Econ 3542: Experimental and Behavioral Economics Exam #1 Review Questions

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1 Econ 3542: Experimental and Behavioral Economics Exam #1 Review Questions Chapter 1 (Intro) o Briefly describe the early history of market experiments. Chamberlin s original pit market experiments (1948) at Harvard were intended to show the imperfections in monopolistically competitive markets. One of his students, Vernon Smith was a subject in the original experiments, and did his own market experiment experiments, adding centralized information feedback and repetition. Smith s experiments helped show the amazing competitive tendencies of the double auction institution. o Suppose you design an experiment to examine the effects of communication (i.e., communication or no communication) on players in a simple game. You run experiment sessions with 16 subjects per session, and in all cases Treatment 1 is the communication treatment, and Treatment 2 is the no-communication treatment. What problem do you see with this design? There is no counterbalancing of the treatment order. So, every time there is a no-communication treatment, it is also the case that subjects are more experienced in the game and have perhaps learned. The proper design would run half the experiments in each treatment order o Why do context-laden experiments (as opposed to using neutral-language in instructions and setup) run the risk of loss-of-control to the experimenter? Context in the instructions or scenario of an experiment may possibly bring back past experiences or other social confounds. For example, suppose a simple bargaining experiment is cast as one subject being management and the other being union (context is quite common to most business simulations). If one subject used to be a militant union member, then this may create an unmeasurable confound affecting that subject s bargaining decisions. Chapter 2 (Pit Market) o Describe two different market institutions (and what we mean by institution in this context) One would be the double auction institution (buyers make bids and sellers make asks, and bilateral trades are made). Another is a postedoffer market (sellers post take-it-or-leave-it offers to buyers). A third would be a call market (bids and asks are collected, arrayed into pseudo supply and demand curves to determine the market clearing price. All trades occur at the market clearing price) o Setup the parameters for a market experiment if you will have 3 buyers, 3 sellers, and you want to have a predicted equilibrium price of $ and quantity traded of Q*=6. Draw this market setup. (hint: you need to decide what buyer values and seller costs to use, and how many units each buyer and seller can trade). The following setup will work (though so would many others). 3 buyers who can each buy up to two units. Buyers have value of $12 for the first unit and $11 for the second unit. Sellers can each sell up to 3 units, and

2 each seller has costs of $8 for the first unit, and $ for their second and third units. The graph of this parameterization looks as follows (the width of each step indicates the numbers of units at that value or cost). P S Q Chapter 3 (simple games) o Define dominant strategy, dominant strategy equilibrium and Nash equilibrium. DS: a strategy that s best no matter what the other player does. DS equilibrium, is an equilibrium when both players are playing a dominant strategy. Nash equilibrium is a simultaneous best-response. Each player is doing the best she can given what the other player is doing. o Design a simple two-strategy simultaneous move game that has a (pure strategy) Nash equilibrium, but no dominant strategies for either player. The following game has one pure strategy Nash equilibrium (Up, Left), but no dominant strategy for Player 1 (please verify) [sorry, it is not possible to make it such that neither player has a dominant strategy, but yet there is still a pure strategy Nash equilibrium Player 2 Left Right Player 1 Up 2, 1 0, 0 Down 0, 0 1, -1 Chapter 4 (risk and decision-making) o Use a simple graph of one s utility function to show how diminishing marginal utility (i.e., a concave utility function) results in risk averse behavior. Suppose Bob has utility function U(x)=x 1/2. Bob faces a gamble with 75% chance of getting $2,000,000, versus a 25% chance of getting $1,000,000. The expected value of this gamble is $1,750,000, but you can calculate to find that Bob would get the same utility out of receiving $1,728,721 with certainty as with the gamble. So, he is willing to accept less than the expected payout of this gamble to avoid the risk Bob is risk averse. D

3 U(x) U(2,000,000) Bob s utility function U(x)=x 1/2.75*U(2,000,000) +.25*U(1,000,000) U(1,000,000) 1,000,000 2,000,000 x 1,718,721 o Does it matter if we use hypothetical or real payoffs (or high or low payoffs) in experiments? (You can answer this specifically for risky choice experiments, but it is an important question for any experiment really). Results from lottery choice experiments show that individuals tend to display more risk aversion for real versus hypothetical payoffs, and a lot more risk aversion when the real payoff stakes are high (say, $0 average payoff or more). So, payoff factors do seem to matter, and may lead one to do payoff scale treatments in other experiments as well. Chapter 5 (games with randomized strategies) o Consider the payoff matrix below that one could use to describe the final penalty kick during the shootout that determined the winner of the 1999 Women s World Cup (the U.S. won, by the way). U.S. Kicker Kick to Goalie s right Kick to Goalie s left Chinese Goalie Dive to the right 0, 0 -, Dive to the left -, 0, 0 Show that there is no pure strategy Nash equilibrium in this game, and calculate the mixedstrategy (i.e., randomized) equilibrium. Draw the reaction functions that graphically depict the mixed-strategy equilibrium (you ll notice that, fundamentally, this is nothing more than a game of matching pennies). If the Chinese goalie has expected payoff to diving right as q*0 + (1-q)*(-) = q-, and the expected payoff of diving left is now q*(-) + (1-q)*0 = -q, then she will dive right as long as the expected payoff is higher for doing so. In other words, she ll dive right if q- > -q, or q > ½. Similarly, the U.S. kicker will kick to the goalie s right when p < ½. So, as long as p 1/2 the U.S. kicker has a dominant strategy, and as long as q 1/2 the Chinese goalie has a dominant strategy. We can depict this situation in the simple graph below.

4 P (Chinese Goalie) Penalty Kick Game 1 1/2 Goalie Reaction Kicker Reaction 1 q (U.S. Kicker) 1/2 and you can see that the only equilibrium is a mixed strategy equilibrium where is each is taken with probability ½ (by both players). o Without doing any calculations (they would be real hard!), use intuition to describe what the mixed-strategy equilibrium is for the game of rock-paperscissors. This is like a 3-strategy version of matching pennies. Intuition likely tells us that we should play each strategy 1/3 of the time. This is the randomized (mixed-strategy equilibrium) play Rock, Paper, and Scissors each with probability 1/3. Chapter 6 (Monopoly and Cournot) o How can we evaluate the efficiency of Monopoly market experiment outcomes? Does this efficiency tell us about the fairness of the outcomes? Efficiency can be examined in any market experiment by looking at the total earnings of buyers and sellers (aggregated together), and comparing that to the total possible market surplus. Market surplus (i.e., buyer plus seller gains to trades made in the market) is a measure of well-being of all market participants. This total market surplus is maximized at supply=demand free-market outcome for most markets. So, comparing actual surplus to the maximum possible is a natural measure of efficiency. o Suppose you want to design a Cournot experiment (i.e., 2 seller market). If you set it up so that market demand is P=12-Q (P is market price, and Q is the market quantity determined by both firms production, or Q=q 1 +q 2 ), and each firm has marginal cost equal to 2. What are the reaction functions of each firm? (hint: because MC=2 for both firms, the reaction functions will be symmetric). What is the predicted Cournot outcome? Market demand can be rewritten as P=12-Q or P=12-q 1 -q 2. From Firm 1/s perspective, its total revenue function is therefore Pq 1 =(12-q 1 -q 2 )q 1 or TR=12q 1 - q 2 TR 1 -q 1 q 2. So, Firm 1 s marginal revenue MR1 = =12-2q 1 -q 2. Similarly, we q1 TR can find that marginal revenue for Firm 2 is MR2 = =12-2q 2 -q 1. So, Firm 1 q2 maximizes profit by setting MR 1 =MC 1, which implies 12-2q 1 -q 2 =2. So, Firm 1 s reaction function can be written as r 1 (q 2 ) q 1 =5-(1/2)q 2. Similarly, we can solve for Firm 2 s reaction function q 2 =5-(1/2)q 1. We simultaneously solve by substituting one into the other, so q 1 =5-(1/2)[5-(1/2)q 1 ]=3.33. So q * 1 =3.33 and we can then solve to find q * 2 =3.33 also. This is shown in the graph below (note: you

5 should rewrite Firm 1 s reaction function as q 2 =-2q 1 to have it in slopeintercept form for the graph below). q 2 r 1 (q 2 ) 5 * q 2 =3.3 Cournot (Nash) equilibrium r 2 (q 1 ) q 1 * =3.3 5 q 1 Chapter 8 (Market Power) o Think about three somewhat distinct experiments that could all be used to examine the general issue of market power (think about games too) Monopoly experiment Cournot experiment Prisoner s dilemma (which mimics duopoly a bit) Market experiment with few sellers relative to buyers (and perhaps a Posted-Offer Institution Market experiment with communication allowed between sellers o Suppose a market experiment is designed so that the number of sellers is small relative to the number of buyers. What type of trading institution might you use for the experiment, and why? Probably a Posted-offer market, because this most closely simulates most retail market institutions o What results related to price convergence paths have market experiments shown when the elasticities of supply and demand differ greatly (i.e., the design of supply and demand is unbalanced in some sense)? prices tend to converge towards equilibrium in a way that balances actual surplus earned. That is, if supply is more elastic than demand, then prices converge to equilibrium from above, whereas they converge from below is demand is more elastic than supply (these are typical results from double auction experiments, at least) Chapter 11 (Asset Markets) o Describe the difference between a rational versus an irrational asset market price-bubble. A rational bubble would be one where prices trade above fundamental value of the asset, but not more above that the best possible dividend draws might reward. If price trade even higher than what one could possibly earn back on the best possible dividend draws, then we could say the bubble is irrational (although, in a different sense you might argue that it should be called rational, because you might rationally expect that someone else will still buy the asset from you at an even higher price.the bigger idiot theory)

6 o Graph the design of a 5-round asset market experiment where there is no redemption value for shares held at the end of round 5 (they re worth zero). In each round, however, a dividend is drawn at the end of each round and will pay either a high ($2.00) or low ($1.00) dividend for each share a trader holds. There is a 50% chance that either high or low dividend will be drawn, so the expected dividend is $1.50 per share in each round (the dividend draw occurs in round 5 also). Show the fundamental value of each asset share in your graph, along with the rational vs. irrational bubble boundary. $ $ rational bubbles in here irrational bubbles out here fundamental value most optimistic fundamental value (assuming best possible dividends every round) Rounds