Towards understanding the guessing game: a dynamical systems’ perspective

The so-called “Guessing Game” or α-Beauty Contest serves as a paradigmatic conceptual framework for competitive price formation on financial markets beyond traditional equilibrium finance. It highlights features that are reasonable to consider when dealing with price formation on real markets. Nonetheless this game is still poorly understood. We propose a model which is essentially based on two assumptions: (1) players consider intervals rather than exact numbers to cope with incomplete knowledge and (2) players iteratively update their recent guesses. It provides an explanation for typical patterns observed in real data, such as the strict positivity of outcomes in the 1-shot setting, the skew background distribution of guessed numbers, as well as the polynomial convergence towards the game-theoretic Nash equilibrium in the iterative setting.