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# Outline - PowerPoint PPT Presentation

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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Presentation Transcript
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

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

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