Managerial Economics Game Theory Aalto University School of Science Department of Industrial Engineering and Management January 12 – 28, 2016 Dr. Arto Kovanen, Ph.D. Visiting Lecturer

 We have considered three models of industrial structures, monopoly, pure competition, and monopolistic competition (everything in between)  In the last two cases the action of each firm depends on the actions of other firms  We can assume that the actions of other are given to a firm if each firm is relatively small  When there are few firms, each firm constitute a rather large part of the market; this is called oligopoly General considerations

 When there are only two firms, the structure is called duopoly  With few firms in the market, strategic interaction between the firms become an important part of the outcome  In what follows, we discuss alternative strategic interactions between firms and how they impact production and pricing decisions  To limit the power of oligopolies, there are public policy issues which we discuss later General considerations

 Game theory analyzes strategic interaction  Payoff matrix describes the strategic interaction  Assume two individuals  Person A will write one of two words on a piece of paper, “top” or “bottom”  Simultaneously, person B will independently write words “left” or “right” on a piece of paper  Suppose that the payoff matrix of the game will be Person B LeftRight Person ATop 1,20,1 Bottom 2,11,0 Game theory

 What will be the outcome of the game?  For person A it is always better to say “bottom”  For person B it is always better to say “left”  In this game, there is a dominant strategy: bottom/left  This will be also the equilibrium strategy  However, dominant strategies do not always happen  Suppose there is no dominant strategy for the game  Then the optimal choice depends on what the player thinks the other person is going to do Game theory

Person B LeftRight Person ATop 2,10,0 Bottom 0,01,2  Nash equilibrium: a pair of strategies where A’s choice is optimal given B’s choice and B’s choice is optimal given A’s choice  Neither person know what the other is going to do, but can have expectations about it  In the above table, the combination of “top”/”left” is a Nash equilibrium (this is optimal for both) Game theory

 The Nash has some problems:  First, there may be more than one equilibrium (choice “bottom”/”right” is a feasible)  Some games have no Nash equilibrium  See also:  Mixed strategies: pure and mixed  Prisoner’s dilemma  Repeated games  Sequential games Game theory

 Prisoner’s dilemma – payoff matrix (years in prison) Prisoner B ConfessDeny Prisoner AConfess-3, -30, -6 Deny-6, 0-1, -1  What is the best outcome?  If both deny, they would of course be best off! Is it credible?  If one denies, the other one is better off by confessing  Lack of coordination important for the outcome! Game theory

 Problem is how to coordinate the actions!  This applies to a wide range of economic and political situations  Arms control: if there is no way of making a binding agreement, both sides end up deploying missiles  Cheating in a cartel: if you think the other side will stick to the agreed quota, it will pay off to produce more than your own quota Game theory

 Sequential games  There are situations where one player gets to move first and then the second player responds (Stackelberg)  B chooses Left (1,9) A choosesTop  B chooses Right (1,9)  B chooses Left (0,0) A chooseBottom  B chooses Right (2,1) Game theory

 To analyze this game, work backwards  If player A chooses “Top”, B’s choice does not matter for his payoff (1, 9)  If player A chooses “Bottom”, it matters what B chooses  But player A is better of choosing “Bottom”  Practical example: monopoly fights to avoid entrance of a new firm in the market (“pre-emptive” action)  Could also apply to a oligopoly where a dominant firm encourages entry by lowering the threshold price below cost for others (for instance, Saudi oil and US shale gas) Game theory

 This model is relevant for markets where two firms are competing, but also applies to markets with few firms (e.g., Coca-Cola and Pepsi)  Firms produce homogeneous products  There are many buyers  Each firm determines its output based on the other’s action (estimated)  Example. Let market demand be P = 400 – 2*(Q1+Q2)  Each firm has MC = $ 40 and no fixed costs Game theory – Cournot model

 Profits of each firm are as follows: π1 = (400 – 2Q1 – 2Q2)Q1 – 40Q1 = 360Q1 – 2Q2 2 – 2Q1*Q2 (The second firm has a similar profit function)  Solve for optimal output for firm 1: dπ1 = dQ1 = 0, which gives us Q1 = 90 – 0.5Q2  Note that firm 1 does not know the value of Q2 with certainty and therefore has to estimate it (e.g., based on total market demand forecast in which Q2 would be a residual) Game theory – Cournot model

 The equilibrium is found in the intersection of the firms’ optimal positions (which depend on the other firm’s reaction function)  That is, solve for Q1 = 90 – 0.5Q2 Q2 = 90 – 0.5 Q1  Since firms are identical, the optimal Q1 = Q2 = 60 for both firms  Given total production of 120, P = 400 – 2*120 = $ 160  Illustrate the strategic interaction between these firms in the market Game theory – Cournot (cont.)

 The game changes a bit if one of the firms is a “leader” while the other is a “follower”  For the follower the optimal outcome is the same as above (i.e., follower is taking into account the leader’s possible action)  The leader, on the other hand, does not account for the follower’s action when determining its output  P(L) = 400 – 2*[Q(L) + (90 – 0.5*Q(L))]  = 220 – Q(L) π(L) = (220 – Q(L))*Q(L) – 40*Q(L), which gives us Q(L) equal to 90 (which is higher than 60 above) Game theory – Cournot (cont.)

 The follower will then produce Q(F) = 45 and P = $ 130  Comparison to Cournot equilibrium, we observe that  P is lower  Q(L) is higher and Q(F) is lower  Profits of the leader are higher and profits of the follower are lower  Total industry profits lower because total output is higher and hence price has to come down in equilibrium  Examples of market leaders: Is Apple a market leader in smart phone markets (not homogeneous products and what is means for pricing)?  Homogeneous products: Banks and cuts in loan rates? Game theory – Cournot (cont.)