Axiomatization of an exponential similarity function

Billot, Antoine; Gilboa, Itzhak; Schmeidler, David

doi:10.1016/j.mathsocsci.2007.08.002

Cited by 45 publications

(32 citation statements)

References 9 publications

(11 reference statements)

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“…Pape and Kurtz (2013) found that, consistent with the evidence from psychology (Shepard 1987), the similarity function has the following form, which was provided with an axiomatic foundation by Billot et al (2008). We assume this functional form here:…”

Section: The Camera and Casari (2009) Experiments And Cbsamentioning

confidence: 60%

Predicting human cooperation in the Prisoner’s Dilemma using case-based decision theory

Guilfoos

Pape

2015

Theory Decis

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In this paper, we show that Case-based decision theory, proposed by Gilboa and Schmeidler (Q J Econ 110 (3): 1995), can explain the aggregate dynamics of cooperation in the repeated Prisoner's Dilemma, as observed in the experiments performed by Camera and Casari (Am Econ Rev 99:979-1005, 2009). Moreover, we find CBDT provides a better fit to the dynamics of cooperation than does the existing Probit model, which is the first time such a result has been found. We also find that humans aspire to a payoff above the mutual defection outcome but below the mutual cooperation outcome, which suggests they hope, but are not confident, that cooperation can be achieved. Finally, our best-fitting parameters suggest that circumstances with more details are easier to recall. We make a prediction for future experiments: if the repeated PD were run for more periods, then we would be begin to see an increase in cooperation, most dramatically in the second treatment, where history is observed but identities are not. This is the first application of Case-based decision theory to a strategic context and the first empirical test of CBDT in such a context. It is also the first application of bootstrapped standard errors to an agent-based model.

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Section: The Camera and Casari (2009) Experiments And Cbsamentioning

confidence: 60%

Predicting human cooperation in the Prisoner’s Dilemma using case-based decision theory

Guilfoos

Pape

2015

Theory Decis

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“…Billot et al (2008) provide conditions on similarity-weighted averages that are equivalent to the similarity function taking the form…”

Section: Empirical Similarity Modelsmentioning

confidence: 99%

A similarity-based approach to prediction

Gilboa

Lieberman

Schmeidler

2011

Journal of Econometrics

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“…In addition, increasing precision might affect estimations through its perception in form of altered cautiousness (to wrongly eliminate some outcomes) with which the forecast is made and her changed confidence in this forecast 3 . If information becomes more precise, an agent's decreased cautiousness and increased confidence might allow to specify their prediction.…”

Section: Introductionmentioning

confidence: 99%

“…) intersects for all 0 ≤ z ≤ a l (defined above (12)) with the lines (g (1,3) l (z), g (2,3) l (z)) which are parallel to the line (f 1 , f 2 ) and also with all lines (g (1,2) l (z), g (1,3) l (z)) which are parallel to (f 2 , f 3 ). By Lemma B.4 this yields, that all simplicical points of the (l + 1)-th partition, which lie on the line (b 1 l+1 (1), b 3 l+1 (1)) are satisfying equation (11).…”

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confidence: 99%

Cautious Belief Formation

Bleile

2014

SSRN Journal

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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. Terms of use: Documents in AbstractWe provide an axiomatic approach to a belief formation process in an informational environment characterized by limited, heterogenous and differently precise information. For a list of previously observed cases an agent needs to express her belief by assigning probabilities to possible outcomes. Different numbers of observations of a particular case give rise to varying precision levels associated to the pieces of information. Different precise information affects the cautiousness and confidence with which agents form estimations. We modify the Concatenation axiom introduced in Billot, Gilboa, Samet and Schmeidler (BGSS) (Econometrica, 2005) in a way to capture the impact of precision and its related perceptional effects, while still keeping its normative appealing spirit. We obtain a representation of a belief as a weighted sum of estimates induced by past cases. The estimates are affected by cautiousness and confidence considerations depending on the precision of the underlying observed information, which generalizes BGSS. The weights are determined by frequencies of the observed cases and their similarities with the problem under consideration.

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Axiomatization of an exponential similarity function

Cited by 45 publications

References 9 publications

Predicting human cooperation in the Prisoner’s Dilemma using case-based decision theory

Predicting human cooperation in the Prisoner’s Dilemma using case-based decision theory

A similarity-based approach to prediction

Cautious Belief Formation

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