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Modeling, Math and Sciencefor Building Games that Improve
Organization Operation,and Workforce Effectiveness
Christopher J. Hazard, PhD
Christopher J. Hazard, PhD August, 2016 2
Hazardous Software Serious Games
Christopher J. Hazard, PhD August, 2016 3
Image from user boysdean on Flickr.com
Image from user BLANCOBILL on TripAdvisor.com
Who is a Gamer?
Christopher J. Hazard, PhD August, 2016 4
Play = immersion + learning +
minimized actual risk + time travel
Christopher J. Hazard, PhD August, 2016 5
Simulation-Based Serious Games
Close Combat – Modern Tactics, Matrix Games
CyberCIEGE, NPS & Rivermind
EteRNA, CMU
Christopher J. Hazard, PhD August, 2016 6
More Serious GamesWith OR Aspects
Code of Everand, UK Department for TransportMMORPG, 2009-2011
Cargo Dynasty, Serious Games Interactive,TSU, TUR
Wildfire game, Lincoln Labs
Christopher J. Hazard, PhD August, 2016 7
Not aboutVirtual Worlds &
Chocolate Covered Broccoli
Second Life
Christopher J. Hazard, PhD August, 2016 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 9
Implicit Grinding(and optimal downtime)
Just Cause 2
Niel de la Rouviere, Stellenbosch University
Christopher J. Hazard, PhD August, 2016 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 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 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 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 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 15
A Simple Game...
• Strategist• Negotiator• Artist• Logician (e.g., programmer/lawyer)• Impulsivist or risk seeker• Risk avoider
Christopher J. Hazard, PhD August, 2016 16
Bidding Game Rules
Card is cost:
A: 1
2: 2
3: 3
…
J: 11
Q: 12
K: 13
• Bid each round• Winning bidder gets
price – cost• Highest profit wins
Christopher J. Hazard, PhD August, 2016 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 18
NASCAR: Drafter's Dilemma
• 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
Cooperate Defect
Cooperate 3 3 -5 3
Defect 2 -5 1 1
Christopher J. Hazard, PhD August, 2016 19
Mixed Strategy & Risk
• Intransitivity• “Every unit overpowered”• Forced risk
P S
R 0, 0 -1, 1 1, -1P 1, -1 0, 0 -1, 1S -1, 1 1, -1 0, 0
Street Fighter 4
Christopher J. Hazard, PhD August, 2016 20
Payoff, Risk, Commitment
Stag Hare
Stag 10 10 0 8
Hare 8 0 7 7
Swerve Straight
Swerve 0 0 -1 +1
Straight +1 -1 -1000 -1000
Christopher J. Hazard, PhD August, 2016 21
Creeping Sniper's Dilemma
Original image from ShadowShield.com
Christopher J. Hazard, PhD August, 2016 22
Creeping Sniper's Dilemma
Single sniper position, σ, as a function of time:
• Multiple sniper: match quickest visible discount strategy unless too risky
Pos
ition
of
Sni
per
Near Target
Far Target
Christopher J. Hazard, PhD August, 2016 23
Operations Research: Lanchester's LawsGang 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 24
Balancing With Game Theory: Strength and Utility
Hammer Spear Curse
Hammer 1 3 0.5
Spear 0.33 1 0.5
Curse 2 2 1 Hammer Spear Curse
Hammer 0.000 -0.043 0.095
Spear 0.043 0.000 -0.070
Curse -0.095 0.070 0.000Cost
Hammer 0.23
Spear 0.56
Curse 0.21
S (strength: # of player 1 to defeat player 2)
C (cost)
U (utility)
One player loses all utility, another fractionSpear vs Hammer:
gain - loss0.23 - (1/3 * 0.56)
Symmetric!
Christopher J. Hazard, PhD August, 2016 25
Balancing With Game Theory: Probabilities
Hammer Spear Curse
Hammer 0.000 -0.043 0.095
Spear 0.043 0.000 -0.070
Curse -0.095 0.070 0.000
U (utility)Probability
Hammer 0.336
Spear 0.456
Curse 0.208
P (probability)
Probability
Hammer 0.333
Spear 0.334
Curse 0.333
P (probability)Cost
Hammer 0.255
Spear 0.545
Curse 0.200
C (cost)Hammer Spear Curse
Hammer 0.000 -0.073 0.073
Spear 0.073 0.000 -0.073
Curse -0.073 0.073 0.000
U (utility)
Christopher J. Hazard, PhD August, 2016 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 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 28
Complexity of Behavior
Christopher J. Hazard, PhD August, 2016 29
Information Conveyance
Christopher J. Hazard, PhD August, 2016 30
Corpse PartyChapter 1 Infirmary
Christopher J. Hazard, PhD August, 2016 31
Corpse PartyChapter 1 Infirmary
Christopher J. Hazard, PhD August, 2016 32
Infirmary Flow
take match from furnace
try door
try door
try match
try match
get rubbing alcohol
try door
exit
• Actual branching factor: 12• Perceived branching factor: 11• Exaggerated expectation
[Hilbert, PSYCHOL BULL '12]
– P(progress | revisit item) higher than anticipated
Christopher J. Hazard, PhD August, 2016 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 means1/12 * ln( (1/12) / 0) = 1/12 * ln(∞) = ∞
Massive surprisal if assume no repeat actions advance game
Christopher J. Hazard, PhD August, 2016 34
Measuring Difficulty By Decision Information Rate
X X
X3 out of 6 paths lose
1
11
0
0 No loss, no information
Average 1 bit of information
Average 0.5 bits of information
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 35
Christopher J. Hazard, PhD August, 2016 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 37
Time Manipulation in Gaming• Time zones • Reverse time
ChronoTrigger Braid
• Fixed jump back• Time loop
Ratchet & Clank
Majora'sMask
Christopher J. Hazard, PhD August, 2016 38
Time Manipulation Transforms Gameplay
Obstacle/Combat Course (FF12) Maze
Gran Turismo Sudoku (Optimization)
+Undo
+Timeline
Christopher J. Hazard, PhD August, 2016 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 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 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 42
Understanding Probability Distributions
Christopher J. Hazard, PhD August, 2016 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