The risk function formalizes the notion that an agent's willingness to risk conflict is the ratio of the utility that agent would lose by accepting the other agent's proposal to the utility that agent would lose by causing a conflict.
The risk function outlines the concept that an agent's propensity for risk-taking in disputes is quantified as the ratio of the loss in utility resulting from accepting another party's offer to the loss in utility resulting from provoking a confrontation.