Managerial Economics Kyle Anderson Game Theory Managerial Economics Kyle Anderson Indiana University Kelley School of Business

Grading scheme: Choose a plan, Red or Blue. Matched with a classmate (anonymously). If you both choose the blue grade scheme, you both get an A-. If you both choose the red grade scheme, you both get a B. If you choose the blue scheme and your matched partner chooses red, you get a B- and your partner gets an A. If you choose the red scheme and your matched partner chooses blue, you get an A and your partner gets a B-. Which grade scheme do you choose?

Grading Game B+, B+ B-, A A, B- B, B Player 2 Two players Simultaneous moves Perfect information One-time game Blue Red B+, B+ B-, A A, B- B, B Player 1 Normal form

Grading Game 3, 3 1, 4 4, 1 2, 2 Player 2 Blue Red Player 1 Red is the better strategy for Player 1, regardless of what Player 2 does. Dominant Strategy Player 2 has the same dominant strategy. Nash Equilibrium – each player is doing as well as it can do given its rivals actions. Player 2 Blue Red 3, 3 1, 4 4, 1 2, 2 Player 1 Normal form A = 4, B+ = 3, B = 2, B- = 1

Nature of a game Frequency of movement Elements Nature of movement One-shot game Finitely repeated game Infinitely repeated game Nature of movement Simultaneous-move game Sequential move game Elements Players Strategies Payoffs Information Rationality

Pricing Game Simultaneous move, one-shot game Two firms, each firm picks a price level (high or low), products are close substitutes. Firms have some fixed costs.

Pricing Game 0, 0 40, -10 -10, 40 10, 10 Heron low price Heron high price Anderson low price 0, 0 40, -10 Anderson high price -10, 40 10, 10 What strategies should the firms’ pursue? *Anderson’s payoff is listed first, followed by Heron

Prisoners’ Dilemma Heron low price Heron high price Anderson low price 0, 0 40, -10 Anderson high price -10, 40 10, 10 One or more of the firms has a dominant strategy. Pursuing the dominant strategy leads to an outcome that is sub-optimal for the players. Of course, what is sub-optimal for the firm(s) may be optimal for others (i.e. customers).

Games with 3 or more options Bar 2 $2 $4 $5 Bar 1 10 , 10 14 , 12 14 , 15 12 , 14 20 , 20 28 , 13 15 , 14 13 , 28 25 , 25 in thousands of dollars If P2 plays $2: 5 > 4 > 2 Dominated Strategy: one that always leads to a lower payout than another available strategy. If P2 plays $4: 4 > 2 > 5 If P2 plays $5: 4 > 5 > 2

Simultaneous Move Game Two players, each with a choice between Yellow and Blue. If they both make the same choice, they earn $1. If they don’t match, they earn $0. September 21, 2018

Coordination Game Yellow Blue 1, 1 0, 0 How many NEs are there?

Simultaneous Move Game Two players, each with a choice between Yellow and Blue. If they both choose Yellow, Player 1 gets $5 and Player 2 gets $1. If they both choose Blue, Player 1 gets $1 and Player 2 gets $5. If they don’t match, they earn $0. September 21, 2018

Coordination Game, sort of Player 2 Yellow Blue Player 1 5, 1 0, 0 1, 5 How many NEs are there?

Monitoring Game -1, 0 2, -5 0, 0 -2, 2 Business Pay taxes Shirk on taxes IRS audit -1, 0 2, -5 don’t audit 0, 0 -2, 2 How many NEs are there? There are no pure strategy NEs There is a mixed (randomized) strategy NE

Repeated Pricing Game 0, 0 40, -10 -10, 40 10, 10 Heron low price Heron high price Anderson low price 0, 0 40, -10 Anderson high price -10, 40 10, 10 What strategies should the firm’s pursue? *Anderson’s payoff is listed first, followed by Heron

Infinitely repeated game Cooperation may occur if the benefits of cooperating exceed benefits of cheating. Compare PV of cooperating with PV of cheating. Does it pay? Prof(cheat) = πcheat + πNash + πNash… Prof(coop) = πcoop + πcoop + πcoop…

Infinitely repeated game Does cooperation pay? As long as the discount rate is less than 1/3 (33%), then it is better to cooperate.

Simultaneous move games Why do hotels franchise? Compare NE in one-shot vs. repeated. Hotel – decent quality Hotel – low quality Stay 5, 5 -10, 10 Don’t stay 0, -5 0, 0

Sequential move games Accommodate 10, 10 Price War -10, 5 Enter Incumbnt Price War -10, 5 Enter Accommodate 0, 20 Don’t Newbie Incumbnt 0, 8 Price War Solve by Backward Induction – Last stage first What outcome do we expect? *Payoffs for Newbie are listed first

Three stage game What outcome do we expect? Can Player 1 do better? Fight -5, -10 Defend 1 2 Attack -1, 9 Retreat 1 Surrender 10, -5 Don’t 0, 10 What outcome do we expect? Can Player 1 do better?

Integer game Strategically choose an integer between 1-100. Submit that number to me. I will calculate the average of all the numbers. The winning number will be the number that is 2/3 of the average of all submissions. I will pay the winner $10.

Division game There is a potential joint venture between player 1 and player 2. The joint venture will net a total of $10. Player 1 gets to choose how that $10 is divided between the two players. Player 2 can then either accept or reject the offer. The game then ends without any negotiation. Kyle Anderson September 21, 2018