Parameters and can be understood as envy and guilt weights respectively. Indeed, the former reduces utility when the other player’s payoff is greater than one’s payoff, while the latter reduces utility if the focal player’s payoff is greater than the other’s. In the characterization of the parameters, the assumption ! implies that players suffer more from inequality that is to her disadvantage, and less if it is to her advantage. In our understanding of this approach, it appears that the introduction of these parameters is motivated by how players react emotionally to different allocations. Under this perspective the model represents players’ choices as a combination of income maximization moderated by an emotional rejection (aversion) to inequality. However, there is no explanation for the mechanism behind this reaction, and each individual is characterized by her envy and guilt parameters without further connection to her emotional mechanisms at work. Notice also that in this model players are not able to know accurately what the preferences of others are, in so far as they don’t know the value of their parameters. For that reason, proposers have to overcome several problems in order to estimate an optimal offer. For instance, she must assume that the other player is also influenced by envy and guilt (although in an unknown way) and try to estimate her minimum acceptable offer (MAO) with this incomplete information. A different approach was proposed by Rabin [9], who developed a theory of fairness equilibria for two-player games in normal form. His 2013/480630 model is motivated by the truth that individuals behave nicely to individuals who treat them nicely and punish those that usually are not nice to them, with each motivations getting a higher effect on behavior because the material expense of sacrificing becomes smaller sized. Such model incorporates a representation of subjective judgements and beliefs from the players, primarily based around the psychological games framework of Geanakoplos [19]. So as to analyze this model [3] [20], let ai j.adolescence.2013.ten.012 be the technique chosen by player i, bj player i’s belief in regards to the tactic selected by player j, and ci player i’s belief regarding the player j’s belief in regards to the strategy selected byPLOS A single | DOI:10.1371/journal.pone.0158733 July 6,3 /Emotions and Strategic Behaviour: The Case on the Ultimatum Gameplayer i. Then, the utility function (social preference) is defined as: Ui i ; bj ; ci ??pi i ; bj ?? j j ; ci ?? j j ; ci i i ; bj ?f f where i(ai, bj) may be the monetary payoff to player i, fi i ; bj ?? j j ; ai ??pfair j = max j ??j j min ; c ?? ; b ??pfair = max ??p is player i’s kindness toward player j, f ij j j j i i i j i i ipmin 1 would be the perceived kindness by player i with respect to how she is getting treated by player 1 j, pmax j ?and pmin j ?are respectively the Lodoxamide (tromethamine) site highest and lowest achievable payoffs for player j, and j j pfair j ?is an equitable fair payoff defined because the average on the highest and lowest payoffs. j As a way to make the model additional tractable and define a fairness equilibrium, Rabin assumes that players are willing to maximize their social utilities and that all higher-order beliefs match actual behavior (i.e ai = bj = ci) [3].