Topic: Re: Pioneers and vodka

Hello, Kodt, you wrote: the Question: to what strategy the leader should adhere to maximize the advantage a minus costs? Well and accordingly, what pioneers should undertake? About scorings of pioneers from successful drinking in different places you did not tell. I think that for the leader there will be optimal a casual choice of a place of check. The probability of a choice of each place should be different. It is possible to minimize both average and maximum losses from loss.

Re: Re: Pioneers and vodka

Hello, Kodt, you wrote: the Question in that, how looks allocation of probabilities. Let probabilities of a choice of pioneers are known and equal w_i Then target function of the leader looks as an average scoring gain (v) = sum ((gain_i*w_i - loss_i * (1-w_i)) *v_i) = sum ((5*w_i - loss_i * (1-w_i)) *v_i) v_i - probability components selected by the leader, gain_i = 5 for all i loss_i = {1 2 3 4}; This linear programming - to us needs to be found a maximum of the linear function at the linear restrictions. {0 <=v_i <=1, sum (v_i) = 1} - a convex polyhedron, therefore the decision will be or a) to coincide from one of edges b) will belong to it one of edges will concern one of peaks. We check up a case as the idle time. Let max (gain) it is not reached in one of peaks. Let target function in peaks reaches values G_i, Rassm. Such peak j in which G_j it is maximum among all peaks. Then going on one of edges on a step e we receive magnification gain. I.e. (1) gain (0. 010. 0) = G_j = 5*w_j - loss_j (1-w_j) (2) gain (0. e (1-e) 0. 0) = (5*w_j - loss_i (1-w_j)) (1 e) + (5*w_k - loss_k (1 w_k)) *e = G_j - eG_j + eG_k = G_j - e (G_j - G_k) At the given constants G_k it is not equal G_j at w_j, w_k unequal 0 (it is possible . A difference, substituting constants). Therefore G_j-G_k always it is more 0 => at leaving on an edge we receive reduction of target function instead of growth. Came to the contradiction, means all the same c). Wrote an unpretentious script that it to check up. At casually selected w_i, always we roll down to one of type points v_i = [0. 010. 0] Then did not withstand and watched film