Teaching Game Theory to Kids and Limits of Prediction

Technical Report · Fri Jun 29 04:00:00 EDT 2018

DOI:https://doi.org/10.2172/1459605· OSTI ID:1459605

Outkin, Alexander V. ^[1]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

I have once been asked to read a lecture to a group of 6th graders on Game Theory. After agreeing to it, I realized that explaining the game theory basics to 6th graders my be difficult, given that terms such as Nash equilibrium, minimax, maximin, optimization may not resonate in a 6th grade classroom. Instead I've introduced game theory using the rock-paper-scissors (RPS) game. Turns out kids are excellent gametheoreticians. In RPS, they understood both the benefits of randomizing their own strategy and of predicting their opponent's moves. They offered a number of heuristics both for the prediction and opening move. These heuristics included optimizing against past opponent moves, such as not playing rock if the opponent just played scissors, and playing a specific opening hand, such as "paper". Visualizing the effects of such strategic choices on-the-fly would be interesting and educational. This brief essay attempts demonstrating and visualizing the value of a few different strategic options in RPS. Specifically, we would like to illustrate the following: 1) what is the value of being unpredictable?; and 2) what is the value of being able to predict your opponent? In regard to prediction of human players, the question 2) has been reflected in Jon McLoone's entry in Wolfram Blog from January 20, 2014[1]. McLoone created a predictive algorithm for playing against human opponents, that learns to beat human opponents reliably after approximately 30 - 40 games. I use McLoone's implementation to represent a predictive and random strategies. The rest of this documents 1) investigates performance of this predictive strategy against a random strategy (which is optimal in RPS) and in 2) attempts to turn this predictive power against the predictive strategy by allowing the opponent the full knowledge of the predictor's strategy (but not the choices made using the strategy). This exposes a weakness in predictions made without taking risks into account by illustrating that predictive strategy may make the predictor predictable as well.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Contributing Organization: Wolfram, Champaign, IL (United States). Wolfram Summer School
• DOE Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1459605
• Report Number(s): SAND2018-7137R; 665331
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING