Incentive Designs under Disparate Probabilistic Outlooks Across Decision Makers

Incentive design problems entail asymmetry in the decision-making process in multi-agent systems, where in simplest terms one agent (inducer) attempts to control the decision outcome of another agent (inducee) to his (inducer's) favor (though variations exist where the numbers of inducers and inducees could be more than one). The basic framework allows the inducer and the inducee to share a common (noisy) information on the state of the environment, but in addition for the inducer to have access to the decision (action) of the inducee and possibly also additional private information on the state. Most incentive design literature heretofore has addressed the problem where all random variables are defined on a common probability space, which is common knowledge to all agents. In this paper, we relax this basic assumption that the agents work with the same probability model, and endow them instead with disparate probability measures, such as for example them having different perceptions (beliefs) on second moments of the underlying random variables. We investigate the extent to which such "probabilistic multi-modeling"affects the design of effective incentive policies, both when this disparity is common knowledge to the agents and when it is not. Finally, we present results for the extended framework when there are multiple inducees with multiple probabilistic outlooks, with the solution concept capturing their interaction being Nash equilibrium.