Fairness in an Ultimatum Game

We present a controlledlaboratory environment in which we use an ultimatum game to generate twoendogenous fairness indices. We use these as alternatives to the moreconventional exogenous measure, the offer index, in a model of offer-acceptancewhich includes measures of social value orientations and risk attitudes asvariables for explaining the acceptance or rejections of offers in an ultimatumgame. In particular we are interested in providing an explanatory model whichcan support situations in which the likelihood to accept unfair offers (asmeasured by the offer index) will exceed the likelihood of rejecting a fairoffer (again, as measured by the offer index). The offer index in the ultimatumgame setting is the amount offered by a sender divided by the total endowmentof the sender. Our endogenous fairness indices meet our condition of thelikelihood of acceptance of an unfair offer exceeding the likelihood ofrejecting a fair offer even though the explanatory power of theoffer-acceptance models with the endogenous fairness indices is not significantlydifferent from that with the exogenous fairness index.