Game Theory for Managers Uncertainty and Information

Lecture 10 Game Plan „ Hidden actions, moral hazard, and incentives „ Hidden traits, adverse selection, and signaling/screening Hidden Information “A little knowledge is a dangerous thing. So is a lot.” - Albert Einstein Strategic Manipulation of Hidden Information „ Hidden Actions: Incentives • Associates others’ unobservable actions with observable outcomes „ Hidden Traits: Signaling & Screening • Associates others’ unobservable traits with their observable actions Incentives „ High hurdle and a lot of money „ Low hurdle and a little money Hidden Effort „ You are contracting a project to an outside firm. The project has an uncertain outcome „ „ „ Probability of success depends on firm’s effort • prob. of success = 0.6 if effort is routine • prob. of success = 0.8 if effort is high Firm has cost of effort • cost of routine effort = $100,000 • cost of high effort = $150,000 Project outcome = $600,000 if successful Compensation Schemes I. II. Fixed Payment Scheme Observable Effort III. Bonus Scheme IV. Franchise Scheme Incentive Scheme 1: Fixed Payment Scheme „ If firm puts in routine effort: • Profit = Payment - $100,000 „ If firm puts in high effort: • Profit = Payment - $150,000 „ „ Firm puts in low effort! Æ “moral hazard” Optimal Payment: lowest possible. • Payment = $100,000 „ Expected Profit = (.6)600,000 - $100 = $260K Incentive Scheme 2 Observable Effort „ „ Firm puts in the effort level promised, given its pay Pay $100,000 for routine effort: • E[Profit] = (.6)600,000 – 100,000 = $260,000 „ Pay additional $50K for high effort: • E[Profit] = (.8)600,000 – 150,000 = $330,000 Æ want to induce high effort „ Expected Profit = $330K Problems „ Fixed payment scheme offers no incentives for high effort • High effort is more profitable „ Effort-based scheme cannot be implemented • Cannot monitor firm effort Incentive Scheme 3 Wage and Bonus Suppose effort can not be observed „ Compensation contract must rely on something that can be directly observed and verified. „ Project’s success or failure „ •Related probabilistically to effort •Imperfect information Salary + Bonus Schemes A successful scheme must 1. Be “Incentive Compatible” „ Firm must prefer to put in high effort 2. Induce Participation „ Firm must prefer to take the job On-Line Game #7 Incentive Pay Incentives Cost of routine effort: „ Cost of high effort: „ Added cost of high effort: „ Benefit of routine effort: „ Benefit of high effort: „ Added benefit of high effort: „ $100K $150K $50K .6b .8b .2b Incentive Compatibility „ Firm will put in high effort if s + (0.8)b - 150,000 ≥ s + (0.6)b - 100,000 „ „ (0.2)b ≥ 50,000 marginal benefit > marginal cost b ≥ $250,000 Participation Expected salary must be large enough to make work worthwhile „ If induce high effort: b>$250K expected salary = s+.8b but even if s=0: .8b = $200K > $150K „ No base salary needed! „ Profitability Summary „ „ Greatest Profit from inducing high effort: $280K (unless s<0) Greatest Profit from inducing low effort: $260K „ „ „ „ „ Using the “no brainer” solution Salary = $100K, no bonus Do we want to induce high effort? Carefully. Don’t give away the farm to do it. Optimal Salary and Bonus „ Incentive Compatibility: „ „ Participation: „ „ Firm will put in high effort if b ≥ $250,000 Firm will accept contract if s + (0.8)b ≥ 150,000 Solution „ „ Minimum bonus: b = $250,000 Minimum base salary: s = 150,000 – (0.8)250,000 = -$50,000 Negative Salaries? Ante in gambling „ Law firms / partnerships „ Work bonds / construction „ Startup funds „ Interpretation „ „ „ $50,000 is the amount of capital the firm must put up for the project $50,000 is the fine the firm must pay if the project fails. Expected profit: (.8)600,000 – (.8)b – s = (.8)600,000 – (.8)250,000 + 50,000 = $330,000 „ Same as with observable effort!!! Incentive Scheme 4 Franchising „ Charge the firm f regardless of profits • Contractee takes all the risks and becomes the “residual owner” or franchisee „ Charge franchise fee equal to highest expected profit • Routine effort: .6(600K)-100K = 260K • High effort: .8(600K)-150K = 330K „ Expected Profit: $330K Summary of Incentive Schemes „ Observable Effort • Expected Profit: • Expected Salary: „ 150K Salary and Bonus • Expected Profit: • Expected Salary: „ 330K 330K 150K Franchising • Expected Profit: • Expected Salary: 330K 150K Upside of Assigning Risk Assign risk to the agent, the party that has control of the hidden action „ This leads to „ more efficient outcome „ more profit for the principal „ Downside of Assigning Risk „ Employees (unlike firms) are rarely willing to bare high risks „ Salary and Bonus • 0.8 chance: 200K • 0.2 chance: –50K „ Franchising • 0.8 chance: 270K • 0.2 chance: –330K Risk Aversion Risk Seeking Risk Neutral Lottery (small stakes) Risk Averse Corporations one-time deals Multiple Gambles Insurance (big stakes) Summary So Far „ „ Suppose you know agent’s payoffs but can’t observe its actions. You can still induce agent to take action you want by making it bear more risk „ „ „ Franchising Salary and bonus Such schemes can give as much profit as if you could observe actions perfectly! Venture Capital „ A venture’s success depends on whether a new technology will work 50% chance it works „ venture worth $20M if it works „ venture worth $0 if it doesn’t work „ „ Entrepreneur knows whether the technology works or not Venture Capital „ „ Entrepreneur approaches you: “I am somewhat risk averse and hence prefer to take a smaller than 100% stake” How much are you willing to pay if she offers you „ 50% stake? „ 90% stake? Problem of Adverse Selection „ Expected value of venture given that she wants to sell 50% • (50%*20 + 50%*0 ) = $10M „ Expected value of venture given that she wants to sell 90% • 100%*0 = $0M „ Because of this “adverse selection”, you are willing to pay less for a larger stake!! Problem of Average Selection „ Only “bad” entrepreneur is willing to sell 90% of venture „ „ But both “good” and “bad” are willing to sell 50% of venture „ „ adverse selection if you buy 90% average selection if you buy 50% Still not ideal: you only want to invest when technology works! Signaling & Screening Screen = “Jump over this while I watch” Signal = “Watch while I jump over this” High hurdle and a lot of money „ Low hurdle and a little money „ How to Screen „ Want to know an unobservable trait „ Identify a “hurdle” such that: „ „ „ „ those who jump the hurdle get some benefit but at some cost “good” types find the benefit exceeds the cost “bad” types find the cost exceeds the benefit This way we get self-selection: only “good” types will jump the hurdle Auto Insurance „ Hidden Trait = high or low risk? Half of the population are high risk, half are low risk „ High risk drivers: „ • 90% chance of accident „ Low risk drivers: • 10% chance of accident „ Accidents cost $10,000 Example: Auto Insurance The insurance company can not tell who is high or low risk „ Expected cost of accidents: „ • (½ .9 + ½ .1 )10,000 = $5,000 Offer $6,000 premium contract to make $1,000 profit per customer „ What happens? „ Self-Selection „ High risk drivers: • Don’t buy insurance: (.9)(-10,000) = -9K • Buy insurance: = -6K • High risk drivers buy insurance „ Low-risk drivers: • Don’t buy insurance: (.1)(-10,000) = -1K • Buy insurance: = -6K • Low risk drivers do not buy insurance „ Only high risk drivers buy insurance Adverse Selection „ Expected cost of accidents in population • (½ .9 + ½ .1 )10,000 = $5,000 „ Expected cost of accidents among insured • .9 (10,000) = $9,000 • Insurance company loss: $3,000 „ „ Cannot ignore this “adverse selection” If only going to have high risk drivers, might as well charge more ($9,000) Screening „ Offer two contracts, so that the customers self-select „ Compare contracts aimed at highand low-risk drivers. Which will have the higher premium? „ Which will have the higher deductible? „ “New Issues Puzzle” „ „ „ Firms conducting seasoned equity offerings (SEOs) afterwards perform worse on average than other firms Loughran and Ritter (J Finance 1995) argue you lose 30% over five years investing in a SEO 1970-1990 data. Comparison is relative to performance of “matched firm”, i.e. one having similar characteristics that did not have any SEO in the following 5 years SEO Underperformance For this table, please see Table II from: Loughran, Tim, and Jay Ritter. “The New Issues Puzzle” Journal of Finance 50, no. 1 (1995): 23-51. Is the market failing? „ „ Why doesn’t the market assimilate this information immediately? One possible explanation: positive selection „ „ “Matched firms” are chosen retrospectively to be firms that will not have any SEO in next five years Even if the market had already priced in the negative info, it might not have assimilated the (future) positive info about the matched firm! Signaling „ The seasoned offering is a signal about the status of the companies current projects as well as future ones. Seek outside equity LOW Fund projects internally HIGH Profitability of current/future projects … & Adverse Selection „ If the current projects are not profitable, the cost (in dilution) to the ownermanager of issuing new share is lower. „ Therefore, seasoned offering is likely associated with „ „ bad news about the firm’s present condition low threshold for profitability of new project. Dividends “It would be uneconomic as well as pointless [for firms to pay dividends and raise capital simultaneously]” - Merton Miller and Kevin Rock, 1982 Dividends „ Why might it be make sense for a firm to issue a dividend and for investors to view this positively? Bargaining with a Customer Customer either willing to pay $20 or $10, equally likely „ Your price is $15 (zero costs), but customer asks for a deeply discounted price of $5 „ You don’t know whether the customer has value $20 or $10 „ Bargaining with Customer “Nature” moves first Buy Don’t Don’t High Value (prob p) Give Discount Don’t Low Value (prob 1-p) Don’t Give Discount 0, 0 5, 15 Buy p = 50% 15, 5 15, -5 0, 0 5, 5 Information set represents that seller can’t distinguish whether buyer has high or low value Solving for “Sequential Eqm” Buy Don’t High Value (prob p) 15, 5 Don’t Give Discount 5, 15 Buy Low Value (prob 1-p) Don’t Don’t Give Discount 0, 0 5, 5 Seller’s equilibrium choice depends on its belief about likelihood of High Value vs. Low Value • By Don’t Discount, seller is “risking 5 to gain 10” • Don’t Discount if p > 1/3 Other Approaches? „ If a customer “pleads poverty” for a discount, you have other options than simply to grant/refuse request „ What else might you do? Clearance Sale 15, 5 No Sale Sale Value 20 (prob p) Clearance (q) 5, 15 Buy Now Wait Value 10 (prob 1-p) 14, 5 5q-1, 15q 0, 0 No Sale Sale Clearance (q) Running the Clearance Sale costs 1 5, 5 Buy Now Wait Product only available with prob. q for those who Wait -1, 0 5q-1, 5q Clearance Sale as Screen 15, 5 No Sale Sale Value 20 (prob p) Clearance (q) 5, 15 Buy Now Wait Value 10 (prob 1-p) 14, 5 5q-1, 15q 0, 0 No Sale Sale Clearance (q) 5, 5 Buy Now Wait -1, 0 5q-1, 5q Clearance is an effective screen if q < 1/3 Clearance Sale? Clearance Sale or Sale? 1/3 Clearance Sale or No Sale? p = Pr(High) p > 1/3: No Sale better than Sale „ p < 1/3: Sale better than No Sale „ When (not) to have Clearance Sale (p < 1/3) Clearance Sale or Sale? Clearance Sale or No Sale? 1/3 „ Clearance Sale vs. Sale „ „ „ p = Pr(High) Clearance gives +9 more on High Clearance loses 1 + 5(1-q) on Low Only have Clearance when chance of High is sufficiently large When (not) to have Clearance Sale (p > 1/3) Clearance Sale or Sale? Clearance Sale or No Sale? 1/3 „ Clearance Sale vs. No Sale „ „ „ p = Pr(High) Clearance gives –1 + 5q more on Low Clearance loses 1 on High Only have Clearance when chance of High is sufficiently low When to have Clearance Sale (p = 1/3) Clearance Sale or Sale? 1/3 „ Clearance Sale or No Sale? p = Pr(High) If Clearance is ever your best strategy, it must be when you are indifferent between Sale and No Sale (p = 1/3) „ “when you can’t decide whether to offer a High- or Low-Quality product, offer both!!” Versioning „ Suppose that high-quality/high-cost item will be equally profitable as low-quality/low-cost item „ In this case, you can always do better offering a menu of both items that acts as a consumer screen Versioning: Example Customer willingness -to-pay GOOD BAD PRODUCT PRODUCT HIGH CUSTOMER $35 $20 LOW CUSTOMER $20 $15 Good product costs $5, bad product $0 Versioning: Example HIGH CUSTOMER LOW CUSTOMER „ „ „ GOOD PRODUCT BAD PRODUCT $35 $20 $20 $15 Sell only Good Æ 2*($20-$5) or ($35-$5) Sell only Bad Æ 2*($15-$0) Sell both Æ ($15-$0) + ($30-$5) Good-quality vs. Bad-quality $35 $20 $35 or $20 $15 $15 Good-quality only = Consumer surplus Bad-quality only = Profit Menu of both = Cost Summary „ Strategic issues arise when different players have different information „ Moral hazard given hidden action „ „ Adverse selection given hidden trait „ „ role for incentives / tying one’s hands role for screening / signaling Next time: using hidden traits about yourself to make a credible commitment