Comparative Statics by Adaptive Dynamics and the Correspondence Principle

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Reasons and Means to Model Preferences as Incomplete

Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review some of the reasons that have been put forward to justify more complex modeling, and review some of the techniques that have been proposed to obtain models of such preferences

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

How do risk attitudes affect measured confidence?

We examine the relationship between confidence in own absolute performance and risk attitudes using two confidence elicitation procedures: self-reported (non-incentivised) confidence and an incentivised procedure that elicits the certainty equivalent of a bet based on performance. The former procedure reproduces the “hard-easy effect” (underconfidence in easy tasks and overconfidence in hard tasks) found in a large number of studies using non-incentivised self-reports. The latter procedure produces general underconfidence, which is significantly reduced, but not eliminated when we filter out the effects of risk attitudes. Finally, we find that self-reported confidence correlates significantly with features of individual risk attitudes including parameters of individual probability weighting

Belief elicitation when more than money matters: controlling for "control"

Incentive compatible mechanisms for eliciting beliefs typically presume that the utilty of money is state independent or that money is the only argument in utility functions. However, subjects may have non-monetary objectives that confound these mechanisms. In particular, psychologists have argued that people favour bets where their ability is involved over equivalent random bets - a so-called preference for control. We propose a new belief elicitation method that mitigates the control preference. Using this method, we determine that under the ostensibly incentive compatible matching probabilities method, subjects report self-beliefs 18% higher than their true beliefs in order to increase control. Non-monetary objectives account for at least 68% of what would normally be measured as overconfidence. We also find that control manifests itself only as a desire for betting on doing well; betting on doing badly is perceived as a negative. Our mechanism can be used to yield better measurements of beliefs in contexts beyond the study of overconfidence