seminar2

Economics of Organization Seminar 2

Today was a seminar. I found it was easy but actually, not so easy.
But it is so interesting!!!

(a)
Owner　Invests if
－1－r+δ/1－δ＞－1
ｒ＜δ/1－δ＝－１＋１/1－δ＜２
And customer knows it. Therefore, the assumption is reasonable.

(b)
owner
she chooses not invest because r>p>2.
It can be said there is no open shop.

(c)
f=fee for a gun-man
owner's incentive constraint
(1-f)(1+δ+δ2+...)>0
(this is when f>1)

a gum-man's incentive constraint
-rg+nf(1+δ+δ2+...)>0
n>rg(1-δ)/δf

(d)
c means customer has additional cost (c)for rob.
custmer's constraint changes;
1+δ/1-δ>3-p+δ/1-δ-c
p>2-c
(if p>2-c, customer pays)
It means sometimes r become more than p( if r>2 and p+c>2, r=p+2 r-2=p r>p means punishment cost is larger than punishment itself)
This means sometimes shop owner punishes by himself. But gum-man may create threat to keep their business.


(e)(f)
Quite interesting!!!

(i)short-run thinking where no investment is sustainable
one game, sometimes chicken or prisoner dilemma.
(ii)long-run thinking where investment is occur if δ is sufficiently large
Communication is important. Reputation, gossip credibility are affect efficiency.
(iii)the idea of costly punishment
If there are punishment, negotiation become efficient. Society became bigger and bigger but sometimes efficiency is not reached because punishment is costly and waste and it also has a limit.
(iv)the idea of third-party punishment
Former situation causes professional enforcer and it contribute efficient negotiation. But it enforcer sometimes creates threat by himself because if there is no threat he goes out of business. It makes inefficient situations.
(v)the idea of democratic control over punishment
Democratic society provide police. It does not have incentive to create threat because their salary is decided other way, from tax. It makes most efficient society among five.

2.
(a)
If p1 commits s1, s2' maximum share is 1-s1. In this case, p2 commits 1-s1 as s2.
reverse is the same and this means it is Nash Equilibrium.

(b)
If p1 commits s1, s2' maximum share is 1-s1. In this case, p2 commits 1-s1 or flexible
But if p2 commit flexible at first, s1 commit 1 . This is not synmetrical.
It means it is not Nash equilibrium.

(c)
(i)
If p1 commits s1, s2' maximum share is 1-s1-c.
In this case, p2 commit flexible because 1-s1>1-s1-c.
But If p2 commit flexible at first, s1 commits 1. It means previous equilibrium can be reached no longer.
(ii)
If p1 commits 1 first, p2 commits flexible because there is no room.
If p2 commits flexible p1 commits 1. Its synmetrical, and Nash equilibria.
and vice versa because of the synmetrical condition.

(d)
(i)
(If c>0, s1+s2=1 is impossible)
Nash equilibriums are S1=S2=1, and B1=B2=1/2.
Player1:
Expected payoff of S1: c=commit, f=fail to commit, w=wait, (but there is no choice of p2=w because c>0)
(p1,p2)=(c,f)+(f,c)+(f,f)=q(1-q)1+(q-1)q+(1-q)(1-q)*b1-c
if p1 choose w, expected payoff is
(p1,p2)=q0+(1-q)b1


if p1 commits s1 and it works(with q), equilibria can be reached when p2 choose flexible or fail to commit(1-q).
(ii)
Probability of disagreement is qq, therefore, agreement is given by 1-qq.

(iii)
No. why is it?

(e)
Features which fits the disagreement;
・zero sum game(whole amount of teritory is fixed)
・2 players, commitment is done at the same time.
・commitment stick(because of political power???)


features not be captured by the model;
・third palty's infulence(U.N.,U.S,)(it is impossibe to
・repeated game(not finshed in only once)
・If s1+s2>1, benefit is not lose. Negotiation repeats.