**Econ 243 September 30, 2015**

**Cooperation and Net Present Value**

• “A bird in the hand is worth two in the bush.”

– more precisely, P dollars today is worth P(1+r)^{2} dollars in two years, where “r” is the rate of return.

→ alternatively, if we have π^{M} dollars two years from now, that is worth (present value) PV = π^{M}/(1+r)^{2} dollars today

» if we put that PV in the bank, two years’ compounding gives us π^{M}

– we use this constantly when thinking about strategy: if we do something today, how does the cost (benefit) up front compare with the benefit (cost) down the road?

• fact: if r > 0 then for t = 1 to t = ∞ we have ∑ 1/(1+r)^{t} = 1/r (geometric series)

» This bio as president of THE American Political Science Association was written by Elinor Ostrom, a subsequent Nobel Laureate in economics.

– I can’t find my copy; the internet is wonderful! Of the 14 programs in his competition, the “tit-for-tat” of the (well-known) psychologist Anatol Rapaport won.

– Axelrod did his PhD in the late 1960s, but his seminal paper on this topic was from 1981 and his book from 1984: The Evolution of Cooperation (Basic Books).

» His book is by the way both short and a good read.

– details the “all quiet” phenomenon in WWI and otherwise noted that despite incentives that would seem to obviate cooperation, cooperation is in fact widespread. his work influenced social scientists across disciplines, and stimulated work by population ecologists and behavioral biologists.

– Tit-for-Tat: adopt the strategy of the previous period

» as usual for strategy, Tit-for-Tat is successful only in certain types of “Prisoner’s Dilemma” settings and depends on the details of how the tournament is conducted: Is Tit-for-Tat the Answer? On the Conclusions Drawn from Axelrod’s Tournaments

• let’s look at an even simpler two-firm price war strategy:

→ cooperate both today and henceforth or

→ betray today and face retaliation tomorrow and henceforth

– so we compare two firms splitting profits π^{M} now and henceforth

→ ∑ π^{M}/(1+r)^{t} = ½ π^{M}/r versus

→ π^{M} + 0 thereafter

» a bit of arithmetic: you always cheat for r > ½ as the future matters little

• generalize

– more willing to cooperate if profits are growing

» ([1+g]/[1+r])^{t} is always bigger than 1/(1+r)^{t}

– more willing if interact frequently: 1/(1+r/f) if you set prices f times a year

– more willing to cooperate if interact across multiple markets, especially when their positions are asymmetric [strong some, weak others]

» easy to see if you think about a price war across all product lines: in the management meeting about launching the new strategy, those with profitable and growing product lines will complain vociferously!!

» SABMiller and InBevAB have premium, regular and discount brands; cereal companies interact across an array of products

– less willing to cooperate if obsolescence is at hand

• for Friday: OK, but how do you cooperate?