Outline

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 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 Experimental Economics

3. Game Theoretic Predictions • Risk-neutral Nash equilibrium (RNNE) • The winner is the person who has the highest xi (efficient allocation) • Mean sales price and variance are: 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: Experimental Economics

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

7. Constant Relative Risk Aversion • Arrow-Pratt’s Relative Risk Aversion • Power Utility Function: U(y) = y r Experimental Economics

8. Two Equations • Bid Function: • Power Utility Function: 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) Experimental Economics

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

11. Foregone Income: Metric 1Harrison’s Experiment Experimental Economics

12. Foregone Income: Metric 2Harrison’s Experiment 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 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? Experimental Economics

15. Responses ? 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) 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). 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. 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?) Experimental Economics

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