ECS1050.09.post

ECS1050.09.post - Unit IV: Thinking about Thinking Choice...

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Unit IV: Thinking about Thinking Choice and Consequence Fair Play Learning to Cooperate Summary and Conclusions 7/28
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Learning to Cooperate The Bar Problem The Logic of Collective Action Changing the Rules of the Game The Problem of Trust Limits of Strategic Rationality Tournament Update
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[H]umans, in economic decision contexts that are complicated or ill-defined use not deductive, but inductive reasoning. That is, in such contexts we induce a variety of working hypotheses or mental models, act upon the most credible, and replace hypotheses with new ones if they cease to work. Inductive reasoning leads to a rich psychological world in which an agent's hypotheses or mental models compete for survival against each other, in an environment formed by other agents' hypotheses or mental models -- a world that is both evolutionary and complex. Inductive reasoning can be modeled in a variety of ways. “Inductive Reasoning & Bounded Rationality,” Arthur, AER, 1994 The Bar Problem
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The Bar Problem (Arthur, 1994) Each week, a group of people decide whether or not to go a particular bar. Space is limited, so when too many people go, no one enjoys the experience. There is no way to know for sure how many will attend, but a person will “go” if she expects less than X show up “stay home” if she expects more than X to go
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The Bar Problem There is no obvious (deductive) model to predict attendance. Common expectations are self-defeating If all believe few will go, all will go If all believe many will go, none will go “Oh that place is so crowded, nobody goes there any more” – Yogi Berra
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The Bar Problem Let’s assume there are 100 people who might go to the bar on particular night, and an individual will go if she expects less than 60 to attend, stay home , if she expects 60 or more. Each individual can form several predictions as a function of past attendance. For example, attendance over the past w weeks might be: …44 78 56 15 23 67 84 34 45 76 40 56 22 35
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The Bar Problem …44 78 56 15 23 67 84 34 45 76 40 56 22 35 They may have predictors such as: predict next week’s attendance to be the same as last week’s [35] a mirror image around 50 of last’s week [65] 67 [67] a (rounded) average of last 4 weeks [49] the trend in last 8 weeks [29] the same as 2 weeks ago (2-period cycle detector) [22] the same as 5 weeks ago (5-period cycle detector) [76] etc….
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…44 78 56 15 23 67 84 34 45 76 40 56 22 35 Each agent can only keep track of a subset of possible predictors. She decides to go or stay home based on the most accurate predictor in her current set (the active predictor ). After all decisions are made, each agent learns the new attendance and updates her active predictors. The process might look like this:
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ECS1050.09.post - Unit IV: Thinking about Thinking Choice...

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