1. January 29, 2004 Experimental Economics 1 Outline  In-class experiment on IPV First-Price Auctions  Data from Cox, Robertson, and Smith (1982)  Glenn Harrison’s (1989) Critique  Responses by Kagel and Roth (1992) and Merlo and Schotter (1992)  Key Lessons

2. January 29, 2004 Experimental Economics 2 First-Price Auctions  N bidders, individual values are i.i.d. draws from  Values are denoted by  Subject bids are  Subjects are risk-neutral

3. January 29, 2004 Experimental Economics 3 Game Theoretic Predictions  Risk-neutral Nash equilibrium (RNNE)  The winner is the person who has the highest x i (efficient allocation)  Mean sales price and variance are:

4. January 29, 2004 Experimental Economics 4 Example: (N=3, v=0.1, v = 4.90)  If 0.5, 2.3, 3.5 were drawn, then optimal bids would have been:  The winner is the person whose value is 3.5  Mean sales price and variance are:

5. January 29, 2004 Experimental Economics 5 Cox, Robertson, and Smith (CSW): Theoretical and Observed Sales Prices

6. January 29, 2004 Experimental Economics 6 Empirical Regularities  Subject bids are consistently higher than the risk- neutral Nash equilibrium (RNNE)  The data are consistent with game theoretic predictions if subjects are risk-averse and each has a different constant relative risk aversion (CRRA)

7. January 29, 2004 Experimental Economics 7 Constant Relative Risk Aversion  Arrow-Pratt’s Relative Risk Aversion  Power Utility Function: U(y) = y r

8. January 29, 2004 Experimental Economics 8 Two Equations  Bid Function:  Power Utility Function:

9. January 29, 2004 Experimental Economics 9 Foregone Income  Foregone Income = Income from Predicted Bid – Income from Actual Bid  Metric 1:  Assume other bidders are risk neutral and use equation (1) (E(r) = 1.0)  Bidders are risk neutral and use utility function (2) to optimize (r=1.0)  Metric 2:  Assume other bidders are risk-averse and use equation (1) (E(r) = 0.7)  Bidders are risk neutral and use utility function (2) to optimize (r=1.0)

10. January 29, 2004 Experimental Economics 10 Foregone Income: An Example (Cox, Robertson and Smith’s Experiment)

11. January 29, 2004 Experimental Economics 11 Foregone Income: Metric 1 Harrison’s Experiment

12. January 29, 2004 Experimental Economics 12 Foregone Income: Metric 2 Harrison’s Experiment

13. January 29, 2004 Experimental Economics 13 Experimental Design  Three Treatment Variables  Experience (Played once before versus none)  RNNE robots versus human subjects  Points versus dollars  Dependent variables (Bid deviation and foregone expected income)  Missing cells

14. January 29, 2004 Experimental Economics 14 Issues of Debate  Dependent variable: “message” versus “payoff” ?  Is constant relative risk aversion (CRRA) the “right” theory for explaining over-bidding in independent first-price auctions?

15. January 29, 2004 Experimental Economics 15 Responses ?

16. January 29, 2004 Experimental Economics 16 Responses  Experimental tests on “low-cost deviation” conjecture  Responses are not random (over-bidding)  Raise the costs of deviation: Increase the conversion rate (CSW) (no effect when conversion rate is increased by a factor of 3)  Other predictions of “low-cost deviation” conjecture  Increase the range should reduce “over-bidding” (Table 2 from KR)  Merlo and Schotter: Shape of the payoff function cannot have any effect on subject behavior unless they are able to perceive it either deductively before experiment or learn during experiment  Theorists (deductively either rightly or wrongly)  Choose what they predict is the optimal choice and persist in that choice  never learn about the actual payoff function  Harrison’s criticism would have no force  Experimentalists (learn)  subjects won an average of 4.1 times and there are simply no enough data for them to detect the flatness of the payoff function  Harrison’s criticism would hold little force (Table 1 in MS)

17. January 29, 2004 Experimental Economics 17 Responses  Experimental tests on “risk-aversion” theory  Can the same theory apply to other IPV auctions?  Second-price auctions: Dominant strategy to bid their value irrespective of risk attitudes (subjects consistently bid above their values by a small amount)  Multiple-unit discriminative auctions: Bids are significantly less than RNNE  What other predictions does risk-aversion make?  Profit earned as a % of predicted RNNE profit should decrease with increases in N (Table 4 from KR).

18. January 29, 2004 Experimental Economics 18 Camerer’s Review  In the kinds of tasks economists are most interested in, the overwhelming finding is that increased incentives do not change average behavior substantially (although the variance of responses often decrease)  There is no replicated study in which a theory of rational choice was rejected at low stakes in favor of a well-specified behavioral alternative, and accepted at high stakes.

19. January 29, 2004 Experimental Economics 19 Lessons  The power of replication (to verify a research finding)  Only robust research findings will survive  The power of control (i.e., super easy to test competing hypotheses)  Shift the focus of debate onto data  Knowledge accumulates based on experimental data not arm-chair theorizing  The boundaries of a theory (should a behavioral theory of first-price auctions generalize to second-price auctions?)

20. January 29, 2004 Experimental Economics 20 A Question Is Glenn Harrison’s article bad for experimental economics?