OK. So, to get the array to have the first dim as the player selector, you can go:
cat(1,map(x->reshape(1,size(x)),array_of_arrays) Anyway, keeping with the same payoff_matrix as before, I realized you might just want a boolean array which is true if entry is a best response (for the appropriate player according to last dim). It is the same flavor of my previous one-liner, with `maximum` replacing `indmax` and a `.==`: isbr = payoff_matrix .== cat(nplayers+1,(mapslices(x->fill(maximum(x),size( payoff_matrix,i)), payoff_matrix[fill(:,nplayers)...,i],i) for i=1:nplayers )...) Anyway, gotta go now. Have a good one. On Sunday, September 25, 2016 at 11:46:26 AM UTC-4, Brandon Taylor wrote: > > For now, I have an array of arrays. 1 payoff array for each player. The > arrays can be zipped to get the strategy profiles. It seems to work, but > having everything in 1 array just seems so much more neat. Which is why I > was looking for a neat implementation of broadcast_slices to match. > > On Sunday, September 25, 2016 at 10:53:57 AM UTC-4, Dan wrote: >> >> Have you found the right implementation? >> >> Fiddling a bit, I tend to agree with Steven G. Johnson `for` loops would >> be the most efficient and probably the most understandable implementation. >> >> Also, would it not be easier to have the first index in the >> `payoff_matrix` determine which player's payoff are we using? >> >> Finally, following is an implementation using `mapslices` which seems to >> work: >> >> nplayers = last(size(payoff_matrix)); >> >> bestresponse = cat(nplayers+1,(mapslices(x->fill(indmax(x),size( >> payoff_matrix,i)), payoff_matrix[fill(:,nplayers)...,i],i) for i=1: >> nplayers)...) >> >> The `bestresponse` array is the same shape as `payoff_matrix`, with each >> entry in `bestresponse[..,..,..,..,i]` denoting the strategy number which >> is a best response to the others choices for player `i` (chosen in the last >> index). The other player's strategies are determined by all the `..,...,..` >> indices before, with the choice of player `i` immaterial (since a single >> best response is chosen by the `indmax` function. >> >> This is a good exercise, perhaps another question on Stackoverflow would >> yield interesting variations. >> >> On Saturday, September 24, 2016 at 9:40:54 PM UTC-4, Brandon Taylor wrote: >>> >>> Or I guess that should be >>> >>> broadcast_slices(best_response_dimension, player_dimension, >>> payoff_matrix, players) >>> >>> On Saturday, September 24, 2016 at 9:38:55 PM UTC-4, Brandon Taylor >>> wrote: >>>> >>>> I guess, but I'm trying to write a generic program where I don't know >>>> the size of the array? I'm trying to find Nash Equilibrium for an n >>>> dimensional array, where the player strategies are along dimensions 1:n-1, >>>> and the players are along dimension n. So: >>>> >>>> equals_max(x) = x .== maximum(x) >>>> >>>> best_response_dimension(payoff_matrix, dimension) = >>>> mapslices(equals_max, payoff_matrix, dimension) >>>> >>>> I'd want to do something like this: >>>> >>>> player_dimension = ndims(payoff_matrix) >>>> other_dimensions = repeat([1], inner = player_dimension - 1) >>>> number_of_players = size(payoff_matrix)[player_dimension] >>>> >>>> >>>> players = reshape(1:number_of_players, other_dimensions..., >>>> number_of_players) >>>> >>>> broadcast_slices(best_response_dimension, payoff_matrix, players) >>>> >>>> On Thursday, September 22, 2016 at 9:00:51 PM UTC-4, Steven G. Johnson >>>> wrote: >>>>> >>>>> At some point, it is simpler to just write loops than to try and >>>>> express a complicated operation in terms of higher-order functions like >>>>> broadcast. >>>>> >>>>
