Hi Brandon, you might find some inspiration from this package <https://github.com/gasagna/ArraySlices.jl>.
Davide On Sunday, September 25, 2016 at 8:33:54 PM UTC+1, Dan wrote: > > Nice. > It is easier when the payoffs are in vector form. My last iteration: > > is_nash_equilibrium(po) = > !reduce(|,falses(po[1]),(broadcast(<,po[i],mapslices(maximum,po[i],i)) for > i=1:length(po))) > > A one-liner :) > > On Sunday, September 25, 2016 at 2:25:45 PM UTC-4, Brandon Taylor wrote: >> >> Cool! The implementation I have is: >> >> equals_max(x) = x .== maximum(x) >> >> best_response_dimension(payoff_matrix, dimension) = >> mapslices(equals_max, payoff_matrix, dimension) >> >> is_nash_equilibrium(payoffs) = @chain begin >> payoffs >> broadcast(best_response_dimension, _, 1:length(_) ) >> zip(_...) >> map(all, _) >> end >> >> On Sunday, September 25, 2016 at 11:57:47 AM UTC-4, Dan wrote: >>> >>> Oops, that `cat` code was supposed to be: >>> >>> cat(1,map(x->reshape(x,1,size(x)...),array_of_array)...) >>> >>> Mew! >>> >>> On Sunday, September 25, 2016 at 11:54:43 AM UTC-4, Dan wrote: >>>> >>>> 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. >>>>>>>>> >>>>>>>>
