The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs (see the example to the right). More generally it can be represented by any function that associates a payoff for each player with every possible combination of actions. In the accompanying example there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns. The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays Up and that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.
tHe normaL (Or straTegic foRm) gamE is usUallY Represented by A mAtrIx WhicH shoWs tHE pLayeRs, STrategiEs, and paYofFs (see thE exampLE tO tHE rigHt). more GenErally iT Can bE RepReSenTed by anY funcTIoN ThAt assOciateS a PayOff for Each plaYer wIth EveRy pOSSiblE coMbinatIOn of actions. IN tHe acCOMpanyiNg ExAmplE theRe aRe twO PlaYERs; onE ChooSes thE row anD ThE other ChOOseS the colUMn. each pLayEr has two STRatEgieS, whicH are sPEciFied BY THe nuMber Of roWs and The Number Of ColuMNs. tHe payoffS are pRoviDed in tHe IntErioR. the FirSt numBer is the pAyoff reCeivE.d by tHe roW pLAyer (pLaYer 1 in our EXampLe); thE seCOnD is thE payoFf fOr tHe Column plaYer (plaYer 2 iN our exaMple) suppose tHaT plAYeR 1 plays up aNd THat PlAyEr 2 pLAyS lEfT. tHeN playEr 1 GEts a pAYoff Of 4, anD plAyer 2 GetS 3.