Section B Please answer ONE question. 3. Consider a standard die-roll experiment

Question

Section B Please answer ONE question. 3. Consider a standard die-roll experiment where subjects roll a fair six-sided die in private and are paid according to the outcome that they report: E1 if they report "1"; £2 if they report "2", E3 if they report "3"; E4 if they report "4"; E5 if they report "5"; E6 if they report a) What is the optimal reporting strategy of an individual whose utility is equal to: where r is the outcome reported, t is the number truly drawn by the individual, and 8/10 and ,-1/4 b) Discuss the extent to which a model combining fixed and co explain the experimental evidence on lying aversion.

Explanation / Answer

Optimal strategy is to report outcome observed that is r= t

We have utility function equals to r when revealed outcome is true

Or we have utility function is r-theta1-theta2(r-t)^2

Let's assume that if we can have highest outcome if we don't reveal true outcome

Then utility will be maximised when function is maximised with respect to r

Then FOC will be

1= theta2*2(r-t) we have theta2=1/4

2=r-t

r= 2+t

Which shows if he needs to deviate from true outcome

For example if r=5 and t=2 then utility will be 5-0.8-0.25(3)^2=1.95 that is less then t hence no equilibrium. Similarly if r-t =5 then U=6-0.8-0.25(25)=-1.05

Hence if r-t =2 then U= r-0.8-0.25(4)=r-1.8=t+2-1.8=t+0.2 >t

Therefore if he needs to deviate from true outcome then he should report t+2=r

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