Most realistic strategy game?

Why is it that in game theory, any deviation from the best strategy (equilibrium mix) results in a suboptimal strategy, even if the best strategy is to not go for the decisions with the biggest playoffs?

• How does the calculation of an equilibrium take into consideration the strategy of the opponent. How does the calculated equilibrium know what decisions your opponent will make? For example, let's say you calculated a strategy in a boxing match for the student you are training. The equilibrium you have calculated advises you to throw 10 left punches for every 13 right punches you throw. How does the equilibrium know what your opponent's strategy is going to throw back at you? What if instead of throwing 10 left punches, you throw 17 left punches for every 13 right punches? Why does game theory suggest that that is a bad idea (to go against the calculated equilibrium mix)?

• Answer:

  First what you are asking is quite difficult to explain. Taking your boxing example, if both opponents have same physical characteristics, opponents coach will also devise a strategy to throw 10 left punches for every 13 right punches, since it is an optimal strategy. Then eventually, both opponents will go down in the end, and we will see Lose-Lose, since there is very small chance, of getting back on feet if the time is stipulated then it will be a tie to Win-Win. Non co-op game theory analyses every move of an opponent which mean they will have strategy for your 10 left and 17 right punches, as this is a boxing game. Those strategies will stretch to a long list. That's why, most of the times, game theory, best work with two unequal opponents. For example, an opponent is left handed, then we can put up a strategy, to use right hand for guarding effectively reducing the punches with right hand. It's called co-operative game theory which will effectively eliminate all the strategies with an equal opponent and focus on the opponent with left hand. We only opt for sub optimal strategies when we are looking for win-lose situation, it generally used to evaluate your current strategy if the opponent changes his/her strategy suddenly, and our strategy becomes obsolete. As far as I know, sub optimal strategy never generates big payoffs, so if you want to win you have to chose optimal strategy. I seriously hope you understood this and sorry as I can't explain it properly.