Conference Design for Consensus under KL Acceptance

We study consensus formation and information acquisition in conferences where DeGroot-type opinion updating is constrained by an acceptance rule based on Kullback-Leibler divergence. Players choose private information experiments before deliberation, and these choices determine both their posterior distributions and acceptance tolerances. We establish sufficient conditions for global consensus under specified conference structures, including repeated bilateral conferences organized by a fully receptive mediator. Under full reimbursement of the mediator's conference costs, the information-acquisition game has a weighted potential and admits a pure-strategy Nash equilibrium. We develop a numerical procedure using verified payoff bounds over the continuous posterior domain to certify approximate equilibria and assess partial reimbursement policies that preserve a given equilibrium profile. The binary state, three-player examples illustrate how conference order interacts with state variance. At larger variances in the tested range, placing the demanding nonmediator last is associated with lower conference costs and lower certified sufficient planner reimbursement, but greater information acquisition expenditure by the mediator. These findings reveal a trade-off between the planner's fiscal expenditure and the mediator's private burden, and show that the conference structure matters economically.