Question
\nPROBLEM SET 2
\nEcon 650
\n1. WATSON Chapter 7, Exercise 2.<\/p>\n
2. Differentiated Bertrand Competition. There are two firms i = 1, 2 simultaneously
\nchoosing prices pi ? [0, 1]. The demand of firm i is Di (pi , p?i ) = 1 ? 3pi + p?i and
\nit has zero production costs. That is, firm i\u2019s payoff is pi Di (pi , p?i ).
\n(a) Find the best response function of firm i.
\n(b) Find the set of 1-rationalizable, 2-rationalizable and 3-rationalizable strategies.
\n(c) Do you think there is a unique rationalizable strategy profile? Justify your
\nanswer.<\/p>\n
3. Consider the following Guessing Game. There are n = 10 players simultaneously
\nchoosing a number in {1, 2, 3}. The winners are those closest to 1\/2 the average
\nguess (they evenly split the prize between the winners if there is more than one).
\nFind the set of rationalizable strategy profiles. Justify your answer.<\/p>\n
4. Two players find themselves in a legal battle over a patent. The patent is worth 20
\nfor each player, so the winner would receive 20 and the loser 0. Given the norms of
\nthe country they are in, it is common to bribe the judge of a case. Each player can
\nsecretly offer a bribe of 0, 9 or 20, and the one whose bribe is the largest is awarded
\nthe patent. If both choose not to bribe, or if the bribes are the same amount, then
\neach has an equal chance of being awarded the patent. (If a player decides to bribe
\nthen the judge pockets it regardless of who gets the patent).
\n(a) Derive the game matrix.
\n(b) Is the game dominance solvable? If so, find the strategy profile surviving
\nIDSDS. 1<\/p>\n","protected":false},"excerpt":{"rendered":"
Question PROBLEM SET 2 Econ 650 1. WATSON Chapter 7, Exercise 2. 2. Differentiated Bertrand Competition. There are two firms i = 1, 2 simultaneously choosing prices pi ? [0, 1]. The demand of firm i is Di (pi , Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-237130","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/237130","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=237130"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/237130\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=237130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=237130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=237130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}