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. >>>>>>>> >>>>>>>
