\u201cBetting on nature\u201d or \u201cbetting on others\u201d: anti-coordination induces uniquely high levels of entropy

Gabriele Chierchia,Giorgio Coricelli,Rosemarie Nagel

doi:10.1038/s41598-018-21962-1

Abstract

Uncertainty in the form of risk or ambiguity can arise from the interaction with nature and other players, while strategic uncertainty arises only in interactions with others. Here, we systematically compare binary decisions between a safe option and a potentially higher paying but uncertain option in four experimental conditions with the same potential monetary outcomes: coordination vs. anti coordination games, as well as risky and ambiguous lotteries. In each condition, we progressively increase the value of the safe option and measure subjects’ certainty equivalents (i.e., the specific safe payoff-threshold that makes a subject indifferent between the two options). We find that anti-coordination games and ambiguous lotteries elicit equally high aversion to uncertainty, relative to the other domains. In spite of this similarity, we find that subjects alternate between the safe and uncertain options much more frequently, thus displaying higher entropy, under anti-coordination relative to any of the other environments. These differences are predicted by theories of recursive reasoning in strategic games (e.g., thinking what others think we think etc.). Indeed, this can occur when interacting with intentional counterparts, but not with nature.

Highlights

“Half a century ago, when decision theory and game theory were young, it was common to perceive a dichotomy between (i) games against nature, in which the “adversary” is a neutral “nature”—and (ii) strategic games, in which the adversary is an interested party [...]
In line with this, signed-rank tests confirmed that certainty equivalents (Fig. 3) were higher in the stag hunt than in any of the other environments and were higher in the risky lotteries than the ambiguous ones (p < 0.01)
In this study we provide an empirical answer to an old question: whether betting on others is perceived like betting on nature[1]

Summary

Introduction

“Half a century ago, when decision theory and game theory were young, it was common to perceive a dichotomy between (i) games against nature, in which the “adversary” is a neutral “nature”—and (ii) strategic games, in which the adversary is an interested party [...]. In games against nature, this state of the world is the result of a mechanistic process, while in games against others, it is the result of a motivated decision process, where others may form beliefs about what we will choose, or iteratively, about what we think they will choose etc. With this in mind, Aumann and Dreze argue, the structure of the game can change. SHs involve pure coordination - situations in which agents should match their actions - while EGs involve anti-coordination - situations in which agents should choose opposite actions

Methods

Results

Conclusion