Question

5. (a) James and Anne have reached the final of a gameshow. The final game is worth a total of €5,000. Each player has the option of sharing the prize money ("share") or keeping all of the prize money for themselves ("keep"). If both James and Anne vote "share", they each get 2,500. If they both vote "keep", neither player gets any money. However, if one player votes "share" and the other player votes "keep", the player who votes to share gets 1,000 and the person who votes to keep the money gets 4,000. [4 marks] i. Represent this game in normal form. ii. Is there a dominant strategy in this game? If so, state the dominant strategy. 1 mark i. Are there any Nash equilibria in this game? If so, identify it (them). If not, explain why not. 5 marks (b) Frank wishes to invest on investing all of the money in one company only.) The amount of money he will make depends on the economic conditions over the next year. The following table shows the amount of money Frank could make or lose in each a sum of money in one of three companies. (He intends case: Economic Conditions Stable Declining Growing €3,000 €3,700 €3,600 Company A €2,000 Company B€2,400 Company C€1,000 €800 - 400 €500 Apply the mini-max regret approach to determine the company in which Frank should invest his money. [10 marks

Answer 1

motatons dome rinst denote et us 5. (a) Jk James James 'shane J Anne shane Ak Anne shane A is heprisentes The arme Anne AK As 1000, 4000 JA2500, 2500 James Jk 4000, 1000 0 0 dominant frategy ND, mo HRis game Naoh ilibria Fining Fhe pure indcate by HRe urdorlinas rakegy f James pure Fon every Anne npeies of dacst AK A J250D, 250000 400o JK4000DO0 radgy of James is ndicate) by Re undenlies Anne, Ra pur Azain, ron ery est fplies f pure Ak A& JA 2500, 25TD o00,4000 k tuo utls togethe two aahui bnia fratagy fon te game, JA, Ak) Pulting given teay and Jk

payaff The given table of Re game (b) Gnowing Declining Stable 3 000 80o 2000 A company company B 3 700 2400 3600 company C given try declining table ugnet He Now Мaxcтит Stalofe kursrasig 700 700 400 A ompany 1200 20 0 Con tomfamy B (oo 400 3 00 400 comfony negret table He maximum element of finot choose column and hen we determine HAe To a all elements off tRe coumn trm Aubrfract he maxinmum onR men /20D, q0o 100 Now Frank hld invest his money in Hence tompany c