Table 3 The joint distribution of player A’s and A’s score, with interactions. A2’s score Joint Prob -1 0 +1 -1 pa1,-1pa2,-1+ i-1,-1 pa1,-1pa2,0+ i-1,0 pa1,-1pa2,+1- i-1,-1- i-1,0 pa1,-1 A1’s score 0 pa1,0pa2,-1+ i0,-1 pa1,0pa2,0+ i0,0 pa1,0pa2,+1- i0,-1- i0,0 pa1,0 +1 pa1,+1pa2,-1- i-1,-1-i0,-1 pa1,+1pa2,0- i-1,0- i0,0 pa1,+1pa2,+1 + i-1,-1+ i-1,0+ i0,-1+ i0,0 pa1,+1 pa2,-1 pa2,0 pa2,+1 1