tthe questions are attached below.

._ 1. ,. ....... "EF"l QUESTION I You have been arrested for allegedly committing a very serious crime. Three judges. Alice, Beth and Clara {ont nowon referred toas A, B and C} have heard all the evidence and are now going to vote on tlse verdict. There are three possible verdicts: Acquittal. Life sentence and Death penalty. During the trial it has become common knowledge among everybody [in particular, you and the dueejudges} that thejudges' preferences over the possible verdicts are as follows: '"'___ A's ranking: 3': ranking: C's ranking: East Death Life neuronal Middle Life noqnitIsI Death Worst Acquitlal Dearth Life The legal system allowsme chooaet'he procedure by which thejudgeareach a verdict. There one three different procedures. All oftbern involve two stages: in Stage 1 thejudges simitltancously and secretly vote on a first issue; atthe end of'the rst stage. it is made public what the rst-stage votes were (in. which issue eschjudge voted for} and in Stage 2 there is a second simultaneous and secret vote on the second issue. in each stage the cmespcnding issue is decided by majority voting. The judges are strategic and the objective ot'eochjudge is to try to bring about an outcome 1tltl'tich is best according to her ranking. I. Innocenti'Guilty procedure [1G]. in this prose-dune the rst vote is on the issue of whether you are innocent or guilty. if a majority of the judges votes for innocence in the rst stage then the outcome is thatyouare acquitted; otherwisethe second vote is on which of the two punishments should be applied to you. 2. Sequential Punishment procedure {SP}. In this procedure the rst vote is on the issue of whether you should be sentenced to death: if a majority ofthejudges votes Yes, then the outcome is the death penalty. if a majority votes No in the rst stage then inthe second stage the vote isct'tthc issue ol'whetherycu should begiven a life sentence; ifs majority votes Yes, then the outcome is life in prison. otherwise the outcome is acquittal. 3. The Punishment Assessment procedure {PA}. in this procedure the rst vote is on which punishment is appropriate For the crime {whether you committed it or not]: life sentence or death penalty. The second vote is whether you are innocent (so that the outcome is acquittal} or guilty [in which case the outcome is the punishment picked in the rst vote by a majority of the judges}. (a) Represent the IG procedure as an extensive-form game-frame (a sufficiently informative sketch is enough; no need to write the payoffs). (b) Represent the SP procedure as an extensive-form game-frame (a sufficiently informative sketch is enough; no need to write the payoffs). (c) Represent the PA procedure as an extensive-form game-frame (a sufficiently informative sketch is enough; no need to write the payoffs). (d) For the PA procedure write down one of the strategies of judge A. How many strategies does she have? (e) For the IG procedure find a subgame-perfect equilibrium of the extensive-form game that represents it, by using - whenever possible - either the notion of dominant-strategy equilibrium (DSE) or the notion of Iterated Deletion of Weakly Dominated Strategies (IDWDS). (f) For the SP procedure find a subgame-perfect equilibrium of the extensive-form game that represents it, by using - whenever possible - either the notion of DSE or the notion of IDWDS. (g) For the PA procedure find two subgame-perfect equilibria of the extensive-form game that represents it, by using - whenever possible - either the notion of DSE or the notion of IDWDS. (h) Which procedure will you ask the panel of judges to use?