You solve games by having solution criteria . Unfortunately, for any reasonable list of solution criteria you will always be able to find games where the result doesn't seem to make sense. Also, there is no set of obviously correct and complete solution concepts. Consider the following game:

Two rational people simultaneously and secretly write down a real number [0,100]. The person who writes down the highest number gets a payoff of zero, and the person who writes down the lowest number gets that as his payoff. If there is a tie they each get zero. What happens?

The only "Nash equilibrium" (the most important solution concept in all of game theory) is for both players to write down 0, but this is a crazy result because picking 0 is weakly dominated by picking any other number (expect 100).

Game theory also has trouble solving many games where (a) Player Two only gets to move if Player One does a certain thing, (b) Player One's strategy is determined by what he expects Player Two would do if Player Two gets to move, and (c) in equilibrium Player Two never moves.