Social learning model with parrondo's paradox

Abstract

Parrondo’s game is invented by J. M. R. Parrondo, by the inspiration of flashing ratchet. Parrondo’s game includes two losing games named game A and game B. Game A is a coin-tossing game with winning probability p_a = 1/2 − ∈. Game B is also a coin-tossing game with winning probability p_b = 1/10 − ∈ when the capital is divisible by a integer parameter M, winning probability p_g = 0.75 − ∈ otherwise. Parrondo’s study shows that the long-term capital is decreasing either playing one of the games, but the combination of two games may give the result that the long-term capital is increasing. This phenomenon is called Parrondo’s effect. We reviewed the Parrondo’s effect with both mathematical description and numerical simulation. Two combining strategies for Parrondo’s games: deterministic switching and stochastic mixing are introduced to demonstrate the Parrondo’s effect. We have studied the Parrondo’s game in a group of players with the condition that the games’ properties are blinded to the players. Players are interacted with one of the strategies: ‘Follow the winner’ and ‘Avoid the loser’. The two strategies show the phenomenon of Parrondo’s effect, the capital is decreasing for either one of the strategies and mixture of them may give a winning result. We also studied the situation that minimal information can be transferred among players. Players can adopt one of learning scheme: ‘Follow the winner belief’ and ‘Avoid the loser belief’. The opinion of games mapping among the players may converge to correct mapping when the first learning scheme is adopted. The mixture of learning schemes does not show the Parrondo’s effect, the time to convergence does not decrease. The convergence time is shortened when one of the rewiring schemes: ‘Rewiring from loser to winner’ and ‘Rewiring from the poorest to the richest’ is applied. We found that adding more game (such that there are three games or four games) will not increase the difficulty of learning significantly, the times to convergence are close for both cases two to four games.

Date of Award	2016
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology