game

• the column chooser's options names all 2 of them in one to three characters ×2
• the row chooser's options names all 2 of them in one to three characters ×2
• a cell carries both marks exactly when neither chooser can gain by moving alone ×1
• a rational is a whole numerator over a non-zero whole denominator ×1
• a rational is never divided by zero ×1
• all the traffic arrives at T ×1
• all the traffic leaves S after the link is added ×1
• all the traffic leaves S before the link is added ×1
• at least one column holds the row chooser exactly to the value ×1
• at least one order of elimination was run ×1
• every cell of the matrix was put to both tests ×1
• every order of elimination reaches the same surviving set ×1
• every payoff is a whole number no larger than 20 in size ×1
• every traveller is strictly slower after the zero-cost link is added ×1
• no mixing weight on the sweep guarantees the row chooser more than the peak ×1
• no mixture on the lattice holds the row chooser below the value ×1
• no route is cheaper than the one everybody is on, so the flow after is an equilibrium ×1
• no split of the traffic on the lattice costs less in total than the computed optimum ×1
• some pair of columns achieves the column chooser's best mixture ×1
• the best use of the added link is somewhere between none of the traffic and all of it ×1
• the bimatrix carries two payoffs in every cell ×1
• the bimatrix drawn by the payoff mode is one of coordination, none, dominant, three ×1
• the bimatrix has between 2 and 4 columns ×1
• the bimatrix has between 2 and 4 rows ×1
• the bimatrix is rectangular — every row offers the same columns ×1
• the closed form for the least possible total agrees with pricing its own flow edge by edge ×1
• the column chooser's mixture holds the row chooser to at most the value against every row ×1
• the computed optimum is itself a point of the lattice ×1
• the cost of a fixed-cost link is a whole number between 1 and 400 ×1
• the cost per unit of flow on a congestible link is a whole number between 1 and 10 ×1
• the equilibrium costs strictly more in total than the optimum ×1
• the exact arithmetic stays inside the safe integer range ×1
• the exact value and its decimal recomputation agree ×1
• the fixed-cost link is cheap enough that the old routes beat the new one ×1
• the fixed-cost link is dear enough that the added link is taken by everybody ×1
• the mode of the game family is one of payoff, mixed, dominance, network ×1
• the ratio of the equilibrium's total to the least possible total is exact ×1
• the row chooser's maximin and the column chooser's minimax are the same number ×1
• the row chooser's mixture is worth at least the value against every single column ×1
• the surviving column is a best reply to the surviving row ×1
• the surviving row is a best reply to the surviving column ×1
• the traffic entering the network is a whole number between 3 and 40 ×1
• the two routes cost the same before the link is added, so nobody moves ×1
• the zero-sum matrix has between 2 and 4 columns ×1
• the zero-sum matrix has exactly two rows — the mixing probability is one number ×1
• the zero-sum matrix is rectangular — every row offers the same columns ×1
• what arrives at A leaves A ×1
• what arrives at B leaves B ×1

The whole library · What the figures prove