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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

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

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

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

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

Cox, Robertson, and Smith (CSW): Theoretical and Observed Sales Prices

Experimental Economics


Empirical regularities

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

Constant Relative Risk Aversion

  • Arrow-Pratt’s Relative Risk Aversion

  • Power Utility Function: U(y) = y r

Experimental Economics


Two equations

Two Equations

  • Bid Function:

  • Power Utility Function:

Experimental Economics


Foregone income

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

Foregone Income: An Example(Cox, Robertson and Smith’s Experiment)

Experimental Economics


Foregone income metric 1 harrison s experiment

Foregone Income: Metric 1Harrison’s Experiment

Experimental Economics


Foregone income metric 2 harrison s experiment

Foregone Income: Metric 2Harrison’s Experiment

Experimental Economics


Experimental design

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

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

Responses

?

Experimental Economics


Responses1

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


Responses2

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

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

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

A Question

Is Glenn Harrison’s article bad for experimental economics?

Experimental Economics


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