  In this paper, we delve into the problem of using monetary incentives to
encourage players to shift from an initial Nash equilibrium to a more favorable
one within a game. Our main focus revolves around computing the minimum reward
required to facilitate this equilibrium transition. The game involves a single
row player who possesses $m$ strategies and $k$ column players, each endowed
with $n$ strategies. Our findings reveal that determining whether the minimum
reward is zero is NP-complete, and computing the minimum reward becomes
APX-hard. Nonetheless, we bring some positive news, as this problem can be
efficiently handled if either $k$ or $n$ is a fixed constant. Furthermore, we
have devised an approximation algorithm with an additive error that runs in
polynomial time. Lastly, we explore a specific case wherein the utility
functions exhibit single-peaked characteristics, and we successfully
demonstrate that the optimal reward can be computed in polynomial time.
