Best replies in a coordination game

• moving participant 1 from state 0 lowers the potential by exactly what they save ×12
• the run from 0.05 has closed on the rest point ×5
• the run from 0.05 has moved away from the rest point ×5
• nobody improves by moving alone out of state 1 ×4
• 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
• the time drawn is between 2 and 40 ×2
• a caption for the matrix is a short description, or not given ×1
• a caption renames the game only when the placement supplies its own payoffs ×1
• 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
• a win and a loss are whole numbers between one and four ×1
• above one, investing pays even if the other certainly does not ×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
• and a move that does not improve raises it by exactly what it costs ×1
• and above it, keeping it does ×1
• and at that belief the two actions are worth exactly the same ×1
• and below nothing, staying out pays even if the other certainly invests ×1
• and it is a region rather than a segment ×1
• and none pays the column chooser less ×1
• and so is the closed form for breaking it ×1
• and the bracket has closed to a small fraction of what it started at ×1
• and the optimistic one never falls ×1
• and the two never cross ×1
• and when a win and a loss are equal no invader does worse there than the centre does ×1
• at least one column holds the row chooser exactly to the value ×1
• at least one order of elimination was run ×1
• at least one state has no improving move, so an equilibrium exists ×1
• at the centre every pure strategy earns the same, so a third each is an equilibrium ×1
• at the critical discount factor the two streams are worth exactly the same ×1
• at the cutoff a chooser believes the other is above it with probability exactly a half ×1
• at the mixed equilibrium the leader earns the same from either row ×1
• at the rest point both strategies earn the same, so it is the mixed equilibrium ×1
• at the symmetric cutoff the other is believed above it with probability exactly a half ×1
• below it, breaking the agreement pays more ×1
• between four and forty rounds are drawn ×1
• between one and four starting mixtures, each three positive shares adding to one ×1
• between one and six starting shares, each strictly between nought and one ×1
• between two and four participants ×1
• both of them sit on the diagonal, which is what makes the two tie-breakers comparable ×1
• committing is worth at least as much as every equilibrium of the simultaneous game ×1
• each step moves the share the way the flow points ×1
• every cell of the matrix was put to both tests ×1
• every distribution on the lattice was tested ×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
• in a zero-sum game committing is worth exactly the value, and nothing more ×1
• in this game committing is worth strictly more than any equilibrium ×1
• no commitment on a lattice of 121 does better than the best candidate ×1
• no equilibrium pays the row chooser less than the minmax ×1
• no mixing weight on the sweep guarantees the row chooser more than the peak ×1
• no mixture of the punisher's holds the other below the minmax ×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
• nothing an equilibrium of the stage game pays is outside what repetition sustains ×1
• some pair of columns achieves the column chooser's best mixture ×1
• the agreement is worth more than the punishment and less than breaking it ×1
• the best correlated equilibrium is at least as good as the best pure one ×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 centre resists every invader exactly when a win is worth more than a loss ×1
• the closed form for keeping the agreement is the limit of its own terms ×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 correlated mode draws a two-by-two game ×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 critical discount factor is a real fraction of the way between nothing and certainty ×1
• the crossing sits strictly inside the unit interval ×1
• the drawn distribution is a correlated equilibrium ×1
• the drawn distribution is whole numerators ×1
• the drawn distribution sums to one ×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 first option is the better reply above the crossing and the worse below it ×1
• the first resource never gets cheaper as more use it ×1
• the first resource prices every load it can carry, as whole numbers no larger than forty ×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 four payoff pairs are not all on one line ×1
• the game drawn has exactly two pure equilibria ×1
• the game the commitment mode draws is one of chicken, stag, battle, stengel, pennies ×1
• the game the correlated mode draws is one of chicken, stag, battle ×1
• the game the replicator mode draws is one of hawk, stag ×1
• the game the selection mode draws is one of chicken, stag, battle ×1
• the lattice contains at least one correlated equilibrium ×1
• the lattice of distributions has a denominator between 4 and 24 ×1
• the mixed rest point attracts exactly when no invading mixture can do as well against it as it does against itself ×1
• the mode of the game family is one of payoff, mixed, dominance, network, correlated, potential, select, replicator, cycle, commit, folk, discount, global, iterate ×1
• the payoff gap is not constant, so the two strategies can tie at most once ×1
• the pessimistic cutoff never rises ×1
• the product of the shares grows at every sampled time ×1
• the product of the shares shrinks at every sampled time ×1
• the pure equilibrium AA is a correlated equilibrium too ×1
• the pure equilibrium BB is a correlated equilibrium too ×1
• the pure equilibrium CD is a correlated equilibrium too ×1
• the pure equilibrium DC is a correlated equilibrium too ×1
• the pure equilibrium HH is a correlated equilibrium too ×1
• the pure equilibrium SS is a correlated equilibrium too ×1
• the ratio of the equilibrium's total to the least possible total is exact ×1
• the reading is off by between two and forty hundredths ×1
• the region above both minmax values has an interior ×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 second never gets cheaper as more use it ×1
• the second prices every load it can carry, as whole numbers no larger than forty ×1
• the selection mode draws a two-by-two game ×1
• the shares still add to one at the end of the run, so the integration stayed on the triangle ×1
• the simultaneous game has an equilibrium to compare against ×1
• the stage game carries two payoffs in every cell ×1
• the stage game has between 2 and 4 columns ×1
• the stage game has between 2 and 4 rows ×1
• the stage game is rectangular — every row offers the same columns ×1
• the stage game the discount mode repeats is one of prisoner, stag, chicken ×1
• the stage game the folk-theorem mode repeats is one of prisoner, stag, chicken ×1
• the state of least potential is one of them ×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 tie falls strictly inside the population, so there is a mixed rest point ×1
• the traffic entering the network is a whole number between 3 and 40 ×1
• the two lines are not parallel, or there is no crossing to draw ×1
• the two lines meet at the mixed equilibrium ×1
• the two routes cost the same before the link is added, so nobody moves ×1
• the two sequences bracket that half at every stage, this one included ×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
• with a win worth a loss the product of the shares is conserved along the orbit ×1
• with two columns ×1

The whole library · What the figures prove