Hello, Kodt, you wrote: Then it is necessary gain_i = {5-1, 5-2, 5-3, 5-4} because in case of success (w_i*v_i) the leader spends a heap of time for searches and spares on sobering. Yes it is possible and so. Important that there is a Price of a scoring and the price of loss and there is an average scoring - actually a subject for optimization. At pioneers simply optimized sum (-v_i*w_i) - on your condition (they actually only pay for loss when them burned). A>> It. I simply tried to prove that at ANY w_i from a simplex and coefficients from a condition, we receive v_i in peaks of a simplex for a maximum of target function of the leader at set w_i. I.e. v_i a type [0. 010. 0] at a maximum of target function of the leader. You about about a maximum on Neshu write (concept new to me which I just looked in and understood from lecture as the games theory I do not know absolutely) - it too concerns maxima about which I spoke (one of them). Here the error in the logician somewhere hid. Yes in my text a vagueness - it is necessary to read it so: "I simply tried to prove that at ANY w_i from a simplex and coefficients TAKEN from a condition..." . Certainly, generally the boundary can coincide with an edge or a simplex edge about what at once and wrote. It is a pity that muffledly quitted. The freebie with peaks was only for yours (well can still what) dial-ups . On the one hand, - it is valid, for any specific mixed strategy of pioneers the optimum of the leader will be on simplex boundary, and at least one peak (i.e. pure strategy) there gets. But focus that - besides default strategy, that is, fixings of losses, - for each specific strategy of pioneers this pure strategy of the leader will be different. Roughly speaking, it argmax (gain_i*w_i-loss_i * (1-w_i)). That is, to look, where () pioneers visit more often, and there and to go. If argmax ambiguous the boundary contains some peaks and has appropriate dimensionality. For this reason with a minimax did not begin to communicate. In . To radio engineering both (average loss and a minimax) have the right to life and are used. Or you minimize the worst loss, or - average. I about average wrote. But after all pioneers too not fools. If they know a train of thought of the leader (and know, in case of ambiguity he selects which pure strategy) they refine the mixed strategy, nullifying probability of a matching component. Then the leader enumerates argmax, selects other pure strategy, and pioneers and this component nullify. And so they get into a mess before, as pioneers will have a pure strategy, and the leader directly to them on a visit goes. And then to pioneers all roads from a hole - only upwards, and they for improving take any strategy - pure or mixed - at which that's it this component zero, on a bast, make a fresh start. Pioneers not that what not fools. At all without knowing strategy of the leader (we assume that at us probability game) they always should estimate it on draws. The leader - it is similar. I.e. it will turn out that after strategy change one of the sides strongly loses any time, therefore she adapts and minimizes losses (maximizes a scoring, perhaps). Again we have balance for the selected strategy. It follows from this that such method of serial improvings - a basis of the linear programming - is unacceptable. As a matter of fact, it was from the very beginning clear. Game on opposition, and a merit function, satisfying both sides, almost everywhere is equal to zero (except default strategy when one of the sides surrenders and minimizes the losses). I also did not have anything when tried gradually changing on coordinates to reach a stable state of all system - when a scoring of pioneers and the leader feeblly change. I.e. All worked so - pioneers and the leader adapted for strategy each other, then someone changed the a little to increase a scoring proceeding from strategy of the opponent, then other side adapted and too changed the strategy too a little to increase own scoring, etc. process to balance of Nesha did not converge. Generally to any balance did not converge - scorings of pioneers and the leader had oscillating character from draw number - probabilities in strategy were swung between components. It by the way for balance Not all is possible for +100 author of the analytical decision modeling. It for was specific these values. It agree completely. PS and here if the leader was much more strongly to find pioneers, its equilibrium scoring E would be equal G*w1-L1 = G*w2-L2 = G*w3-L3 = G*w4-L4 = E 4E = G - (L1+L2+L3+L4) E = (G - (L1+L2+L3+L4))/4 where G - the expected income at good luck, L1. . L4 - unconditional expenditures and if it above a default-min (L1, L2, L3, L4) =-L1 the leader will have the mixed strategy - with some probabilities to glance in everyone . to count specific target function in simplex peaks (the blessing, is not enough of them) easier. If it different for all peaks - we have a maximum in peaks. It is identical to two peaks - on an edge, For 3 - on the verge. A polyhedron at us, thank God, the correct.