  This paper investigates the robust {non-zero-sum} games in an aggregated
{overfunded} defined benefit (abbr. DB) pension plan. The sponsoring firm is
concerned with the investment performance of the fund surplus while the
participants act as a union to claim a share of the fund surplus. The financial
market consists of one risk-free asset and $n$ risky assets. The firm and the
union both are ambiguous about the financial market and care about the robust
strategies under the worst case scenario. {The union's objective is to maximize
the expected discounted utility of the additional benefits, the firm's two
different objectives are to maximizing the expected discounted utility of the
fund surplus and the probability of the fund surplus reaching an upper level
before hitting a lower level in the worst case scenario.} We formulate the
related two robust non-zero-sum games for the firm and the union. Explicit
forms and optimality of the solutions are shown by stochastic dynamic
programming method. In the end of this paper, numerical results are illustrated
to depict the economic behaviours of the robust equilibrium strategies in these
two different games.
