experiment choice results and estimate subject utility from socials preferences model

[PRIVARD BRIN]

Dear Statlist member,

Could you help me to resolve this problem?

A subject X takes 5 distinct decisions over 5 periods.
The utility function of the subject X is represented by a function type
U (β) = constant or U (α) according to the periods. α and β represent social preference parameters (table 1)

My objective is to measure the weight of the parameters α and β on all 5 observations of the subject.
Which econometric test with notions of optimization (optimum parameters β and α) can be considered in this case?

Table 1 : Subject X utility estimate in 5 periods

Round 1	U= 13-1,8β
Round 2	14-1,2β
Round 3	0,6α+14
Round 4	0,2α-15,33
Round 5	15,66-0,8β

[PRIVARD BRIN]

Reminder :
The term with alpha "envy is a relevant parameter of disadvantageous inequality" measures the utility loss from disadvantageous inequality
The term with beta "the guilt parameter" measures the loss from advantageous inequality
Following assumption, our model combined with Ferh and Schimidt (FS) model assume that
β< α and 0<β<1