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Meredith L.
Patterson
BSidesLV
August 5, 2014
STRATEGIES
WITHOUT
FRONTIERS
 I hate boring problems
 I especially hate solving tiny variations on the same
boring problem over and over again
 The ...
 Information theory
 Probability theory
 Formal language theory (of course)
 Control theory
 First-order logic
 Hask...
 When an unknown agent acts, how do you react?
 Observation of side effects
 Signals the agent sends
 Past interaction...
 Everything You Actually Need to Know About
Classical Game Theory
 in math …
 … and psychology
 Changing the Game
 Ex...
EVERYTHING YOU ACTUALLY
NEED TO KNOW ABOUT
CLASSICAL GAME THEORY
 Players
 Information available at each decision point
 Possible actions at each decision point
 Payoffs for each outc...
a, b c, d
e, f g, h
A NORMAL FORM GAME
Cooperate
Defect
Cooperate Defect
 Pure strategy: fully specified set of moves for every
situation
 Mixed strategy: probability assigned to each possible
...
PRISONER’S DILEMMA
-1, -1 -3, 0
0, -3 -2, -2
Cooperate
Defect
Cooperate Defect
d, e > a, b > g, h > c, f
MATCHING PENNIES
1, -1 -1, 1
-1, 1 1, -1
Heads
Tails
Heads Tails
a = d = f = g > b = c = e = h
DEADLOCK
1, 1 0, 3
3, 0 2, 2
Cooperate
Defect
Cooperate Defect
e > g > a > c and d > h > b > f
STAG HUNT
2, 2 0, 1
1, 0 1, 1
Stag
Hare
Stag Hare
a = b > d = e = g = h > c = f
CHICKEN
0, 0 -1, 1
1, -1 -10, -10
Swerve
Straight
Swerve Straight
e > a > c > g and d > b > f > h
HAWK/DOVE
𝑽
𝟐
,
𝑽
𝟐
0, V
V, 0
𝑉−𝐶
2
,
𝑉−𝐶
2
Share
Fight
Share Fight
e > a > c > g and d > b > f > h
BATTLE OF THE SEXES
3, 2 0, 0
0, 0 2, 3
Opera
Football
Opera Football
(a > g and h > b) > c = d = e = f
 Games can be zero-sum or non-zero-sum
 Games can be about conflict or cooperation
 Actions are not inherently morally ...
 Cournot equilibrium: each actor’s output maximizes
its profit given the outputs of other actors
 Nash equilibrium: each...
TRANSACTIONAL
ANALYSIS:
GAMES PEOPLE PLAY
MIND GAMES
“As far as the theory of games is concerned,
the principle which emerges here is that any
social intercourse wh...
 Procedures
 Operations
 Rituals
 Pastimes
 (Predatory) Games
TYPES OF INTERACTIONS
 “Hands” or roles = players
 Extensive form; players move in response to each
other
 Advantages
 Existential advantage...
 Kick Me
 Goal: Sympathy
 Find someone to beat on you, then whine about it
 “My misfortunes are better than yours”
 A...
 Now I’ve Got You, You Son Of A Bitch
 Goal: Justification (or just money)
 Three-handed version is the badger game
 R...
 “Schlemiel,” in Berne’s glossary
 Moves:
 Provocation → resentment
 (repeat)
 If B responds with anger, A appears ju...
 Social media
 Organic responses against predatory games
 Predator Alert Tool
 /r/TumblrInAction “known trolls” wiki
...
DISSECTING A
SIGNALING GAME
THE SETUP
THE TYPE
Split Steal
1
BOTH SPLIT
BOTH SPLIT
Split Steal
1
1 1
A
B
Split
Split
2
2
6800,
6800
6800,
6800
ONE SPLITS, ONE STEALS
ONE SPLITS, ONE STEALS
Split Steal
1
1 1
A
B
Split
Split
6800,
6800
6800,
6800
2
2
A
Split
2
Steal
Steal
B
Split
2
0,
1360...
BOTH STEAL
BOTH STEAL
Split Steal
1
1 1
A
B
Split
Split
6800,
6800
6800,
6800
2
2
A
Split
2
Steal
Steal
B
Split
2
0,
13600
0,
13600
1...
NORMAL FORM
Also known as the Friend-or-Foe game.
1, 1 0, 2
2, 0 0, 0
Split
Steal
Split Steal
d = e > a = b > c = f = g = h
OBSERVATION
FIRST MOVE: NICK’S CHOICE
Split Steal
1
1 1
“I’m likely to split”
“I’m likely to steal”
Split
Split
6800,
6800
6800,
6800
...
SIGNALING
SECOND MOVE: NICK’S SIGNAL
Split Steal
1
1 1
“I’m likely to split”
“I’m likely to steal”
Split
Split
6800,
6800
6800,
6800...
THE BIG REVEAL
THE COMPLETE PATH
Split Steal
1
1 1
“I’m likely to split”
“I’m likely to steal”
Split
Split
6800,
6800
6800,
6800
2
SplitS...
GAMES IN THE
TRANSPARENT SOCIETY
 Strategies now depend on payoff matrix and history
 Axelrod, 1981: how well do these strategies perform
against each ot...
 Nice: S is a nice strategy iff it will not defect on
someone who has not defected on it
 Retaliatory: S is a retaliator...
 Ord/Blair, 2002: what happens when strategies can
take into account all past interactions?
 We can express strategies i...
EVOLUTION IS A HARSH MISTRESS
Tit-for-Tat All-Cooperate Spiteful-Bully
PEACEKEEPING
Police All-Cooperate Spiteful-Bully
 In a society, niceness is more nuanced
 Individually nice: will not defect on someone who has not
defected on it
 Meta...
 Peacekeepers don’t always agree
 Police will defect on Vigilantes and vice versa
 Peacekeepers protect non-peacekeepin...
REDUCTIO AD ABSURDUM: ABSOLUTIST
∃t ∃j D(r, j, t) ⊕ D(c, j, t)
Tit-for-Tat All-Cooperate Spiteful-Bully Absolutist
ABSOLUTISM UBER ALLES
Tit-for-Tat All-Cooperate Spiteful-Bully Absolutist
REASONING UNDER
UNCERTAINTY
 Frequentist: probability is the long-term frequency of
events
 Reasoning from absolute probabilities
 What happens if ...
 Probability distribution function: assigns
probabilities to outcomes
 Discrete: a finite set of values (enumeration)
 ...
 Game theory is great when you know the payoffs
 What can you do if you don’t know the payoffs?
 Or what the game tree ...
 Figure out what distribution to use
 Figure out what parameter you need to estimate
 Figure out a distribution for it,...
 Prerequisites:
 A Markov chain with an equilibrium distribution
 A function f proportional to the density of the distr...
A GAME WITHOUT PAYOFFS
type Outcome = Measure (Bool, Bool)
type Trust = Double
type Strategy = Trust -> Bool -> Bool -> Me...
CHOOSING WHICH HOLE TO FILL IN
play :: Strategy -> Strategy ->
(Bool, Bool) -> (Trust, Trust) -> Outcome
play strat_a stra...
LET’S PLAY A GAME
games = [Just (toDyn False), Just (toDyn False),
Just (toDyn False), Just (toDyn True),
Just (toDyn Fals...
HOW MUCH TINFOIL IS IN THAT HAT?
MORE STRATEGIES
allCooperate :: Trust -> Bool -> Bool -> Measure Bool
allCooperate _ _ _ = conditioned $ bern 0.1
allDefec...
STRATEGY AS A RANDOM VARIABLE
data SChoice = Tit | GrimTrigger | AllDefect | AllCooperate
deriving (Eq, Ord, Enum, Typeabl...
LET’S PLAY ANOTHER GAME
iterated_game2 :: Measure (SChoice, SChoice)
iterated_game2 = do
let a_initial = False
let b_initi...
WHO’S WHO?
 Probabilistic SIPD
 Extensive form SIPD with signaling
 And channels with decidable vs. heuristic recognisers
 Coordi...
QUESTIONS?
mlp@upstandinghackers.com
@maradydd
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Strategies Without Frontiers

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Predicting your adversary's behaviour is the holy grail of threat modeling. This talk will explore the problem of adversarial reasoning under uncertainty through the lens of game theory, the study of strategic decision-making among cooperating or conflicting agents. Starting with a thorough grounding in classical two-player games such as the Prisoner's Dilemma and the Stag Hunt, we will also consider the curious patterns that emerge in iterated, round-robin, and societal iterated games.

But as a tool for the real world, game theory seems to put the cart before the horse: how can you choose the proper strategy if you don't necessarily even know what game you're playing? For this, we turn to the relatively young field of probabilistic programming, which enables us to make powerful predictions about adversaries' strategies and behaviour based on observed data.

This talk is intended for a general audience; if you can compare two numbers and know which one is bigger than the other, you have all the mathematical foundations you need.

Published in: Data & Analytics
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Strategies Without Frontiers

  1. 1. Meredith L. Patterson BSidesLV August 5, 2014 STRATEGIES WITHOUT FRONTIERS
  2. 2.  I hate boring problems  I especially hate solving tiny variations on the same boring problem over and over again  The internet is full of the same boring problems over and over again  Both in the cloud …  … and in the circus  Not my circus, not my monkeys MOTIVATION
  3. 3.  Information theory  Probability theory  Formal language theory (of course)  Control theory  First-order logic  Haskell ALSO APPEARING IN THIS TALK
  4. 4.  When an unknown agent acts, how do you react?  Observation of side effects  Signals the agent sends  Past interactions with others  Formal language theory (if you’re a computer)  Systematic knowledge about the structure of interactions and the incentives involved in them IT IS PITCH BLACK. YOU ARE LIKELY TO BE EATEN BY A GRUE.
  5. 5.  Everything You Actually Need to Know About Classical Game Theory  in math …  … and psychology  Changing the Game  Extensive form and signaling games  Multiplayer and long-running games  Reasoning Under Uncertainty, Over Real Data OUTLINE
  6. 6. EVERYTHING YOU ACTUALLY NEED TO KNOW ABOUT CLASSICAL GAME THEORY
  7. 7.  Players  Information available at each decision point  Possible actions at each decision point  Payoffs for each outcome  Strategies (pure or mixed)  Or behaviour, in iterated or turn-taking games  Equilibria  Different kinds of games have different kinds of equilibria WHAT’S IN A GAME?
  8. 8. a, b c, d e, f g, h A NORMAL FORM GAME Cooperate Defect Cooperate Defect
  9. 9.  Pure strategy: fully specified set of moves for every situation  Mixed strategy: probability assigned to each possible move, random path through game tree  Behaviour strategies: probabilities assigned at information sets STRATEGIES
  10. 10. PRISONER’S DILEMMA -1, -1 -3, 0 0, -3 -2, -2 Cooperate Defect Cooperate Defect d, e > a, b > g, h > c, f
  11. 11. MATCHING PENNIES 1, -1 -1, 1 -1, 1 1, -1 Heads Tails Heads Tails a = d = f = g > b = c = e = h
  12. 12. DEADLOCK 1, 1 0, 3 3, 0 2, 2 Cooperate Defect Cooperate Defect e > g > a > c and d > h > b > f
  13. 13. STAG HUNT 2, 2 0, 1 1, 0 1, 1 Stag Hare Stag Hare a = b > d = e = g = h > c = f
  14. 14. CHICKEN 0, 0 -1, 1 1, -1 -10, -10 Swerve Straight Swerve Straight e > a > c > g and d > b > f > h
  15. 15. HAWK/DOVE 𝑽 𝟐 , 𝑽 𝟐 0, V V, 0 𝑉−𝐶 2 , 𝑉−𝐶 2 Share Fight Share Fight e > a > c > g and d > b > f > h
  16. 16. BATTLE OF THE SEXES 3, 2 0, 0 0, 0 2, 3 Opera Football Opera Football (a > g and h > b) > c = d = e = f
  17. 17.  Games can be zero-sum or non-zero-sum  Games can be about conflict or cooperation  Actions are not inherently morally valenced  Payoffs determine type of game, strategy WHAT HAVE WE SEEN SO FAR?
  18. 18.  Cournot equilibrium: each actor’s output maximizes its profit given the outputs of other actors  Nash equilibrium: each actor is making the best decision they can, given what they know about each other’s decisions  Subgame perfect equilibrium: eliminates non- credible threats  Trembling hand equilibrium: considers the possibility that a player might make an unintended move EQUILIBRIUM
  19. 19. TRANSACTIONAL ANALYSIS: GAMES PEOPLE PLAY
  20. 20. MIND GAMES “As far as the theory of games is concerned, the principle which emerges here is that any social intercourse whatsoever has a biological advantage over no intercourse at all.”
  21. 21.  Procedures  Operations  Rituals  Pastimes  (Predatory) Games TYPES OF INTERACTIONS
  22. 22.  “Hands” or roles = players  Extensive form; players move in response to each other  Advantages  Existential advantage: confirmation of existing beliefs  Internal psychological advantage: direct emotional payoff  External psychological advantage: avoiding a feared situation  Internal social advantage: structure/position with respect to other players  External social advantage: as above, wrt non-players BERNE’S GAMES: STRUCTURE
  23. 23.  Kick Me  Goal: Sympathy  Find someone to beat on you, then whine about it  “My misfortunes are better than yours”  Ain’t It Awful  Can be a pastime, but also manifests as a game  Player displays distress; payoff is sympathy and help  Why Don’t You – Yes, But  Player claims to want advice. Player doesn’t really want it.  Goal: Reassurance BERNE’S GAMES: EXAMPLES
  24. 24.  Now I’ve Got You, You Son Of A Bitch  Goal: Justification (or just money)  Three-handed version is the badger game  Roles  Victim  Aggressor  Confederate  Moves  Provocation → Accusation  Defence → Accusation  Defence → Punishment THE BADGER GAME
  25. 25.  “Schlemiel,” in Berne’s glossary  Moves:  Provocation → resentment  (repeat)  If B responds with anger, A appears justified in more anger  If B keeps their cool, A still keeps pushing TROLLING
  26. 26.  Social media  Organic responses against predatory games  Predator Alert Tool  /r/TumblrInAction “known trolls” wiki  Those just happen to be ones I know about  A truly generic reputation system is probably a pipe dream  Wikipedia  eBay  But for these, we have to extend the basic mathematical model. OTHER MONKEY GAMEBOARDS
  27. 27. DISSECTING A SIGNALING GAME
  28. 28. THE SETUP
  29. 29. THE TYPE Split Steal 1
  30. 30. BOTH SPLIT
  31. 31. BOTH SPLIT Split Steal 1 1 1 A B Split Split 2 2 6800, 6800 6800, 6800
  32. 32. ONE SPLITS, ONE STEALS
  33. 33. ONE SPLITS, ONE STEALS Split Steal 1 1 1 A B Split Split 6800, 6800 6800, 6800 2 2 A Split 2 Steal Steal B Split 2 0, 13600 0, 13600 13600, 0 13600, 0
  34. 34. BOTH STEAL
  35. 35. BOTH STEAL Split Steal 1 1 1 A B Split Split 6800, 6800 6800, 6800 2 2 A Split 2 Steal Steal B Split 2 0, 13600 0, 13600 13600, 0 13600, 0 Steal Steal 0, 0 0, 0
  36. 36. NORMAL FORM Also known as the Friend-or-Foe game. 1, 1 0, 2 2, 0 0, 0 Split Steal Split Steal d = e > a = b > c = f = g = h
  37. 37. OBSERVATION
  38. 38. FIRST MOVE: NICK’S CHOICE Split Steal 1 1 1 “I’m likely to split” “I’m likely to steal” Split Split 6800, 6800 6800, 6800 2 SplitSteal Steal “I’m likely to steal” Split 0, 13600 0, 13600 13600, 0 13600, 0 Steal Steal 0, 0 0, 0 “I’m likely to split” 2
  39. 39. SIGNALING
  40. 40. SECOND MOVE: NICK’S SIGNAL Split Steal 1 1 1 “I’m likely to split” “I’m likely to steal” Split Split 6800, 6800 6800, 6800 2 SplitSteal Steal “I’m likely to steal” Split 0, 13600 0, 13600 13600, 0 13600, 0 Steal Steal 0, 0 0, 0 “I’m likely to split” 2
  41. 41. THE BIG REVEAL
  42. 42. THE COMPLETE PATH Split Steal 1 1 1 “I’m likely to split” “I’m likely to steal” Split Split 6800, 6800 6800, 6800 2 SplitSteal Steal “I’m likely to steal” Split 0, 13600 0, 13600 13600, 0 13600, 0 Steal Steal 0, 0 0, 0 “I’m likely to split” 2
  43. 43. GAMES IN THE TRANSPARENT SOCIETY
  44. 44.  Strategies now depend on payoff matrix and history  Axelrod, 1981: how well do these strategies perform against each other over time?  “Ecological” tournaments: players abandon bad strategies  Rapoport: if the only information you have is how player X interacted with you last time, the best you can do is Tit-for-Tat  TFT cannot score higher than its opponent  Axelrod: “Don’t be envious”  Against TFT, no one can do better than cooperate  Axelrod: “Don’t be too clever” ITERATED GAMES
  45. 45.  Nice: S is a nice strategy iff it will not defect on someone who has not defected on it  Retaliatory: S is a retaliatory strategy iff it will defect on someone who defects on it  Forgiving: S is a forgiving strategy iff it will stop defecting on someone who stops defecting on it PROPERTIES
  46. 46.  Ord/Blair, 2002: what happens when strategies can take into account all past interactions?  We can express strategies in convenient first-order logic, as it turns out  Tit-for-Tat: D(c, r, p)  Tit-for-Two-Tats: D(c, r, p) ∧ D(c, r, b(p))  Grim: ∃t D(c, r, t)  Bully: ¬∃t D(c, r, t)  Spiteful-Bully: ¬∃t D(c, r, t) ∨ ∃s (D(c, r, s) ∧ D(c, r, b(s)) ∧ D(c, r, b(b(s))))  Vigilante: ¬∃j D(c, j, p)  Police: D(c, r, p) ∨ ∃j (D(c, j, p) ∧ ¬∃k(D(j, k, b(p))) SOCIETAL ITERATED GAME THEORY
  47. 47. EVOLUTION IS A HARSH MISTRESS Tit-for-Tat All-Cooperate Spiteful-Bully
  48. 48. PEACEKEEPING Police All-Cooperate Spiteful-Bully
  49. 49.  In a society, niceness is more nuanced  Individually nice: will not defect on someone who has not defected on it  Meta-individually nice: will not defect on individually nice  Communally nice: will not defect on someone who has not defected at all  Meta-communally nice: will not defect on communally nice  Same applies to forgiveness and retaliation  Loyalty: will not defect on the same strategy as itself NICENESS AND LOYALTY
  50. 50.  Peacekeepers don’t always agree  Police will defect on Vigilantes and vice versa  Peacekeepers protect non-peacekeeping strategies at their own expense META-PEACEKEEPING Police All-Cooperate Spiteful-Bully Tit-for-Tat
  51. 51. REDUCTIO AD ABSURDUM: ABSOLUTIST ∃t ∃j D(r, j, t) ⊕ D(c, j, t) Tit-for-Tat All-Cooperate Spiteful-Bully Absolutist
  52. 52. ABSOLUTISM UBER ALLES Tit-for-Tat All-Cooperate Spiteful-Bully Absolutist
  53. 53. REASONING UNDER UNCERTAINTY
  54. 54.  Frequentist: probability is the long-term frequency of events  Reasoning from absolute probabilities  What happens if an event only happens once?  Returns an estimate  Bayesian: probability is a measure of confidence that an event will occur  Reasoning from relative probabilities  Returns a probability distribution over outcomes  Update beliefs (confidence) as new evidence arrives TWO INTERPRETATIONS OF PROBABILITY P(A|X) = P X A P(A) P(X)
  55. 55.  Probability distribution function: assigns probabilities to outcomes  Discrete: a finite set of values (enumeration)  Function also called a probability mass function  Poisson, binomial, Bernoulli, discrete uniform…  Continuous: arbitrary-precision values  Function also called a probability density function  Exponential, Gaussian (normal), chi-squared, continuous uniform…  Mixed: both discrete and continuous  Narrower distribution = greater certainty DISTRIBUTIONS 𝐸 𝑍 𝜆 = 𝜆 𝐸 𝑍 𝜆 = 1 𝜆
  56. 56.  Game theory is great when you know the payoffs  What can you do if you don’t know the payoffs?  Or what the game tree looks like?  Well…  You usually have some educated guesses about who the players are  You have some idea what your possible actions are, as well as the other players’  You can look at past interactions and make inferences  Which of these can be random variables? All of them.  Deterministic: if all inputs are known, value is known  Stochastic: even if all inputs are known, still random YOU DON’T KNOW WHAT YOU DON’T KNOW
  57. 57.  Figure out what distribution to use  Figure out what parameter you need to estimate  Figure out a distribution for it, and any parameters  Observing data tells you what your priors are  Fixing values for stochastic variables  Markov Chain Monte Carlo: sampling the posterior distribution thousands of times DON’T WAIT — SIMULATE
  58. 58.  Prerequisites:  A Markov chain with an equilibrium distribution  A function f proportional to the density of the distribution you care about  Choose some initial set of values for all variables (state, S)  Modify S according to Markov chain state transitions  If f(S’)/f(S) ≥ 1, S’ is more likely than S, so accept  Otherwise, accept S’ with probability f(S’)/f(S)  Repeat CONVERGING ON EXPECTED VALUES
  59. 59. A GAME WITHOUT PAYOFFS type Outcome = Measure (Bool, Bool) type Trust = Double type Strategy = Trust -> Bool -> Bool -> Measure Bool tit :: Trust -> Bool -> Bool -> Measure Bool tit me True _ = conditioned $ bern 0.9 tit me False _ = conditioned $ bern me
  60. 60. CHOOSING WHICH HOLE TO FILL IN play :: Strategy -> Strategy -> (Bool, Bool) -> (Trust, Trust) -> Outcome play strat_a strat_b (last_a,last_b) (a,b) = do a_action <- strat_a a last_b last_a b_action <- strat_b b last_a last_b return (a_action, b_action) iterated_game :: Measure (Double, Double) iterated_game = do let a_initial = False let b_initial = False a <- unconditioned $ uniform 0 1 b <- unconditioned $ uniform 0 1 rounds <- replicateM 10 $ return (a, b) foldM_ (play tit tit) (a_initial, b_initial) rounds return (a, b)
  61. 61. LET’S PLAY A GAME games = [Just (toDyn False), Just (toDyn False), Just (toDyn False), Just (toDyn True), Just (toDyn False), Just (toDyn False), Just (toDyn False), Just (toDyn True), Just (toDyn False), Just (toDyn True), Just (toDyn False), Just (toDyn False), Just (toDyn False), Just (toDyn True), Just (toDyn False), Just (toDyn True), Just (toDyn False), Just (toDyn True), Just (toDyn False), Just (toDyn False)] do l <- mcmc iterated_game games return [makeHistogram 30 (Data.Vector.fromList $ map fst (take 5000 l)) "A's paranoia", makeHistogram 30 (Data.Vector.fromList $ map snd (take 5000 l)) "B's paranoia"]
  62. 62. HOW MUCH TINFOIL IS IN THAT HAT?
  63. 63. MORE STRATEGIES allCooperate :: Trust -> Bool -> Bool -> Measure Bool allCooperate _ _ _ = conditioned $ bern 0.1 allDefect :: Trust -> Bool -> Bool -> Measure Bool allDefect _ _ _ = conditioned $ bern 0.9 grimTrigger :: Trust -> Bool -> Bool -> Measure Bool grimTrigger me True False = conditioned $ bern 0.9 grimTrigger me False False = conditioned $ bern 0.1 grimTrigger me _ True = conditioned $ bern 0.9
  64. 64. STRATEGY AS A RANDOM VARIABLE data SChoice = Tit | GrimTrigger | AllDefect | AllCooperate deriving (Eq, Ord, Enum, Typeable, Show) chooseStrategy :: SChoice -> Strategy chooseStrategy Tit = tit chooseStrategy AllDefect = allDefect chooseStrategy AllCooperate = allCooperate chooseStrategy GrimTrigger = grimTrigger strat :: Measure SChoice strat = unconditioned $ categorical [(AllCooperate, 0.25), (AllDefect, 0.25), (GrimTrigger, 0.25), (Tit, 0.25)]
  65. 65. LET’S PLAY ANOTHER GAME iterated_game2 :: Measure (SChoice, SChoice) iterated_game2 = do let a_initial = False let b_initial = False a <- unconditioned $ uniform 0 1 b <- unconditioned $ uniform 0 1 na <- strat let a_strat = chooseStrategy na nb <- strat let b_strat = chooseStrategy nb rounds <- replicateM 10 $ return (a, b) foldM_ (play a_strat b_strat) (a_initial, b_initial) rounds return (na, nb) do l <- mcmc iterated_game2 games return [makeDiscrete (map fst (take 1000 l)) "A strategy", makeDiscrete (map snd (take 1000 l)) "B strategy"]
  66. 66. WHO’S WHO?
  67. 67.  Probabilistic SIPD  Extensive form SIPD with signaling  And channels with decidable vs. heuristic recognisers  Coordination. Enough said.  System 1/System 2 conflict  Sentiment analysis → payoff data  Start small: the stroke is the smallest unit of interaction  Data where information about players is limited  IP flows  Anonymity networks  Signaling game about type: are two actors the same person? FUTURE WORK
  68. 68. QUESTIONS? mlp@upstandinghackers.com @maradydd

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