Industrial organization and strategy (5)

Gazprom because it’s a monopolist

in Russia and told them that if they

wanted to buy the British company

they should let other companies

enter in the market.

Gazprom refused and threated UE

that they would switch their gas

from UE to China.

UE didn’t accept anyway because this threat was

not credible because :

Because switching from a country to

another is very difficults, the tubes where

gas flow are very costly so building a brand

new structure was a very expensive. So at

the UE refused and ofc Gazprom didn’t

switch to china.

This threat was not credible.

With dyamic games we’ll start to

consider also when companies do

threats or promises which are way of

firms to say “if do this I’ll this this” and

to understand which are the credible

ones.

DYNAMIC GAMES WITH

COMPLETE COMPETITION. are

games where. In a dynamic game

players don’t play simultaneously

like Static games but

consequentially; first firm 1

plays, then firm 2, then firm 1 and

so on, so firms know what other

firms do and can act accordingly.

To represent such games we use

the TREE representation:

-Decisional nodes: the circle with

the number 1. It means that it’s

time for firm 1 to play and make a

move.

-Branch is the decision: firm 1 can play u or U

-Terminal nodes: black nodes where game ends. Next to the terminal node we find a parentesi

with 2 values: these are the payoff of player 1 and player 2

examples of a dynamic game with

complete information. Firm 1 can play u

or d and player 2 can play U or D.

Now we need to transform this game into

a the matrix representation we used in the

past chapter for Bonnie&Clyde. On the

row we have firm 1 and on columns firm 2

with their specific moves u,d, U, D.

We can calculate the nash

equilibrium as we did with the

matrix in the previous chatper

(RIFALLO, VERIFICA QUALI SONO I

NAS EQUILIBRIUM QUA) and we find

out we have 2 nash equilibrium:

(5,2) and (4,4). Now we ask: Is (4,4)

credible? This equilibrium can

happen for example when company

2 makes a threat to firm 1 saying “if

you play “u” I’ll play “D”” in this way they’re threating firm 1 because in that case firm 1 will get

1, but this is not credible because firm 2 will get zero invece if firm 2 plays U they will get 2, so

ofc this is not credible so the Nas Equilibrium (4,4) is not a good prediction of how this game

will end. So to find a nash equilibrium that is a

good prediction of how game will end

we need to find a new structure of the

game that takes into account the

threats in the game, so we use a

SUBGAME so we divide the game into

SUBGAMES which are portion of the

game containing only 1 decisional

node and the branch departing from

it. Now we need to find the SPNE which is

a nash equilibrium which is an

equilibrium for each one of the

subgames of the game. So for example

the nash equilibrium (4,4) which is

d(U,U) is not an equilibrium in subgame

1 because if player 2 plays (U,U) player

1 will never play “d” but “u” so it will be

u(U,U). so (4,4) is not SPNE. How we find an SPNE? We use the backward induction.

Ltt backward induction

We divide the game into

subgames. We start from the

ones having terminal nodes:

subgame 1,2 and 3.

-Subgame1: player 2 will

choose D because 3>1 so

solution here is (1,3,4)

-Subgame 2: (4,3,3)

-Subgame 3: (1,2,6)

Therefore the strategy of player 3 is (D’, U’) Then we substitute each subgame with the

payoff we found, as in this slide. Now we

have a new subgame4.

-subgame 4: (4,3,3)

Therefore the strategy of player 2 is

(D,U).

Finally we have the last subgame:

-subgame 5: (4,3,3)

Therefore the strategy of player 1 is (d).

The SPNE is [d, (D,U), (D’,U’)] and the

output of the game is (4,33).

This is how we apply backward induction

LEZIONE 05: DYNAMIC GAMES PART B Regole del gioco non tornano

con i numeri della slide. Nel PDF

c’è infatti un’altra slide con

numeri diversi, vedi da lì come

funziona il centipede game.

We have 6 moves of the two

players: to find a solution (SPNE)

of the game we can apply the

backward induction as we have

seen in the previous chapter. We

start from the last (6 ) node: since the player 2 prefers 5>4 the solution is to STOP so we

th

substitute this payoff (2,5) to the ramo “Continue” of the 5 move of player 1. Then since

th

player 1 prefers 3>2 the solution is to stop so we substitute this payoff (3,3) to the ramo

“Continue” of the 4 move of player 2. AND SO ON. We can see that for each one of the 6

th

moves, the solution is STOPPING ALWAYS, this is the SPNE. BUT we can see that players

actually get value by continuing (they start with 1,1 and they end at the 6 move with 4,4 so

th

they actually would prefer TO CONTINUE), but with the tools we have right now we cant find

the correct solution, so we’ll see this in chapter 6 because this is the fundamentals for

COLLUSION. Till now we have only focused on

games with complete

information. In the slide there is

a prisoner dilemma game with

incomplete information.

Whenever we see the dotted line

connecting 2 nodes of a player

(in this case of player 2) it