Malice in the Rubinstein bargaining game

This paper incorporates malice into the Rubinstein alternating offers bargaining game. Malicious players obtain a positive payoff in every period in which the other player does not obtain any piece of the pie. This “malice payoff” is independent of whether the malicious player himself obtains the pie or not. I identify a unique SPNE of the bargaining game. With two equally malicious players, the equilibrium shares of the proposer and respondent are more equal than under traditional Rubinstein bargaining. Intuitively, this is because the respondent has the right of first rejection. However, this solution requires an upper bound on the players’ patience; malicious players who are also infinitely patient would not participate in the bargain in the first place. This is in contrast both to the case of “spiteful” preferences (where a player’s spite payoff is decreasing in the share that the other player gets) and “envious” preferences (one-sided inequality aversion), in both of which an interior bargaining solution can occur even if the discount factor approaches one. With one-sided malice, malice confers bargaining advantage. With two-sided malice, and unequal malice parameters, the proposer may obtain a higher or lower share than in the traditional Rubinstein game, and may end up with a lower share than the respondent (even if both have equal discount factors).