It is similar to the guessing of 2/3 of the average, only here we have to guess the average + 1 when numbers are guessed between 1 and 100. What I understood from the 2/3rd game is that - suppose there are 2 players. If both guess 100 and the winning entry is 67, both of them sees a benefit in guessing lower numbers. This goes on and finally both settle at 1. The core idea is that players sees a benefit in reducing, or changing their initial guess.
Coming to the guessing average + 1 game, if both players guess 50. Winning entry is 51 and if one of them wants to increase his guess to 51, he sees a benefit (new winning entry is (50+51)/2 +1 = 50.5+1 = 51.5 ) as his guess of 51 is closer to 51.5. So both the players go on increasing their guesses until they reach the max, which is 100 here.
Is this the right way of evaluating such games or am I making a mistake somewhere ? I assume that both the players play and see what were the numbers played and then take a decision, which is not correct I think. Or should I think of it as a 3rd party where I try to see which state would be fair to all the players so that no one sees a benefit of changing his state ?
So if anyone could nudge me towards the correct approach for approaching and setting up the interaction/thought process of the players, that would be great.