The Evolution of “An Experiment on Exit in Duopoly”

Initial thoughts Began as a predatory pricing experiment We wanted multiple choice variables The ability to choose to voluntarily exit was certainly one A standard IO variable, such as quantity or price There was no “opportunity cost” treatment Fixed cost treatment with “pockets” drawn randomly from a probability distribution

When dreams become derailed … We wanted a theoretic model as a basis None really existed, but the Fudenberg and Tirole (1986) model provided a nice starting point We didn’t know how subjects would behave in this type of environment because …

Fudenberg and Tirole Model

Basic assumptions War of attrition between duopolists Each duopolist receives a cost, c i, from a known distribution over the range [c L, c H ] Both begin “in the market” earning the duopoly revenue, R D, each instant If one firm leaves, the remaining firm earns the monopoly revenue, R M, each instant Exiting firm stops paying costs Exiting firm cannot reenter Range of costs must be such that: c L < R D < R M < c H

F&T Equilibrium There must be some small probability that both firms are profitable in duopoly in order for the unique perfect Bayesian Nash Equilibrium to exist Eq. Strategy is a pair of functions, one for each firm, that specify a time, t *, a firm would exit for all possible costs in [c L, c H ], given that the other firm has not yet exited by t * Parameters R D =100, R M =400 HU ~ U[40,460] LU ~ U[95, 405]

F&T Model Predictions 1. Relatively inefficient firms exit sooner than relatively efficient firms (Darwinian property) 2. An exact time of exit for each cost draw 3. When there is a higher probability of a cost draw below R D (as c L decreases), exit occurs more quickly 4. The unique PBNE remains unchanged regardless of whether the cost is posed as a fixed cost or an opportunity cost

Designing the Experiment

Treatments In a treatment a variable change is made Isolate one variable (if possible) and change it to determine the impact of changing that variable Can have variables change Within a session (same subject, different variable level) – within-subjects design Across sessions (or subjects) – between-subjects design (a particular subject sees only one variable level)

Treatments High and low uncertainty draws HU – Uniform over [40, 460] LU – Uniform over [95, 405] Fixed cost (FC) versus opportunity cost (OC) FC – subjects receive a cash balance and profits are added to (or subtracted from) that balance until they exit OC – payoffs are always increasing, but the OC may be larger than the potential profit from monopoly

Parameter Choices An important aspect of experimental design is how or why the experimenter chooses a particular set of parameters. Sometimes what seems as the most trivial parameter choice can have a large impact on outcomes

Revenue levels of 100 and 400 Wanted Cournot levels for symmetric firms without fixed costs Predicted exit times were not dispersed enough, so had to change the ratio of the profit levels Why stop at 4:1? Why not 8:1? Time constraints – wanted to actually observe exit in the experiment

Cost distributions of uniform [40, 460] and [95, 405] Uniform distribution F&T model requires small probability that both firms are profitable in duopoly Upper bound is irrelevant theoretically, so we kept it symmetric about the revenue levels Chose +/- 5 for LU treatments – “epsilon” below 100 Chose +/- 40 for HU treatments – predicted exit times are different enough from LU, but we don’t have “too many” cost pairs less than 100 or greater than 400

Misc. parameters # of rounds (20) Time constraint # of subjects (10 or 12) Subjects might play each other 2 or 3 times Probability of a round ending (1%) Implied discount rate Pocket size in FC treatment 25,000 ECUs covered any of the predicted exit times without bankruptcy occurring

Final parameter decisions Ending times Cost draws and matching across treatments Payment method – random round draw Salience issue Avoid income accumulation effects

Screen Design What information do you want on the screen? How should the information be displayed? Charts, graphs, color, etc. What language do you use? What actions are allowed?

Prototype

Information on the prototype Per second accounting system Potential payoffs, costs, and total profits Elapsed time Exit button You can see when the other person exits But there’s a lot of charts and numbers …

Opportunity Cost Screen

Fixed Cost Screen

Instructions What do you want to tell your subjects? What DON’T you want to tell your subjects? How (what language do you use) do you convey these concepts to the subjects?

Results

Data Analysis It is important to consider how the data analysis will be done before running the experiment This is not to say that you can’t do something different after collecting the data, but it is a good idea to have thought about statistical/econometric procedures beforehand

Results – within treatments 1. Markets exhibit the 2 Darwinian properties 1. Inefficient firms tend to exit when the difference in cost draws is relatively large 2. Clear, inverse relationship between cost and exit time 2. When costs are relatively high, firms tend to exit markets at times consistent with the theory

Basic Behavioral Check Subjects with costs < 100 did exit This occurred 4 times out of a possible 136 Subjects with costs > 400 did not exit 11 instances where this occurred (out of 156) For 6 of those, the round ended in < 6 seconds For 3 of those, round time was between 9 and 13 seconds For the remaining 2, the other firm exited within the first 4 seconds, and they were not giving up that much (both were in OC sessions) Forced-out subjects 3 times out of 219 possible, all before round 9

Conclusion F&T model predicts well; subjects exit reasonably close to the predicted exit times when costs are high, less so when costs are low Starting point for future research – there seems to be little behavioral difference between the OC and FC treatments Giving subjects an endowment does little to change their behavior in this environment