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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. First-Price Auctions. N bidders, individual values are i.i.d. draws from
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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
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
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
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
Cox, Robertson, and Smith (CSW): Theoretical and Observed Sales Prices Experimental Economics
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
Constant Relative Risk Aversion • Arrow-Pratt’s Relative Risk Aversion • Power Utility Function: U(y) = y r Experimental Economics
Two Equations • Bid Function: • Power Utility Function: Experimental Economics
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
Foregone Income: An Example(Cox, Robertson and Smith’s Experiment) Experimental Economics
Foregone Income: Metric 1Harrison’s Experiment Experimental Economics
Foregone Income: Metric 2Harrison’s Experiment Experimental Economics
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
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
Responses ? Experimental Economics
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
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
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
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
A Question Is Glenn Harrison’s article bad for experimental economics? Experimental Economics