Bounded Rationality Gerhard Riener Department of Economics University of Mannheim WiSe2014 Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 1 / 18
Bounded Rationality We have seen in the last week that people are not always as rational as assumed by standard economic models So it is a natural step to enhance economic modelling incorporate this limited rationality Bounded rationality Maintains the assumption of utility maximization under the constraint of limited cognitive ability Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 2 / 18
Beauty contest experiments How to detect boundedly rational behavior and its implication for decision making in strategic situations. Beauty contest games go back to Keynes General Theory (1936) Investors on financial markets parallel people in a newspaper beauty contest who try to guess what other people are guessing who is voted the most beautiful Keynes, 1936, p 154 We devote our intelligence to anticipating what average opinion the average opinion to be. Same logic is underlying beauty contests or guessing games experiments (Originally designed by Rosemarie Nagel, 1995) Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 3 / 18
The beauty contest game Generic rules Each of n players is asked to choose a number from the interval [0, 100] Winner is the person whose choice is closest to p times the mean of the choices of all players (for example p = 2/3) Winner gets a fixed prize of 10, in case of a tie the prize is split among those who tie Repetitions: With and without information of the average guess Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 4 / 18
Equilibrium in the Beauty Contest Game How to find an equilibrium? Iterated elimination of weakly dominated strategies for p=2/3 Any rational player would not choose a number larger than 100p, since it is dominated by 100p (which is always closer to p times the mean than any higher number) All numbers above 100p 2 are dominated by 100p 2 If players belive that others are rational and that they also believe that all are rational, they will not pick a number above 100p 3 and so on... until all numbers but zero are eliminated So all choosing 0 is the (unique) Nash equilibrium If only integers are allowed there is a second Nash equilibrium where all choose 1 Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 5 / 18
Experiments on the Beauty Contest Game Bosch-Domenech et al. (AER, 2002) compare results from three experiments run on different newspapers (Financial Times, Epansion and German Edition of Scientific American) Comparing newspaper experiments and lab experiments yields a test of the parallelism assumption of the lab and the field Newspaper addresses a more heterogeneous population than the typical student subject pool Some differences between participants from different newspapers Basic pattern similar to lab experiments Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 6 / 18
Results of the beauty contest game Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 7 / 18
Interpretation of the results People do not play the Nash equilibrium A potential process that can explain the observed pattern: Level-k reasoning Suppose you expect participants not to be smart or misundersand and simply choose a random number (level 0) Average will then be 50, so you should choose 2/3 times 50=33.3 (level 1) If you expect that everybody else to get this far in reasoning, you should choose 2/3 times 33.3=22.2 (level 2) If you expect that everybody else to get this far in reasoning, you should choose 2/3 times 22.2=14.9 (level 3) and so on and so forth... Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 8 / 18
Process of iterated best reply The optimal strategy depends on your belief of the reasoning capabilities of others Explanations given by newspaper readers support this logic So if you think that some people play purely random and others play a best response to random play (so 33) how much shall you contribute? Gives rise to a very different outcome than the pure Nash equilibrium Again beliefs over others rationality shape the outcome of the game Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 9 / 18
Remark on results Student participants had less time to prepare for results, so concluding that they are less smart is not valid Some of the newspaper readers ran this experiment themselves with friends before submitting the result, get closer to the winning number than theorists Differences between newspapers Financial Times: 18.91 Spektrum: 22.08 Expansion: 25.47 What do you guess the outcome would be among Bild readers? Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 10 / 18
Being smart helps but being too smart doesn t helps Knowing your opponents is even more important Rather complicated somebody so people belief that not everybody is fully rational in the first period. So this may give rise to a self-fulfilling prophecy. If everybody is full rational but beliefs that the others are not the outcome would still not be Nash (common knowledge of rationality is violated) Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 11 / 18
Beauty contest: Learning over Time Results over more than one period from various experiments Different variations of p with 4/3,.7, 2/3,.5 People quickly learn and make better choices and averages often converge to NE Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 12 / 18
Traveller s dilemma Two travellers have bought some identical antiques on vacation Both of their luggage gets lost on the return flight Airline wants to rduce the claims of the damage and says to them that thy consider claims between 2 and 100. Both will get compensation equal to the smaller claim. But the traveller who stated the larger claim would be fined 2 wheil the one stating the smaller claim will be rewarded 2 NE: Minimum, as it always pays to underbid the other Intuition: size of the fine matters Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 13 / 18
Experiments on the Travellers dilemma Capra et al Claims have to be between.8 and 2 Game is repeated for 10 rounds Between treatments on the fine/bonus R differs R=.05,.1.2,.25.5 and.8 Results All treatments quite far from equilibrium for small R they tend towards the maximum Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 14 / 18
Results Travellers Dilemma Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 15 / 18
Models of Bounded Rationality Players do not choose best response with probability one (as in Nash equi- librium). Players choose responses with higher expected payoffs with higher proba- bility better response instead of best responses. Players have rational expectations and use the true mean error rate when interpreting others actions. Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 16 / 18
Modify Nash equilibrium to incorporate realistic limitations to rational choice modeling of games. Provide a statistical framework (structural econometric approach) to ana- lyze game theoretic data (field and laboratory). If Nash had been a statistician, he might have discovered QRE rather then Nash equilibrium (Colin Camerer) Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 17 / 18
The Logistic Representation QRE has to make assumptions on the response function. You have to define a response function Pr(a i ) = exp[λ a i A i Pr(a i )u i (a i, a i )] a i A exp[λ i a i A i Pr(a i u i (a i, a i)] (1) Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 18 / 18
The choice of action becomes purely random as λ 0, whereas the action with the higher expected payoff is chosen for sure as λ Gerhard Riener (University of Mannheim) Bounded Rationality WiSe2014 18 / 18