 In his own analysis Braithwaite favored the proportional solution to the bargaining problem that selects the point on the Pareto frontier where the payoffs for each agent relative to the nonagreement point are proportionate to some independently specified measure of fair  gains.[6]  Gauthier (1986, 2013), on the other hand, defends the maximin proportionate gain solution that also selects a point on the Pareto frontier by comparing the payoffs for agents relative to the nonagreement point, but which, in addition, takes into account how agents fare relative to their ideal  payoffs.[7]  In the game theory literature, however, the Nash solution has remained the most widely utilized solution concept, and this has arguably been true among philosophers offering game-theoretic treatments of the social contract as well (see, e.g., Binmore 1994, 1998; Muldoon 2016). Roughly speaking, this solution picks out the point that maximizes the cooperative surplus, although some philosophers have offered refinements on the concept that guarantee payoffs also meet a minimum threshold (Moehler  2018).[8]