## Seminario J. Morgan - 21/5/2010 ore 11:30 - aula A6

Speaker: Jacqueline Morgan

Dipartimento di Matematica e Statistica Centre for Studies in Economics and Finance, Università di Napoli Federico II, M. S. Angelo, Via Cinthia, 80126 Napoli, Italia.

Where: Room B6, via Ariosto 25

When: 21/5/2010 ore 11:30

TITLE: Altruistic behavior and Nash equilibria.

ABSTRACT

Two different concepts of refinement of Nash equilibria based on altruistic behavior of the players will be presented, together with an application to models of noncooperative social networks formation

Friendliness Equilibria (De Marco and Morgan, Friendliness and Reciprocity in Equilibrium Selection, Int. Game Th. Review, 10, 2008) are based on a property of robustness of the equilibrium with respect to a particular class of deviations: a player is supposed to move away from the equilibrium even only to guarantee a better payoff to the others and feasible deviations are unilateral and only towards Nash equilibria, that is valid deviations in the sense that there are no incentives to deviate from the deviation.

On the other hand, the concept of Slightly Altruistic Equilibrium (De Marco and Morgan, Slightly Altruistic Equilibria, J. of Opt. Th. And Appl. 137, 2008) is based on a stability property with respect to trembles which capture an idea of reciprocal altruism: each player cares only about himself but his choice corresponds to the limit of choices he would have done in equilibrium if he had cared about the others, provided the others had done the same. In general, a slightly altruistic equilibrium is not necessarily a friendliness equilibrium and viceversa. However, sufficient conditions on the payoffs of the game guarantee that every slightly altruistic equilibrium is a friendliness equilibrium. Moreover, it is possible to enforce the robustness property of friendliness equilibria to obtain strategy profiles which are also slightly altruistic equilibria.

A selection device, by considering altruistic behavior, between architectures which play a fundamental role in social networks has been investigated in De Marco and Morgan (Equilibrium selection and altruistic behavior in noncooperative social networks, TOP 17, 2009).