Pre-auction Investments by Type-conscious Agents

1. Pre-auction Investments by Type-conscious Agents William S. Lovejoy (UM) Joint with Ying Li (Texas A&M) and Sudheer Gupta (Simon Fraser)

2. University of Michigan Ross School of Business Operations and Management Science How did we get here? Operations Research 1940’s World War II OR teams 1950’s IE/OR; LP; Queues 1960’s Heady times

3. University of Michigan Ross School of Business Operations and Management Science How did we get here? Operations Research Business Schools 1940’s World War II OR teams Business school situation 1950’s IE/OR; LP; Queues Ford and Carnegie Foundations 1960’s Heady times Production and Operations Mgmt Self-referential

4. University of Michigan Ross School of Business Operations and Management Science How did we get here? Operations Research Business Schools 1940’s World War II OR teams Business school situation 1950’s IE/OR; LP; Queues Ford and Carnegie Foundations 1960’s Heady times Production and Operations Mgmt Self-referential 1970’s Toyota Production System

5. 1970’s Toyota Production System 1980’s Self-doubt and experimentation 1990’s Regaining the faith, with new humility “You’re only as good as your problems”

6. University of Michigan Ross School of Business OMS Departmental Strategy We will conduct problem-driven research, with senior managers as the intended consumer of our research ideas.

7. Industry Academics Furniture Co. Cost of complexity Glass Mfg. Customer portfolios UM Health System Investments in capacity UMHS and Pharma Pharmaceutical pricing Energy Trading Co. Trading on capacity

8. Applied context Applied paper Theoretical issues Theoretical paper(s)

9. Level 1 Trauma Center 16 surgical services 25-27 operating rooms on main campus $2 billion/year in charges 40% charges directly from OR 80% if including support and follow-on

10. Patient flows preparation operation OR 1 Surgical Demand Holding area OR 2 ASU OR 24 OR 25 discharge discharge PACU General care beds discharge ICU recovery

11. 41% 92% preparation operation OR 1 Surgical Demand Holding area OR 2 ASU OR 24 OR 25 discharge discharge PACU General care beds discharge ICU recovery 81%

12. UMMC has a congestion problem What is the best way to expand capacity? Build new or extend hours? Different stakeholders want different things This is a political problem as well as a physics problem

13. UMMC has a congestion problem What is the best way to expand capacity? Build new or extend hours? Hospital profits Administration Delay to get on schedule Surgeons and staff Start time reliability Patients

14. Hospital profits Administration Surveys of surgeons and surgical staff Would you work an afternoon/evening shift? What would you want in return? Delay to get on schedule Surgeons and staff Start time reliability Patients

15. Cost of providing start-time reliability $ Start time reliability

16. Conclusions • 95% start time reliability and no bonus dominates building new OR’s (Start time reliability is a public good) • Bonus-only dominates for short time horizons (and is more sensitive to the make-up of the evening procedures)

17. UMMC has a congestion problem What is the best way to expand capacity? Build new or extend hours? These two options have different cost signatures Fixed cost optionsVariable cost options Build new buildings Extend hours, lease

18. Supply side competition Beaumont Cardiac bypass UMMC Children Trauma Burn Transplants Cardiac valves Cancer DMC Children Trauma Transplants Cancer HMO Ford Cardiac Trauma Burn Transplants Cancer St. Joe’s Cardiac Level 2 trauma Orthopedics

19. Classical “mechanism design” problem Agents Principal Hospital “type” (cost to serve the contract) known to each hospital Others believe these are drawn from a common-knowledge probability distribution. Knowing this distribution, the HMO declares a mechanism (rules of the game, for example a simple auction). Myerson 1981 Bayes’ Nash equilibrium Revelation Principle Revenue Equivalence

20. But, where does “type” really come from? Conscious investments Conscious investments Conscious investments Conscious investments “Type” is endogenously generated by firms investing in technologies, knowing they will face an auction for supply contracts.

21. Previous work on pre-auction investments Loury 1979 R&D stopping time Firm Conscious investments R&D stopping time Firm Conscious investments Lowest gets V R&D stopping time Firm Conscious investments R&D stopping time Firm Conscious investments Symmetric equilibria Overinvestment due to congestion externality

22. Dasgupta 1979, Piccione and Tan 1996 Random cost Firm Conscious investments Random cost Firm Conscious investments Self-interested buyer designs mechanism Random cost Firm Conscious investments Random cost Firm Conscious investments Symmetric equilibrium exists for sufficiently high Underinvestment due to opportunism by the principal “Sufficiently high” V is very high!

23. Current paper Fixed and variable cost Random type Firm Conscious investments Self-interested buyer designs mechanism Fixed and variable cost Random type Firm Conscious investments Fixed and variable cost Random type Firm Conscious investments Fixed and variable cost Random type Firm Conscious investments Firms know “managerial type” prior to making investments Asymmetry of course Firms may have existing levels of historical investment Focus on the equilibrium cost signatures in the bidding pool

24. Health care contracting exercise • You will be given a cost structure, keep it secret • An HMO is asking each of you to bid on a health care contract to provide care for a known pool of patients • You know the demographic mix and expected cost per patient. • You pay your fixed costs whether or not you get the contract. • If you get the contract, you incur additional variable costs.

25. Health care contracting exercise Fixed costs Additional cost to serve contract above fixed cost $711,000 $1,290,000 If you don’t get the contract, your total profits are - $711,000 If you win the contract your total cost is $711,000 + $1,289,000 = $2M. If you win contract with a bid of $2.1M your total profit is $.1M = $100,000

26. managerial type yi Fixed and variable cost Firm Investment level k Fixed cost gi(k) Self-interested buyer designs mechanism managerial type yi Fixed and variable cost Firm managerial type yi Fixed and variable cost Firm Variable cost to serve contract vi(k,y) managerial type yi Fixed and variable cost Firm Mechanism (p,x) declared based on induced distribution of types Fi(vi(gi(y),y)) Action = investment strategy gi(yi)

27. Known properties of an optimal mechanism Fixed and variable cost Self-interested buyer designs mechanism Fixed and variable cost Fixed and variable cost Fixed and variable cost Mechanism (p,x) declared based on induced distribution of types Fi(vi(gi(y),y))

28. Myerson 1981: Optimal mechanism design given Fi(n) ICDR mechanisms = probability hospital i will get contract if bid vector is = expected payment by hospital i if bid vector is HMO asks for bids ni from each hospital and chooses p to maximize and then set the expected payments as follows: (cost plus information rents) (non-increasing)

29. Derived properties of an optimal investment strategy managerial type yi Firm Investment level k Fixed cost gi(k) managerial type yi Firm managerial type yi Firm Variable cost to serve contract vi(k,y) managerial type yi Firm Action = investment strategy gi(y)

30. Facing mechanism (p,x), agent i knows her cost structure y and chooses an investment level k = gi(yi) to maximize Gi(y) is non-increasing in y (again, from I.C.) Vi(gi(y),y) is strictly increasing in y gi(y) > kiL (global min of g) always No “rent” to the highest “type” so

31. Putting these together An equilibrium is possible No pure strategy equilibrium is possible

34. Defect here to kiL

35. Analytical Conclusions Previous work: Symmetric pure-strategy equilibria when Type-conscious agents: Above still holds, but No pure strategy equilibrium (of any sort) when

36. Applied context Applied paper Theoretical issues Theoretical paper(s)

37. Heuristic Observations An “optimal” mechanism squeezes agents and does the principal no favors. Complete observability begets minimal investment Pre-commitment can garner better results The principal can probably do better with “sub-optimal” behavior, but once you open that can or worms you will have difficulty shutting it.

38. Discussions with the UMMC contracting office The complicated computations in “optimal” mechanisms are not in evidence in conversation . . . Rather, descriptors suggest some mixture of a “relationship” and a second price auction as representing actual negotiations.

39. Existence and nature of mixed strategies n x m competitions Where do I go from here? Cooperation, special relationships in supply relations Values and trust in supply relations

40. Thank you