1. Consider a voting game between two members of a three-member commission. This commission has two potential proposals it can either accept or reject. Member A loves proposal X and will definitely vote for it; she'd prefer that proposal Y didn't pass, but she may or may not also vote for it. The chairperson loves proposal Y and is definitely voting for it; he also likes proposal X, but may or may not vote for it. The commission also includes Member B, who will definitely vote against both X and Y. A proposal will therefore be accepted only if both Member A and the chairperson vote for it. The normal form for this game is represented below (with higher numbers representing more favorable outcomes).

a. Commission votes are taken in the following way: Members A and B announce their votes and then the chairperson announces his. Identify the dominant strategies (if any).

Member A Vote for X only Vote for X and Y Chair Vote for Y only 1,2 3,1 Vote for X and Y 2,4 4,3