I think the conditions that should be made are a>c and a>e, b>f and b>d. Also g
HINT: If U and L are dominant strategies (U,L) will be a unique NE. The players believe that a deviation in their own strategy will not cause deviations by any other players.
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HINT: If U and L are dominant strategies (U,L) will be a unique NE. The players believe that a deviation in their own strategy will not cause deviations by any other players.