Production Games Strategic Behaviour The problem with this analysis is that firms ignore the behaviour of their competitors Consider the short run and suppose there were just two firms. Suppose D(p)= l-p and AC=0 for simplicity. If firm A operates in monopolistic competition, they think they face half the demand: Da(p)=(1-p)/2.They roduce at MR=MC. The inverse demand curve is p= 1-2yA. So MR=1-4yA. They produce at 1-4yi=0 This gives: y*= 1/4. Suppose firm B takes this into consideration. Then the actual inverse demand B faces is AyB=1-1/4-yB and not 1-2yB. Profit maximisation will yield a different quantit In fact, firm B would set MR= MC which yields: 3/4-2yg=0 giving yi= 3/8 Notice if firm B took monopolistic competition profits they would get g= 1/8 With strategic behaviour however, firm B gets TB=(1-1/4-3/8)3/8=9/61. This is better Consider the long run. Is there a way to prevent other firms from entering and hence maintaining positive profits? Game theory is the study of strategic behaviour. A game is three things: 1. Players: The individuals(consumers or firms ete. )involved. 2. Strategies: Each players choice set- what they can do 3. Payoffs: The utilities or profits which depend on the strategies all of the players take Anything which has these three features can be described as a game. Game theory is a useful language for describing all kinds of situations- but that is not allProduction — Games 3 Strategic Behaviour • The problem with this analysis is that firms ignore the behaviour of their competitors. • Consider the short run and suppose there were just two firms. Suppose D(p) = 1 − p and MC = 0 for simplicity. • If firm A operates in monopolistic competition, they think they face half the demand: DA(p) = (1 − p)/2. They produce at MR = MC. The inverse demand curve is p = 1 − 2yA. So MR = 1 − 4yA. They produce at 1 − 4y ∗ A = 0. • This gives: y ∗ A = 1/4. Suppose firm B takes this into consideration. Then the actual inverse demand B faces is 1 − y = 1 − yA − yB = 1 − 1/4 − yB and not 1 − 2yB. Profit maximisation will yield a different quantity. • In fact, firm B would set MR = MC which yields: 3/4 − 2yB = 0 giving y ∗ B = 3/8. • Notice if firm B took monopolistic competition profits they would get πB = 1/8. • With strategic behaviour however, firm B gets πB = (1 − 1/4 − 3/8)3/8 = 9/64. This is better. • Consider the long run. Is there a way to prevent other firms from entering and hence maintaining positive profits? Production — Games 4 Games • Game theory is the study of strategic behaviour. A game is three things: 1. Players: The individuals (consumers or firms etc.) involved. 2. Strategies: Each player’s choice set — what they can do. 3. Payoffs: The utilities or profits which depend on the strategies all of the players take. • Anything which has these three features can be described as a game. • Game theory is a useful language for describing all kinds of situations — but that is not all