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Chris Hazard - Modeling, Math and Science for Building Strategic Serious Games

Chris Hazard, CEO/Founder, Hazardous Software This presentation was given at the 2016 Serious Play Conference, hosted by the UNC Kenan-Flagler Business School. A serious game can be a useful tool to help understand a strategic problem to optimize solutions, manage risks, evaluate processes, and operationalize automation. The speaker will share broadly applicable techniques that have proven useful in designing and developing training games for solving strategic problems as well as company operations. The techniques include concepts from modeling and simulation, game theory, operations research, psychology, artificial intelligence and behavioral economics. The talk is intended for two audiences. The talk will show executives and managers possibilities for using serious games, how serious games overlap with what they may know from management science and how serious games can aid understanding, automating, training and operationalizing various aspects of games for strategic purposes. Serious game developers, will also learn share techniques that have worked for us at Hazardous Software.

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Chris Hazard - Modeling, Math and Science for Building Strategic Serious Games

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  1. Modeling, Math and Science for Building Games that Improve Organization Operation, and Workforce Effectiveness Christopher J. Hazard, PhD

  2. Hazardous Software Serious Games Christopher J. Hazard, PhD August, 2016 2

  3. Who is a Gamer? Image from user boysdean on Flickr.com Image from user BLANCOBILL on TripAdvisor.com Christopher J. Hazard, PhD August, 2016 3

  4. Play = immersion + learning + minimized actual risk + time travel Christopher J. Hazard, PhD August, 2016 4

  5. Simulation-Based Serious Games CyberCIEGE, NPS & Rivermind Close Combat – Modern Tactics, Matrix Games EteRNA, CMU Christopher J. Hazard, PhD August, 2016 5

  6. More Serious Games With OR Aspects Code of Everand, UK Department for Transport MMORPG, 2009-2011 Cargo Dynasty, Serious Games Interactive, TSU, TUR Wildfire game, Lincoln Labs Christopher J. Hazard, PhD August, 2016 6

  7. Not about Virtual Worlds & Chocolate Covered Broccoli Second Life Christopher J. Hazard, PhD August, 2016 7

  8. How Different From M&S? • Have human-centric interfaces • Focus on usability • Focus on exercise deployability • Focus on creating & managing reusable scenarios • Focus on realistic communication & controls • Have AAR, AI, help, and tutorials integrated/embedded Christopher J. Hazard, PhD August, 2016 8

  9. Implicit Grinding (and optimal downtime) Just Cause 2 Niel de la Rouviere, Stellenbosch University Christopher J. Hazard, PhD August, 2016 9

  10. Adaptive vs Choice vs Fixed Content Choice of content Adaptive content D. Sharek PhD dissertation at NCSU, 2012. Investigating Real-time Predictors of Engagement: Implications For Adaptive Video Games and Online Training. Christopher J. Hazard, PhD August, 2016 10

  11. Humans Are Rational* *given limited computational bounds, strong heuristics, poor probabilistic reasoning, unfounded beliefs of others, inaccurate capability assessments, inexplicable valuations, and some level of [im]patience Christopher J. Hazard, PhD August, 2016 11

  12. Utility & Currency • Common currency: average-player time – Skilled players & devoted players have most • Find exchange rates for everything – If items purchasable in $, find exchange between player time and $ • Find amortization / discount rate Christopher J. Hazard, PhD August, 2016 12

  13. Skill, Strategy, & Information Gain • Skill – Driven by capabilities, signaling, reputation – Measured using statistics, hindsight • Strategy – Driven by preferences (valuations), sanctioning, trust – Solved using game theory, foresight • Information Gain – Driven by immersion, curiosity, relevance – Provided via narrative, setting, instruction, cues Christopher J. Hazard, PhD August, 2016 13

  14. Keynesian Beauty Pageant: Guess 2/3 the average • Everyone choose number [1,100] • Closest to 2/3 the average wins Image from thedigeratilife.com Christopher J. Hazard, PhD August, 2016 14

  15. A Simple Game... • Strategist • Negotiator • Artist • Logician (e.g., programmer/lawyer) • Impulsivist or risk seeker • Risk avoider Christopher J. Hazard, PhD August, 2016 15

  16. Bidding Game Rules • Bid each round • Winning bidder gets price – cost • Highest profit wins Card is cost: A: 1 2: 2 3: 3 … J: 11 Q: 12 K: 13 Christopher J. Hazard, PhD August, 2016 16

  17. Bidding Game Results • 3-4 rounds to "convergence" • Generally considered "unfair" • Bayesian Nash Equilibrium! – Big reveal of same card: surprise – Lack of reveal: anchoring and bias hook Christopher J. Hazard, PhD August, 2016 17

  18. NASCAR: Drafter's Dilemma Cooperate 3 Defect Cooperate Defect 3 2 -5 -5 3 1 1 • Red ahead, Blue behind, leave line together • Payoff = number of cars passed • Cooperate = allow other to jump back in line • Defect = jump back in line without the other Ronfeldt, First Monday J., '00 Christopher J. Hazard, PhD August, 2016 18

  19. Mixed Strategy & Risk P S R P S 0, 0 -1, 1 1, -1 -1, 1 1, -1 -1, 1 0, 0 0, 0 1, -1 • Intransitivity • “Every unit overpowered” • Forced risk Street Fighter 4 Christopher J. Hazard, PhD August, 2016 19

  20. Payoff, Risk, Commitment Stag10 10 0 Hare 8 Stag Hare 8 7 0 7 Swerve0 Straight+1-1-1000-1000 SwerveStraight 0-1 +1 Christopher J. Hazard, PhD August, 2016 20

  21. Creeping Sniper's Dilemma Original image from ShadowShield.com Christopher J. Hazard, PhD August, 2016 21

  22. Creeping Sniper's Dilemma Position of Sniper Near Target Far Target Single sniper position, σ, as a function of time: • Multiple sniper: match quickest visible discount strategy unless too risky Christopher J. Hazard, PhD August, 2016 22

  23. Operations Research: Lanchester's Laws Gang of N units vs 1, all with sufficient action range X DPS, Y health N each retain Y (1 – 1/N^2) Original image from XCOM: Enemy Unknown Christopher J. Hazard, PhD August, 2016 23

  24. Balancing With Game Theory: Strength and Utility S (strength: # of player 1 to defeat player 2) Hammer Spear Curse Hammer Spear Curse 1 3 1 2 0.5 0.5 U (utility) 0.33 2 1 Hammer Spear 0.000 0.043 -0.095 Curse Hammer Spear Curse -0.043 0.000 0.070 0.095 -0.070 0.000 C (cost) Cost Hammer Spear Curse 0.23 0.56 0.21 One player loses all utility, another fraction Spear vs Hammer: gain - loss 0.23 - (1/3 * 0.56) Symmetric! Christopher J. Hazard, PhD August, 2016 24

  25. Balancing With Game Theory: Probabilities U (utility) P (probability) Hammer Spear 0.000 0.043 -0.095 Curse Probability Hammer Spear Curse -0.043 0.000 0.070 0.095 -0.070 0.000 Hammer Spear Curse 0.336 0.456 0.208 P (probability) U (utility) C (cost) Probability Hammer Spear 0.000 0.073 -0.073 Curse Cost Hammer Spear Curse 0.333 0.334 0.333 Hammer Spear Curse -0.073 0.000 0.073 0.073 -0.073 0.000 Hammer Spear Curse 0.255 0.545 0.200 Christopher J. Hazard, PhD August, 2016 25

  26. Ambiguity as an Interestingness Measure • Find Nash equilibrium – 20% sniper rifle, 30% machine gun, 50% shotgun – 33% sniper rifle, 33% machine gun, 34% shotgun • Control tightness – Ambiguity vs predictability of next game states (discounted) • Difficulty of puzzles & optimal strategy ascertainment – Some ambiguity good, too much boring Christopher J. Hazard, PhD August, 2016 26

  27. Learning & Information Gain • Measure information gain between player strategy and optimal • Mixed strategy Nash equilibria – 1/3 rock, 1/3 paper, 1/3 scissors • How much information left to teach player? – 1/4 rock, 1/4 paper, 1/2 scissors – Info gain to achieve desired Nash equilibrium Christopher J. Hazard, PhD August, 2016 27

  28. Complexity of Behavior Christopher J. Hazard, PhD August, 2016 28

  29. Information Conveyance Christopher J. Hazard, PhD August, 2016 29

  30. Corpse Party Chapter 1 Infirmary Christopher J. Hazard, PhD August, 2016 30

  31. Corpse Party Chapter 1 Infirmary Christopher J. Hazard, PhD August, 2016 31

  32. Infirmary Flow • Actual branching factor: 12 • Perceived branching factor: 11 • Exaggerated expectation [Hilbert, PSYCHOL BULL '12] – P(progress | revisit item) higher than anticipated take match from furnace try door try match try door try match get rubbing alcohol try door exit Christopher J. Hazard, PhD August, 2016 32

  33. Infirmary Surprisal • Player unsure of what to do, so assume uniform distribution over new possibilities: Q(X) ≈ 1/11, Q(Repeat) ≈ 0 => ~3.5 bits • Correct distribution over possibilities, minimizing assumptions: P(X) = 1/12 • Q(repeat) ≈ 0 means 1/12 * ln( (1/12) / 0) = 1/12 * ln(∞) = ∞ Massive surprisal if assume no repeat actions advance game Christopher J. Hazard, PhD August, 2016 33

  34. Measuring Difficulty By Decision Information Rate No loss, no information 0 1 1 Average 1 bit of information 0 1 Average 0.5 bits of information X X X 3 out of 6 paths lose 1.5 bits of total information to win 1.5 bits / 2 steps = 0.75 bits per step to win Christopher J. Hazard, PhD August, 2016 34

  35. Christopher J. Hazard, PhD August, 2016 35

  36. Mutual Exclusion Between Mechanical and Social Reasoning (Jack et al., Neuroimage, 2012) Working Memory Capabilities & Affective Control (Schweizer et al., J Neuroscience, 2013) Christopher J. Hazard, PhD August, 2016 36

  37. Time Manipulation in Gaming • Time zones • Reverse time Chrono Trigger Braid • Time loop • Fixed jump back Majora's Mask Ratchet & Clank Christopher J. Hazard, PhD August, 2016 37

  38. Time Manipulation Transforms Gameplay Obstacle/Combat Course (FF12) Maze +Undo Sudoku (Optimization) Gran Turismo +Timeline Christopher J. Hazard, PhD August, 2016 38

  39. Time Manipulation & Causality • Dynamically correct plans: blur hypothetical & committed • Long-term thinking about decisions • Just in time vs redundancy • Minmax & Nash equilibria • Qualitative sensitivity analysis: plan fragility • “Newton's Method” of strategy Christopher J. Hazard, PhD August, 2016 39

  40. Time Manipulation Game Mechanics • “Chronoenergy”: causality as a resource – Locality & change magnitude – What is a unit of causality? • Player's intention vs low-level control • AI to assist “when you're not then” • Collaborative planning Christopher J. Hazard, PhD August, 2016 40

  41. Desirability Index • Desirability Index (geometric mean of conflicting metrics) in multicriteria optimization: • Used for optimization in chemistry, chemical engineering, mechanical engineering • Related to Shannon Entropy Maximization • Easy to relate to output as a score, hard to “game” Christopher J. Hazard, PhD August, 2016 41

  42. Understanding Probability Distributions Christopher J. Hazard, PhD August, 2016 42

  43. Little’s Law, MDPs & More OR • L = λW to measure expected length of queue by wait time • MDPs for modeling, visualization into process • MILP, Pareto Frontier Christopher J. Hazard, PhD August, 2016 43

  44. Questions? info@hazardoussoftware.com Christopher J. Hazard, PhD August, 2016 44

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