Dynamic Games

Dynamic Games-Ransom Suppose that one citizen of your country is kidnapped and the raptors demand the payment of a ransom. The threat is that they will kill this person if they do not receive the money. Payoffs: The kidnapers ask $100. If they kill the person, there is a probability that the police will find them and they will go to prison. Assume that this risk has a (expected) cost for the Kidnapers of $50. If they kill the citizen the government has a cost of $100.

Ransom Pay Do not Pay P1 P2 Kill Do not Kill Kill Do not Kill (-200,50) (-100,100) (-100,-50) (0,0) Empty Threat

Entry Game Firm E (P1) is considering entering a market that currently has as single incumbent (P2). If P1 enters the incumbent can respond in two ways: accommodate the entrant, giving up some share of the market without cutting much the price, or it can fight the entrant by dramatically cutting the price, engaging in a predation war.

Entry Game In Out P1 P2 Accommodate Fight (2,1) (-3,-1) (0,2)

Oligopoly Problem Kodak and Fuji are the only producers of photographic films. Industry profits depend on industry-wide output in the following way. Profits are divided in the proportion of output: if Kodak produces 10 and Fuji 90, then Kodak gets $3.2 of profit and Fuji gets $32-$3.2. Suppose that each company can decide to produce 50, 75 or 100 (strategies). Q (industry) Profits

Oligopoly Problem-Simultaneous Game Kodak 16, Fuji 16 21,1420,10 14,2115,1512,9 10,209,125, Fuji Kodak The only Nash equilibrium is (75,75)

Oligopoly Problem-Dynamic Game Kodak Fuji (Kodak 16, Fuji 16) (14,21) (10,20) (5,5) Fuji (21,14) (15,15) (9,12) (20,10) (12,9)

Dynamic Games Backward induction. Flexibility versus commitment. Being flexible is not always preferred (because your opponent knows that you are flexible) (chicken game). Advantages of Playing First or Second. “Battle of the sexes” versus “rock, paper, Scissors”.