingly, we show how under mild assumptions, the equilibria of such affective interactions are Pareto efficient. Moreover, even in a sequential setting, the backward-induction outcomes of affective interactions are Pareto efficient.

Under even milder assumptions, in the games induced by affective interactions of two participants with uni-dimensional strategy sets, their utility functions are 'intertwined', and the gradient dynamics follows the same paths as those of the gradient dynamics of the affective interaction, even though possibly in different speeds and even opposite directions.

Finally, in standard  two-player games with uni-dimensional strategy sets, the gradient dynamics taking as given at each moment the other player's utility rather than her choice - this dynamics is generically undefined at Nash equilibria, and behaves 'wildly' around them. However, when the strategy sets are convex and the utility functions are concave, this dynamics has the attractive property that its set of restpoints contains the Pareto efficient frontier of the game.

(Some of these results are joint with Herakles Polemarchakis and Enrico Minelli, and with Jorge Pena)

Three of the papers: 
Affective interdependence and welfare
The non-dismal science of intergenerational affective interactions
Nash equilibria are extremely unstable in most games under the utility-taking gradient dynamics 

Aviad Heifetz's homepage: https://www.openu.ac.il/en/personalsites/ProfAviadHeifetz.aspx