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Games with saddle points
The 2 by 2 games
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ai,j ai(j balanced game balanced Silverman games central diagonal element ck+1 cm+1 complete the proof consider such fj diagonal in position dj+1 dominates the fj dr+1 e2n+1.b dominates ec+2 ek dominates element of W1 en+k dominates en+k+1 equivalent against W1 f2n+i-d dominates fj fa+1 dominates fj fc+2 fj for n+a+2 fj in W2 fj in W2\W2 fn+1.d dominates fn+a+2 dominates fj full game game matrix game on W1 game reduces game value game with diagonal group are equivalent hypothesis j<i<j+n let c+2 Let n+a+2 Let n+c+3 Let n+k+l Let W1 matrix is shown n+a+l n+c+2 n+l-b n+l-d n+t+l numbers payoff matrix proof is complete proof we show pure strategy reduced game Section shown in Figure strategy sets subdiagonal subgame on W1 symmetric game v+l)p W^W1 is dominated W1 x W2 W2 are optimal W2\W2 is dominated zeros