# Extensive Form - London School of Economics

Frank Cowell: Microeconomics March 2007 Exercise 10.15 MICROECONOMICS Principles and Analysis Frank Cowell Ex 10.15(1): Question Frank Cowell: Microeconomics purpose: Develop simple model repeated-game model of duopoly method: Find profits in cooperative and competitive cases. Build these into a trigger strategy. Ex 10.15(1): Bertrand game Frank Cowell: Microeconomics Suppose firm 2 sets price p2 > c

Firm 1 then has three options: 1= 0, if p1 > p2 1= [p2 c][k p2 ], if p1 = p2 1= [p2 c ][k p2 ], if p1 = p2 For small profits in case 3 exceed those in the other two it can set a price p1 > p2 it can match the price p1 = p2 it can undercut, p1 = p2 > c

The profits for firm 1 in the three cases are: implies that there exists an > 0 such p2 > c firm 1 undercuts firm 2 by a small and captures whole market If firms play a one-shot simultaneous move game firms share the market set p1 = p2 = c Ex 10.15(2): Question Frank Cowell: Microeconomics method: Consider joint output of the firms q = q1 + q2 Maximise sum of profits with respect to q Ex 10.15(2): Joint profit max Frank Cowell: Microeconomics

If firms maximise joint profits the problem becomes choose k to max [k q]q cq The FOC is k 2q c = 0 FOC implies that profit-maximising output is q = [k c] M Use inverse demand function to find price and the (joint) profit are, respectively p = [k + c] M Use pM and qM to find price (joint) profit: = [k c]2 M

Ex 10.15(3): Question Frank Cowell: Microeconomics method: Set up standard trigger strategy Compute discounted present value of deviating in one period and being punished for the rest Compare this with discounted present value of continuous cooperation Ex 10.15(3): trigger strategy Frank Cowell: Microeconomics The trigger strategy is Example:

at each stage if other firm has not deviated set p = pM if the other firm does deviate then in all subsequent stages set p=c suppose firm 2 deviates at t = 3 by setting p = pM this triggers firm 1 response p = c then the best response by firm 2 is also p = c Time profile of prices is: firm 1: 1 pM 2 pM 3 pM 4 c

5 c ... firm 2: pM pM p c c t Ex 10.15(3): payoffs Frank Cowell: Microeconomics

If is small and firm 2 defects in one period then: If the firm had always cooperated it would have got M M [ + 2 + 3 +...] Simplifying this becomes 2 = M Present discounted value of the net gain from defecting is

for that one period firm 2 would get the whole market so, for one period, 2 = M thereafter 2 = 0 M [1 2] / [1 ] So the net gain is non-positive if and only if 1 Ex 10.15(1): Points to remember Frank Cowell: Microeconomics Set out clearly time pattern of profits Take care in discounting net gains back to a base period.

## Recently Viewed Presentations

• Motivating Active and Group Learning Steve Wolfman University of Washington CCSC-NW 2002 Why Active and Group Learning? Flagging attention [McConnell's meds, Bligh's heart rate/memory] Critical/Higher-order thinking [Bloom's Taxonomy] Varied learning styles [Felder's Learning Styles] Constructivist knowledge building "ZoPeDs" [Vygotsky's Zones...
• Absorbance vs Volume EDTA Volume EDTA mL * End Point Determination Equivalence point occurs at intersection of the two straight lines 1. Graphical measurement 2. Algebraic approach. Set rhs of two equations equal, solve for x (where x = volume...
• Network Tomography: II Goal: obtain detailed picture of end-end behavior from internal views network design From internal observations, infer end-end application-level behavior traffic flows workload characterization Traffic Analysis Many applications have well known protocol/port (in packet header) 21 - ftp,...
• While it is getting easier to log into some EHRs at any time from almost anywhere, this is not a requirement for 2014 EHR certification; therefore, CMS should revise this requirement to provide more flexibility for practices. ... Uwe Reinhardt,...
• La mijlocul anilor 1960, cântece precum Papa's Got a Brand New Bag i-au adus porecla "Soul Brother No.1". Brown a avut peste 100 de hituri în SUA şi influenţa lui poate fi auzită şi astăzi în hip-hop, rap şi jazz.
• I can identify the root words in Protestant Reformation and understand their meaning. I can explain what an indulgence is and how it evolved into an abusive practice. I can identify who Martin Luther was and what he wrote. I...
• The Edexcel Board, for example, require that: students to sign the Candidate Record Form (CRF) to confirm that the work submitted is their own you to confirm on the CRF that the work assessed is solely that of the student...
• Online bill payment is a convenient tool to pay bills via ACH credit through a bank's website. From the convenience of their home, or wherever they are, and from the same trusted bank platform they make other payments, customers can...