slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Pre-auction Investments by Type-conscious Agents PowerPoint Presentation
Download Presentation
Pre-auction Investments by Type-conscious Agents

Loading in 2 Seconds...

play fullscreen
1 / 40

Pre-auction Investments by Type-conscious Agents - PowerPoint PPT Presentation


  • 71 Views
  • Uploaded on

Pre-auction Investments by Type-conscious Agents. William S. Lovejoy (UM) Joint with Ying Li (Texas A&M) and Sudheer Gupta (Simon Fraser). University of Michigan Ross School of Business Operations and Management Science. How did we get here?. Operations Research.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Pre-auction Investments by Type-conscious Agents' - leane


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Pre-auction Investments by Type-conscious Agents

William S. Lovejoy (UM)

Joint with Ying Li (Texas A&M)

and Sudheer Gupta (Simon Fraser)

slide2

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

slide3

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

slide4

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

slide5

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”

slide6

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.

slide7

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

slide8

Applied context

Applied paper

Theoretical issues

Theoretical paper(s)

slide9

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

slide10

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

slide11

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%

slide12

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

slide13

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

slide14

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

slide16

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)

slide17

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

slide18

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

slide19

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

slide20

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.

slide21

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

slide22

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!

slide23

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

slide24

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.
slide25

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

slide26

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)

slide27

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))

slide28

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)

slide29

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)

slide30

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

slide31

Putting these together

An equilibrium is possible

No pure strategy equilibrium is possible

slide35

Analytical Conclusions

Previous work:

Symmetric pure-strategy equilibria when

Type-conscious agents: Above still holds, but

No pure strategy equilibrium (of any sort) when

slide36

Applied context

Applied paper

Theoretical issues

Theoretical paper(s)

slide37

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.

slide38

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.

slide39

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