How to maximize the steady state transition probability for a state in a Markov chain by altering that state's outgoing transition probabilities?

Let’s say we have a transition matrix of

which can be solved to come up with steady state transition probabilities of
Alpha: 34.9%
Beta: 24.0%
Gamma: 16.9%
Delta: 24.2%
Now, imagine Alpha, Beta, Gamma, and Delta are agents and they can alter only their own transition rows (i.e. how much they decide to link to the other agents). I’m also imagining that agents cannot link to themselves at all (hence the 0s along the diagonal). How would Delta change its row’s transitions probabilities so as to maximize its own steady state probability? For example, if it unilaterally sent all of its "to" probability to Alpha, its steady state probability would increase to 25.2%, and if shifted all of its probability to Gamma, its steady state probability would increase even more to 25.8%. That’s a bit interesting because Alpha has a higher probability of shifting to Delta than does Gamma, so the heuristic of "shift to the agent that links most strongly to me" doesn’t always maximize one’s own steady state probability.

Abstracting from this example, the general question is: Given a N X N transition matrix of N agents in which rows sum to 1, how can an agent maximize their steady state probability by adjusting only their own row’s transition probabilities? Is the agent’s steady state probability always maximized by assigning a transition probability of 1 to one agent, and 0 to all other agents?