Experimental Research about Learning in Inductive Game Theory

Abstract

In this article we expect to research how do players who are incompletely informed learn about the game from the perspective of experiment. We find that players can form and update their personal views about the rules of the game through interactions and then often choose the best replying strategy according to the Nash equilibrium of the games. The experimental data indicates that there are some factors can influence the effect of learning. Moreover, players are more likely to choose their strategies according to QRE (quantal response equilibrium). Introduction The former researches about learning in games always assume that the rules or the formation of the game is the common knowledge of all players, irrespective of classical game theory, evolutionary game theory and behavioral game theory. Kaneko (2013) noted that former researches neglected to explore how players perceive the game itself and how the cognitions about the game of players updating as time goes on. However, different from game theory and evolutionary game theory, behavioral game theory attempts to use the theory of learning in games to explain the changes of strategy selection. It provides a particular perspective for us to concern how players learning and acting in a game. Devetag (2003) asserted, in her experimental study, that the players’ ability of learning the rules of the game was closely related to the ability of players’ short-term memory which was a measurable proxy of their cognition. Hankie, et al. (2005) explored the strategy learning of players, which occurs in two phases, the long-run phase and the short-run phase. Branas-Garza (2012) identified players’ cognitive ability that was the basement of behavior of players in the beauty contest game by both Raven and Cognitive Reflection tests. But behavioral game theory didn’t research the rules learning in games. However the developing inductive game theory does that. Kailai (1993) suggested that, when players had incomplete objective knowledge of the game, the rules of the game in the players’ mind may not be the objective description of the game, and it could be more likely to be the players’ subjective cognition of the game. Moreover, the equilibrium of the game was also the subjective equilibrium. Oechssler (2002) pointed out that most of the players set up their own subjective game on the basis of the understanding of the objective game, then acted to the Nash equilibrium of the subjective game and the action were usually very close to the Nash equilibrium of the objective game. Kaneko (2006) argued that, the cognition of boundedly rational players about the rules of game was not given exogenously, but inducted from the previous learning of the game. Hanaki (2009) applied computer simulation method to study the influence of long-term memory and short-term memory in the process of learning in the repeated game. In this paper, we will research that how the players who did not fully understand the game learning the game itself and how to choice the strategy in the experiments, considering that players have limited reasoning ability and can learning in playing the game. Inductive game theory and game learning Kaneko& Kline (2008) proposed the inductive theory. They thought that the bounded rationality of players in the case of incomplete understanding the game can cognate the formation of the game by inductive learning. Inductive learning was closely related to the memories of past actions of International Conference on Management Science and Management Innovation (MSMI 2015) © 2015. The authors Published by Atlantis Press 573 players. Hanaki & Ishikawa (2009) considered that players' cognitive ability is related to their short-term memory and long-term memory ability and by computer simulation technology to study the following two questions: Personal views how to form Hanaki, et al. (2009) put out a learning model where it assumes the players are bounded rational, with two forms of memory, short-term memory and long-term memory. Short-term memory records the outcomes of the game, and it will disappear thereafter. a short-term memory can be transformed into a long-term memory which will exists in players’ mind forever, if it repeated for a value that we call it cognition threshold before it disappears. The short-term memory length of player i is represented by mi and the threshold, ki. So only if a outcome (si , sj) be repeated ki times in mi, it can be a long-term memory, and then player i will realizes his or her payoff. The long-term memory may changes over time, and then the personal views also change. Let ∏ be the objective payoff matrix of the game under consideration, and let ∏i represent the part of the payoff matrix that player i receives.