Experimental Results on Interactive Competitive Guessing
A large number of players have to state simultaneously a number in the closed interval (0,100). The winner is the player whose stated number is closed to p-fold average of all chosen numbers, where p is a fixed and commonly known positive parameter. The game is repeated for several rounds. In the first round most of the stated numbers are far away from an equilibrium point. In the succeeding rounds, they approach an equilibrium or converge to it. We propose a simple theory of first round behavior that involves types of players who use finite steps of reasoning. As an explanation of behavior over time, a simple qualitative adaption process based on individual experience is suggested.
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