Analysis of Equilibrium Strategies in a New Number-Guessing Game with Reward and Penalty

Abstract

We propose a new variant of number-guessing games with penalties for failure and consider the equilibrium strategies in the game. In the proposed game, the codemaker selects a number from 1 to n as her private information then the codebreaker guesses the number. The codebreaker can receive the number as her reward when she guesses correctly, but she must pay a penalty for each failed guess. We formalize the game as a linear programming problem to obtain the codemaker's Min-Max strategy and the codebreaker's Max-Min strategy. The strategies are also explored by using Minimax Q Learning. We compare the computational cost of the two approaches in obtaining the equilibrium strategies.