1. M ISCONCEPTIONS AND G AME F ORM R ECOGNITION : C HALLENGES TO T HEORIES OF R EVEALED P REFERENCE AND F RAMING Timothy N. Cason Charles R. Plott Presentation by: Martijn van der Geest

2. I NTRODUCTION Tension among competing theories regarding fundamental properties of preferences Standard theory of preferences: individuals have preferences over outcomes and those preferences are independent of the feasible set of outcomes Non-standard theories of preferences, such as preferences based on framing or endowments, hold that preferences are dependent on and/or even constructed from the context faced by the choosing individual and might have no validity outside that context

3. I NTRODUCTION Critics of standard theories point to the fact that choices in game-experiments are often inconsistent with standard preference theory Choices in experiments often change and do not seem utility maximizing This criticism assumes that choices reflect preferences, relies on the theory of ‘revealed preference’ Ignores the possibility that inconsistencies in choices might reflect systematic mistakes in game form recognition, Cason and Plott explore this

4. M ISTAKES, R EVEALED P REFERENCE AND F RAMING Misconception studied here is a “failure of game form recognition” It is a failure of the decision maker to recognize the proper connections between the acts available for choice and the consequences of choice If the decision maker doesn’t understand this connection preferences and choice cannot be equated

5. E XPERIMENTAL DESIGN Experiment similar to testing a scale by measuring a known weight The experiment employs the Becker, DeGroot and Marschak (1964; hereafter BDM) method to measure the preference for an object for which the subject’s preferences are known—a card that can be redeemed from the experimenter for $2

6. BDM METHOD The BDM mechanism has a long history of use as a tool for measuring preferences. Subject is required to state a value for an object, if buying exercise the subject is required to buy object if a randomly determined price is lower than sated value, if selling exercise subject receives randomly drawn price if higher than stated value Subject doesn’t determine price paid or received only whether it is paid or received, thus dominant strategy is to state subject’s true valuation Cannot lose by stating true value, only gain

7. BDM P LOTT C ASON DESIGN Plott Cason design is a bit unorthodox, instead of seeking subject’s valuation it gives them a valuation and tests whether their choices are consistent with this Inconsistent choices might point to a misconception of the consequences of the choices and this is tested The object used is a ticket for which the valuation is clearly defined, money

8. BDM P LOTT C ASON DESIGN Subject given a card which is stated to be worth $2, subjects has to offer a valuation. They are also told that there is an obscured posted price on the back of the card between 0, $p (p= random maximum in set [4,5,6,7,8] ) If the posted price is above the subject’s offer price the subject is paid the posted price and if not the subject is paid the $2 for the card Experiment is repeated without prior knowledge

9. BDM P LOTT C ASON DESIGN

10. R ESULTS Result 1: With simple instructions and no training or feedback, the BDM does not provide reliable measures of preferences for the induced-value object Result 2: A second round of decisions (including subjects re- reading the instructions and after receiving feedback) nearly doubles the number of subjects stating the correct valuation Result 3 : Subjects that chose the theoretically optimal offer price (near $2) on the first card also usually choose the theoretically optimal offer price on the second card. Subjects who did not choose optimally on the first card tend to choose a different offer price on the second card.

12. R ESULTS : D ATA P ATTERNS Result 4: For both the first and second round choices the pattern of non-optimal price offers are related to the maximum of the posted price range

13. R ESULTS : D ATA P ATTERNS Result 5: Subjects who were “exposed” to their mistake (in the sense that a different offer amount would have increased their payoff) were more likely to choose a correct offer in round 2.

14. Change in ratio for subjects exposed to error in round 1 (left) and those not exposed (right) The figures illustrate the movements toward and away from the optimal $2 offer using the ratio=(offer-$2)/(p- $2) Those exposed to the error move towards the optimum (lower ratio on the y axis, below the 45 degree line) much more consistently suggesting they correct their game form misconception

15. A LTERNATIVE MODELS Three classes of general theories can be evaluated and compared: A. theories based on framing; B. theories based on task understanding but with noise; C. theories based on specific game form misconceptions.

16. M ODEL : FRAMING Experiment cannot distinguish between framing and misconceptions, empirical implications similar Evidence for an endowment effect, there appears to be a WTA/WTP gap consistent with loss aversion Anchor and adjustment, subjects base frame on prominent features to access value, upper bound of the price range. Consistent with results Attraction to the maximum : similar in this case Expectation of trade, if subject does not expect to trade then loss aversion and high offer prices, like in the results

17. M ODEL : OPTIMAL CHOICE WITH NOISE Subjects may understand the BDM task but make errors Errors are cheap in BDM, only 28 percent of subjects who bid more than 5 cents from $2 suffered a monetary cost The higher the upper-bound price draw the lower the expected cost of a mistake due to lower probability

18. M ODEL : OPTIMAL CHOICE WITH NOISE This can be differenced from expected payoff when choosing the optimal offer price $2 for expected loss from mistake.

19. M ODEL : FAILURE GAME FORM RECOGNITION Departures from optimum are not due to framing but mistakes Mistakes are not random but due to game form recognition 29 subjects indicated they should have been paid their offer price even when it was lower, subjects may confuse game for first price auction rather than second price auction First auction price misconception is model that is tested Simplifies to:

20. C OMPARING MODELS To compare optimal model with noise and first price misconception models for the data a quantal choice framework with logit errors is used Lambda indicates how sensitive subjects are to differences in expected payoffs, higher is more sensitive – 0 means all offers equally likely. Higher lambda implies a better fitted model.

22. C OMPARING MODELS First price model performs significantly better for subjects not choosing the optimum price, lambda’s much higher and confidence intervals do not overlap for subjects possibly holding misconception. Models compared trough finite mixture model that estimates a probability θΜ that the 1 st price misconception best describes the data

24. C OMPARING MODELS Nearly two thirds of all the offers are more consistent with misconception model in first round For subjects that do not give optimum offer misconception model performs better in both first and second round, equally so for subjects who are most likely to have a misconception Subjects appear to be of at least two populations ; those who understand the game and behave as standard theory predicts, and those who suffer a first-price misconception and behave as if the lowest price wins

25. C ONCLUSIONS Choices cannot be reliably interpreted as revealing preferences, due the possibility of misconceptions Data generated by BDM can be mistakenly interpreted as supporting non-standard preferences. Because results consistent with game form misconception are also consistent with framing effects, misconceptions should be taken seriously Theory of misconceptions is problematic since it is no overarching consistent theory. Each case might suffer from different misconceptions dependent on the context