Bargaining Game with Altruistic and Spiteful Preferences

Abstract

In real bargaining problems, players care not only about their own shares, but also about others’ shares. In addition, a player’ attitude toward others depends on how this player feels he is being treated. To model such preferences, the Rubinstein bargaining game is reconsidered, where players’ preferences is characterized as altruism and spite. First, a subgame perfect equilibrium (SPE) is constructed, where player’s strategy depends on the opponent’s share through altruistic and spiteful preferences. The uniqueness of SPE is shown if it shares with SPE in the classical Rubinstein case: no delay and stationarity. Then, a comparative statics analysis with respect to players’ altruism and spite is performed. It is shown that the equilibrium share of a player is negatively related to the opponent’s global spite and his own global altruism, and positively to global altruism of the other one and the global spite of himself. It is also found that the impact of the intrinsically altruistic and spiteful levels of a player on equilibrium share depends on this player’s attitudes towards the opponent. Furthermore, it is found that a more positive attitude towards the opponent leads to the increase (decrease) of this player’s share if this player is more (less) intrinsically altruistic than the opponent. Finally, we establish a relationship with asymmetric two-person Nash bargaining game. It is found that bargaining power of a player decreases with the globally altruistic and spiteful preferences of himself, and increases with the opponent’s. It is further found that the effects of players’ attitudes towards the opponent on their own bargaining power depend on the gap between the intrinsic altruistic and spiteful levels of players.