This paper extends the scope of Savage's subjective approach from decision problems under exogenous uncertainty to choice in strategic environments. In these environments the decision maker understands the uncertainty she is facing is affected by other decision makers in a similar situation. This contrast with classical decision making complicates the appropriate specification of the state space: as it is not exogenous, the uncertainty concerns not only the other decision makers' choices but also the behavioral rationale behind them. First, this problem is solved, constructing the state space explicitly -using hierarchies of preference relations -and then showing that this space indeed contains every relevant aspect of the decision maker's uncertainty. Since no restriction on preferences is imposed a priori, these results enable the analysis of behavior in games under any axiomatic structure. Second, conditions on preferences are characterized which imply that the decision maker behaves as if she is sure each other agent has preferences satisfying certain axioms, is himself sure each other agent's preferences satisfy certain axioms, and so on. Third, such characterization is provided for Savage's axioms. It is shown that a sequence of preference relations uniquely identifies the decision maker's utilities and beliefs, and also tells whether according to these beliefs each other agent is an expected utility maximizer, believes each other agent is, and so on.

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform-weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet 1989). We show that convergence in the uniform-weak topology implies convergence in the uniform-strategic topology (Dekel et al. 2006). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games. Terms of use: Documents in

We investigate the impact of conflicts of interests on randomised controlled trials in a game‐theoretic framework. A researcher seeks to persuade an evaluator that the causal effect of a treatment outweighs its cost, to justify acceptance. The researcher can use private information to manipulate the experiment in three alternative ways: (i) sampling subjects based on their treatment effect, (ii) assigning subjects to treatment based on their baseline outcome, or (iii) selectively reporting experimental outcomes. The resulting biases have different welfare implications: for sufficiently high acceptance cost, in our binary illustration the evaluator loses in cases (i) and (iii) but benefits in case (ii).

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Interactive epistemology in dynamic games studies forms of strategic reasoning like backward and forward induction by means of a formal representation of players' beliefs about each other, conditional on each history. Work on this topic typically relies on epistemic models where states of the world specify both strategies and beliefs. Strategies are conjunctions of behavioral conditionals of the form "if history h occurred, then player i would choose action a i ." In this literature, strategies are literally interpreted as (objective) behavioral conditionals. But the intuitive interpretation of "strategy" is that of (subjective) "contingent plan of action." As players do not delegate their moves to devices that mechanically execute a strategy, plans cannot be anything but beliefs of players about their own behavior. In this paper we analyze strategic reasoning in dynamic games with perfect information by means of epistemic models where states of the world describe the actual play path (not behavioral conditionals) and the players' conditional probability systems about the path and about each other conditional beliefs. Therefore, the players' beliefs include their contingent plans. We define rational planning as a property of beliefs, whereas material consistency connects plans with choices on the actual play path. Material rationality is the conjunction of rational planning and material consistency. In perfect information games of depth two (the simplest dynamic games), correct belief in material rationality only implies a Nash outcome, not the backward induction one. We have to consider stronger assumptions of persistence of belief in material rationality in order to obtain backward and forward induction reasoning.