Tag Archives: game
Pricing Game
In November, with Romuald Elie and Jérémie Jakubowicz, we will organize a session during the 100% Actuaires day, in Paris, based on a “pricing game“. We provide two datasets, (motor insurance, third party claims), with 2 years of experience, and 100,000 policies. Each ‘team’ has to submit premium proposal for 36,000 potential insured for the third year (third party, material + bodily injury).
We will work as a ‘price aggergator’ with all the teams, with simple matching rules (the cheapest is chosen, or more complex rules, based on random selection among cheap insurers). The complete description is available on line.
R codes to read the datasets are
> training <- read.csv2( + "http://freakonometrics.free.fr/training.csv") > dim(training) [1] 100021 20 > pricing <- read.csv2( + "http://freakonometrics.free.fr/pricing.csv") > dim(pricing) [1] 36311 15
Everyone is invited to play! The more, the merrier….
Pricing Game (100% Actuaires)
Début Novembre, avec Romuald Elie et Jérémie Jakubowicz, on devrait animer lors la journée 100% Actuaires un “pricing game“. Nous mettons à disposition une base de données, en assurance automobile, avec 2 ans d’observations, avec 100,000 polices d’assurance. Chaque équipe doit envoyer des propositions de primes pour un peu plus de 36,000 assurés potentiels, pour la 3ème année, en RC automobile (matériel et corporel, les deux informations – fréquence et coût – étant dans les bases mises à disposition).
On jouera ensuite le rôle de courtier (ou de comparateur de prix) entre les différentes équipes (avec un principe assez simple, l’assuré choisi l’assureur le moins cher, tous offrant les mêmes garanties, ou quelques autres variantes pour pimenter un peu l’analyse). Le descriptif complet est en ligne.
Les codes R pour lire les bases sont les suivants
> training <- read.csv2( + "http://freakonometrics.free.fr/training.csv") > dim(training) [1] 100021 20 > pricing <- read.csv2( + "http://freakonometrics.free.fr/pricing.csv") > dim(pricing) [1] 36311 15
Tout le monde peut participer, inutile d’être inscrit à la journée pour m’envoyer quelque chose ! Par contre, je veux (comme indiqué dans le descriptif) une base avec le numéro de police, et la prime proposée, mais aussi le code et un rapide descriptif de la méthodologie, et des variables utilisées. Rendez-vous en Novembre pour l’analyse des résultats du jeu.
Modeling Dynamic Incentives: Application to Basketball
I will give a talk on “Modeling Dynamic Incentives: Application to Basketball” at the GERAD (Groupe d’études et de recherche en analyse des décisions) on June, 10th June, 6th. This is some joint work with Nathalie Colombier and Romuald Elie
An important aspect of the strategy of most organizations is the provision of incentives to the employees to meet the organization’s objectives. Typically this implies tying pay to performance (see Prendergast, 1999). In order to reward employees for their effort, firms spend considerable resources on performance evaluations. In many cases, evaluation consists of comparing actual performance to a pre-defined individual target. Another frequently used format is relative performance evaluation. Relative performance evaluation may motivate employees to work harder.But it may also be demoralizing and create an excessively competitive workplace, which may hinder overall performance; see Lazear (1989). Determining the overall impact of relative performance evaluation is crucial for companies. Economic research on relative performance evaluation has mainly focused on the comparison of final performances between competitors,like in tournament theory, and on quantitative and subjective performance ratings (Lazear and Gibbs, 2009). In contrast, what happens during a competition and the impact of feedback frequency on effort have so far received little attention. Following Berger and Pope (2011), we decided to use a basketball application to get a better understanding of the role of the feedback information. Sports datasets allow to observe score and team behavior continuously (during a game but also during the season) which can be use as a proxy of the effort. Berger an Pope (2010) asked ”can loosing lead to winning ?” looking at the impact of the halftime score difference on winning probability in NCAA (college) and NBA (pro) games. More precisely, they studied whether a team loosing at halftime is more likely to win than expected using a logit model. They find that usually the higher the score difference the more likely the are to win. But if the halftime score difference is around 0 they observe a discontinuity: loosing with a small difference (e.g. down by 1 point) can lead to increase the effort and win the game. In this paper we try answer the question ”when loosing lead to winning ?”.
Basketball: score dynamics and game theory
Tomorrow morning, I will be giving a talk at Mont Tremblant, for the Journées de la Société Canadienne de Sciences Economiques. I will present a joint work – in progress – with Nathalie Colombier and Romuald Elie. Since the working paper is not online yet, I will wait a little bit before uploading the slides. But they will be online, someday (hopefully soon)…
“An important aspect of the strategy of most organizations is the provision of incentives to the employees to meet the organization’s objectives. Typically this implies tying pay to performance (see Prendergast, 1999). In order to reward employees for their effort, firms spend considerable resources on performance evaluations. In many cases, evaluation consists of comparing actual performance to a pre-defined individual target. Another frequently used format is relative performance evaluation. Relative performance evaluation may motivate employees to work harder.But it may also be demoralizing and create an excessively competitive workplace, which may hinder overall performance; see Lazear (1989). Determining the overall impact of relative performance evaluation is crucial for companies. Economic research on relative performance evaluation has mainly focused on the comparison of final performances between competitors,like in tournament theory, and on quantitative and subjective performance ratings (Lazear and Gibbs, 2009). In contrast, what happens during a competition and the impact of feedback frequency on effort have so far received little attention. Following Berger and Pope (2011), we decided to use a basketball application to get a better understanding of the role of the feedback information. Sports datasets allow to observe score and team behavior continuously (during a game but also during the season) which can be use as a proxy of the effort. Berger an Pope (2010) asked ”can loosing lead to winning ?” looking at the impact of the halftime score difference on winning probability in NCAA (college) and NBA(pro) games. More precisely, they studied whether a team loosing at halftime is more likely to win than expected using a logit model. They find that usually the higher the score difference the more likely the are to win. But if the halftime score difference is around 0 they observe a discontinuity: loosing with a small difference (e.g. down by 1 point) can lead to increase the effort and win the game. In this paper we try answer the question ”when loosing lead to winning ?”.“
When should I optimally shoot at my son ? (part 2)
Following my previous post of yesterday, online here, assume now that I do not know if my son came when I turned my back at time, and missed me… Then the payoff function is the one propose by Vincent, i.e.
In that particular case,
becomes
i.e.
If we draw those functions, on [0,1], the optimal value is solution of 
i.e. 
(we focus only on solutions in [0,1]). Because here the game is symmetric, my son should also shoot at time 
Thus, the payoff is then
Since we consider here a zero-sum game, this cannot be a solution of the game. So the game does not have pure strategy solution.
Assume that now I have a mixed strategy, i.e. a distribution of the optimal time to shot. My strategy has distribution 
, with density 
(we assume here that the density exists, or we seek only solution that are differentiable). Assume further that there exists 
>0 such that the support of my optimal shooting time (the time to shoot is now a random variable) is (,1] (or [,1] since we assume that is differentiable). There is a discussion at the end of Vincent’s post where he needs that assumption, at the end. Actually, I think we can make it now, since we can rationally assume that
I will not shot at time 0 (even on a neighborhood of 0 since I have zero chance to hit my son).
The expected payoff function, assuming that my son shoots at time y is
Since the zero-sum game is symmetric, again, the expected payoff should be zero. It comes that necessarily,
if 
. Hence, if we differentiate (with respect to y), we have
and if we differentiate one more time, it comes
i.e. a general solution should be of the form 
.
Here, we have the same solution as the one considered in Vincent’s blog. His solution is obtained as follows (with slightly different expressions) conditional to 
, my expected payoff is
i.e.
With a simple integration by parts,
where 
, i.e.
Thus,
So, if we want to be indifferent to ‘s strategy, 
, where
with 
,
Consider solutions 
, then 
=1, i.e. either 
=1 and then 
is constant, or =-1. This means that 
is in proportional to 
.
If we substitute in the equation we had, initially, it comes that
i.e.
If we consider =a and =1, it comes that =1/3 while 
=1/4 (but we don’t really care about that normalizing constant).
It means that we should not start shooting before 1/3 of the tank is fulled. Actually, it makes sense, since
if <1/3 (while 
=0 if >1/3).