algorithm - Updating an grid of "players" by replacing losers with copies of the winner -

i have two-dimensional array of objects. each object has, @ times, (variable) score (i.e. object's score @ time t not object's score @ time t+1). want find efficient algorithm duplicate object greater score neighbour, , place duplicate neighbour's place.¹

my first impulse naive solution:

• create copy of array
• set "changewasmade" flag false
• cycle through positions p
  • compare scores neighbours n
  • if score(p) > score(n), replace n in copied grid copy of p , set "changewasmade" true
• if "changewasmade", discard original grid, , repeat using copy new original; else, return copy

however, n x n array, seems o(n⁴) (n² possible iterations of n² checks), seems pretty slow me. since algorithmic knowledge pretty poor, thought wise ask if there's quicker way this.

update

it's occurred me might quicker make 1 "pass" of replacements, , check newly created (i.e. cloned) objects have highest score of neighbours (i.e. local maximum). if are, great, right thing has happened - if they're not, replace them copy of neighbour highest score. cut down on required iterations (though require book-keeping keep straight!) - there still quicker method?

** footnotes**

1. (for context, have read "the quantum thief", setup of prison described in opening pages)

unless i'm reading problem wrong, obvious solution seems be:

1. create blank array of same size, call old array old , new array new.
2. for each cell new[i][j] in new array, set maximum of 5 possible values: old[i][j], old[i-1][j], old[i][j-1], old[i+1][j], old[i][j+1].
3. new updated array timestep t+1.