Strategic Information Processing from Behavioural Data in Iterated Games

Michael Harré

doi:10.3390/e20010027

Abstract

Iterated games are an important framework of economic theory and application, at least since the original work of Axelrod’s computational tournaments of the early 80’s. Recent theoretical results have shown that games (the economic context) and game theory (the decision-making process) are both formally equivalent to computational logic gates. Here these results are extended to behavioural data obtained from an experiment in which rhesus monkeys sequentially played thousands of the “matching pennies” game, an empirical example similar to Axelrod’s tournaments in which algorithms played against one another. The results show that the monkeys exhibit a rich variety of behaviours, both between and within subjects when playing opponents of varying complexity. Despite earlier suggestions, there is no clear evidence that the win-stay, lose-switch strategy is used, however there is evidence of non-linear strategy-based interactions between the predictors of future choices. It is also shown that there is consistent evidence across protocols and across individuals that the monkeys extract non-markovian information, i.e., information from more than just the most recent state of the game. This work shows that the use of information theory in game theory can test important hypotheses that would otherwise be more difficult to extract using traditional statistical methods.

Highlights

An evolution in economic thinking has recently been transforming the field as researchers reconsider the foundations on which economics is based
In order to look at other potential sources of information from the previous step we consider the total information I (Sn : am n+1 ), which is a strict upper bound on the amount of information m m available from the previous time step, all of the pairwise information sources I, I ( u n : a n +1 ), c m
It can be seen that for all three monkeys when playing against Algorithm 1 there is a general tendency to increasing values of total information used by the monkeys over the sequence of experiments, this is most pronounced for Monkey 3 where the total amount of information used by the end of the experiments is nearly one bit, the theoretical upper limit for a binary choice

Summary

Introduction

An evolution in economic thinking has recently been transforming the field as researchers reconsider the foundations on which economics is based An example of this is Mirowski [1] who has argued for seeing economic markets as evolving computational entities. In this view the focus of research is on the computational laws of the market, not the laws of human nature, see [2] for the history of this idea and further reading. This work aims to illustrate the relationship between economic structure (i.e., the underlying game) and the decision making process (i.e., the strategies) of the agent as distinct but interrelated computations

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Conclusion