- Social Gaming

Maximilian Stark (mail@dakror.de), SS2018

Stand: 21.07.2018

Notiert sind nur Dinge, die ich als wichtig und Neuwissen erachte. Bekannte Elemente werden lediglich zum Teil der Vollständigkeit halber aufgeführt.

- Methods
- empirical
- design science
- deductive

- Influences
- psychology, sociology, socio-psychology
- economy
- informatics, CS, mathematics
- arts

- social aspects implicit
- higher form of play is:
- free activity
- outside ordinary life
- not serious
- fixed rules
- social groups (
**Huizinga**) - no material interest
- make-believe reality (
**Caillois**)

**Sutton Smith**:- progress (development)
- fate (gambling)
- power (conflicts)
- identity (communities)

**Salen & Zimmermann**: 3 categories- being playful
- ludic activities
- gameplay

**Salen & Zimmermann**- system
- players engage
- artifical conflict
- rules
- quantifiable outcome

**Hunicke**- systems building behaviour via interaction
- components (MDA)
**M**echanics**D**ynamics**A**esthetics

**Juul**:- three levels
- game (system)
- player(s)
- world (context)

- transmedial

- three levels
**Frasca**: properties- social
- performance measurement and value

- online
- mobile
- context (sensors)
- spatio-temporal
- social
- physical
- medical
- personal

- location based games
- mobile context != mobile UI

- context (sensors)
- simulations
- social
- hardcore
- casual
**Juul**- characteristics
- instant play
- quick play
- common play

- design principles
- Fiction
- Usability
- Interruptibility
- Difficulty & Punishment
- Juiciness

- characteristics
- overlaps: online, social, mobile
- varieties
- browser
- soc.network games
- mimetic games (Wii Sports)

- pervasive
- cyber-physical system (
**Montola**) - augmented, embedded worlds (
**Kampmann**) - overlaps: mobile, location based, social
- sub-types (
**Magerkurth**)- Smart toys (Tamagotchi)
- Affective gaming (emotional state sensors)
- Augmented tabletop
- Location-aware
- AR
- Gamification

- cyber-physical system (
- serious
- useful side effects (
**Susi**)- education
- training
- information

- Games with a Purpose (GWAP)
- human-based computing
- crowdsourcing (Captcha)

- useful side effects (

- formal criteria missing
- too ridig, graph based classification required
- extensional (based on existing), not intensional
- better:
- classification via mechanics
- genres = sets of mechanics
- additive
- new genres easy

- genre: derived from single pioneer game (
**Costikyan**)

- classification via mechanics

- intrinsic
**Yee**: components for MMOG player types- Achievement
- Social
- Immersion

**Maslov**: achievements- self esteem levels
- belonging love level
- basic needs hierarchy (hi to low priority)
- Physiological
- Safety
- Belonging-Love
- Self Esteem
- Self Actualisation

- detection
**Vinciarelli**: Social Signal processing- galvanic skin response (GSK)
- cardiovascular measures

- EMG (
**Mandryk**) - CV
- audio based

**Ekman**'s 6 key emotions- frustration (anger)
- fear
- surprise
- sadness
- disgust
- amusement (happiness)

**Pluchik**'s wheel of 8 emotions- joy
- trust
- fear
- surprise
- sadness
- disgust
- anger
- anticipation

- Involvement (
**Lazzaro**) - Presence (
**Lombard & Ditton**) - Immersion (
**Bartle**) - Flow (
**Csikszentmihalyi**)

- conditions
- challenge, appropriate level
- clear proximal goals
- immediate feedback

- models
- 3 channel (
**Nakamura & Csikszentmihalyi**) - 4 channel (
**Novak**) - 8 channel (
**Nakamura & Csikszentmihalyi**)

- 3 channel (

- Emotional contagion (
**Hatfield**)- mimic & sync. expressions
- converge emotionally with other person

- Performance: Hawthorne effect

- Macro: all players
- Meso: guilds
- Micro: teams

- internet as platform
- harness network effects
- collective intelligence
- paradigm switch: monolithic software -> network of web based services
- importance of context
- contionous updates
- lightweight dev models
- software above level of single device
- rich UX

- Social Media services & platforms
- Critique: Web 1.0 already providing the above

- web based
- social interaction
- generation & exchange of content
- Issue: constant blurring: professional <-> non professional
- Creative effort: exclude classic messaging from SM?

- set of users

- coherent bundle of SM services
- widely accessible through network technologies

- instance of service / platform
- associated user- & information-base

- SM service software
- SM platform software

- collaborative software
- form of social interaction
- Issue: Social media yes or no?

- characteristics
- openness
- content
- interactive
- dynamics (emergent social effects)
- social information processing paradigm

- collaborative modeling of relations
- technologies
- general enabler technologies
- web protocols
- UI
- Semantic Web (RDF, OWL), Social Semantic Web Ontologies (SIOC, FOAF)
- client & server
- syndication, mash up of content (RSS)
- Social Software

- classification by type of communication (m:n, 1:n)
- characterization
**Kaplan & Haenlein**: 2 axes- Self presentation, self disclosure
- social presence / Media richness

**Kietzmann**: 7 aspects- identity
- presence
- relationships
- reputation
- groups
- conversations
- sharing

- emphasis on communication
- Blogs
- Microblogs
- Wikis
- Discussion Boards
- Social Games
- (Messaging/Chat (n:m, with n too small))
- (IP-Telephony (n:m, with n & m too small))

- collaboration oriented
- Open Innovation platforms, Collaborative Creativity services / platforms
- Knowledge Codification
- (Revision Control)
- (CMS)

- Social Networking
- SN patforms
- MSN platforms
- Location based
- Professional SN
- Company Community
- Dating

- Goal oriented
- Altruistic
- Utopia: support sustainable consumption
- Causes: social issues
- IndieGoGo

- Political
- Occupy
- Wikileaks

- Knowledge Codification

- Altruistic
- emphasis on content
- Event services
- News
- Social Search
- Question Answering
- Information aggregation (Netvibes)
- Knowledge Codification
- (Document management)
- Content Sharing
- Social bookmarking (CiteULike)
- Social recommender

- characterization axes
- Cardinality (x:y)
- Audience specification
- Channel directness
- Sender anonymity
- Threadedness
- Content type
- Transmission style
- UI / Device / Usage Pattern

- abstract characterization axes
- Goals
- Commercialization
- Speech Art characterization
- Context

- common
- leisure time
- communication
- rules
- emergent mechanics
- transmedial access
- flow
- "host" of one another

- distinctive
- communication vs. entertainment
- real life vs. imaginary
- implicit vs. explicit rules
- text, photos, images vs. sprites, objects

- unifying class: leisure time oriented applications, services, platforms

- characterization axes
- intensity
- valence
- hierarchy
- reciprocity
- intimacy
- ...

**Schilit**: where, with whom, what**Dey**: Situation of entity relevant to user interaction with application- classes
- phsical
- individual
- social

- properties
- dynamics
- temporal distinction
- high / low level

- big data
- build social software

- closeness of node & neighbors to complete subgraph (clique)
- Key point: $C_i \text{(directed)} ~= 1/2 * C_i \text{(undirected)}$

- ordinal scale
- types
- degree centrality: $c(u) = \mathrm{deg}(u)$ - direct vote semantics
- eccentricity: $c(u) = 1 / \max{d(u,v); v \in V}$ - minimize max distance
- closeness: $c(u) = \sum_{v\in V} 1 / d(u,v)$ - find central figure, minimize all distances
- centroids: $c(u) = \min_v{(y_u(v) - y_v(u)): v \in V{u}}$ - find niche
- stress: $c(u)$ = sum over amount of shortest paths from a to b over u ($\sigma_ab(v)$)
- shortest paths betweenness (SPB) - $c(u) = \sum \frac{\sigma_ab(v)}{\sigma_ab}$ - control of u on communication in graph (O(|V||E| + |V|^2 log|V|))

- G' (edge graph) = edges of G are vertices
- G'' (incidence graph) = edges of G are vertices between vertices

- delta quality measure of graph with/(-out) vertex v
- measures
- max flow (O(|V||E|log(|V|^2/|E|)))
- max flow betweenness
- Wiener Index (closeness vitality)

- avg. amount of random walks through i while s->t
**Kirchhoff**point law: total current in = total current out- $V_i$ voltage at i (hits of i)
- $k_i$ degree of vertex i
- $D = \mathrm{diag}(k_i)$
- $s_i = \begin{cases} 1,& i=s \ -1,& i = t\ 0\end{cases}$ source vector
- $(D-A)V=s$ (overspecified) -> $V = (D_v - A_v)^{-1}*s$
- $M = A * D^{-1}$
- Hotel california effect: never leave t: $M_it = 0$
- from s -> j in r steps, then to adj. vertex i: $k_j^{-1}[M_t^r]_{js}$

- centrality depends on adj. centrality
- Hubbell index
- Page rank

- old: individualist vs. collectivistic
- new: emergence
- (interdependent) properties
- density (intra cluster coherence)
- compactness (intra coh.)
- mutuality (intra coh.)
- separation (inter decoh.)

**Moon**: Member at least connected to 1/k members- locality: definition over induced subgraph

- complete subgraph
- can overlap
- closed under exclusion
- nested
- Finding Clique of size k: NP-complete
- maximal: $\nexists U' \subseteq G: U \subset U'$
- maximum clique: no bigger clique in G
- "perfect" in
- density
- compactness
- connectedness

**Turan**$\mathrm{if} |E| > |V|^2/2 (k-2)(k-1)$ -> G has clique of size k**Moon & Moser**: at most $ 3^{||v| / 3|} $ maximal cliques in G- alternatives
- N-clique: max distance between all members N (not local) (could have diameter > N)
- N-club: max diameter N
- N-clan: maximal N-clique + N-club

- all N-clans are N-cliques
- all N-clubs are contained in N-cliques
- all N-clans are N-clubs
- not all N-clubs are N-clans
- critique
- socially irrelevant
- not closed under exclusion

- leave out some member edges
- U is N-Plex <=> $\min \mathrm{deg}(v \in U) >= |U| - N$
- closed under exclusion
- nested
- also NP-complete

- demand minimum degree for all members
- U is N-Core <=> $\min \mathrm{deg}(v \in U) >= N$
- U is N-Core -> U is (|V|-N)-plex
- maximum N-core is unique
- not closed under excl.
- not nested
- can be disconnected
- easily computable

**Luccio-Sami**: intra cluster coh., inter cluster decoh.- U is LS-Set <=> all subsets of U more internal than external ties
- no trivial overlaps (counter argument for social construct)
- min deg >= 1/2 outgoing edges of U
- computable

- members more internal connections than to outside set
- in P time computable

- tied to clustering coefficient
- quality of single group structure in G
- Sum of clust. coeff. of structure / Sum of clust. coeff. of Graph \ Structure

- find clusters with no fixed schema
- Unsupervised Classification
- metric spaces (K-means)
- $C$: partition of V into k subsets
- $E(X)$: edges inside X
- $A(G)$: Set of possible clusterings
- quality measure: $A(G) \mapsto R$ formalization of clustering paradigm
- weight function w: similarity
- quality index: $(f(C) + g(C)) / \max{f(C') + g(C'): C' \in A(G)}$, f intra coh. (density), g inter decoh. (sparseness)
- C with k > 1 transformable to C' with k' < k by merging

- coverage
- $y(C) = w(E(C)) / w(E)$
- -> $f = w(E(C)), g=0$
- Maximum value 1 with $C={V}$
- Monotonic behaviour

- conductance
- paradigm: well connectedness
- measure for bottlenecks
- tries to find good, halving cut (C with k=2)
- small conductance <-> good cut possible
- maximum conductance 1 if |V| <= 3 or star shaped
- calculation NP hard, approximation with guarantee O(sqrt(log |V|))
- quality measurement
- 1st measure: cluster too coarse?
- 2nd measure: cluster too fine?

- performance
- count # of correctly classified node pairs
- same cluster & neighbors (f := # edges in clusters)
- not same cluster & not neighbors (g := # nonexisting edges between clusters)

- max f+g: NP-hard
- index: $(f(C)+g(C)) / (|V|(|V|-1))$
- tendency towards many small clusters

- count # of correctly classified node pairs

- Linkage (Agglomeration): coarsen by merging (bottom up)
- iterative
- merge if together minimum global cost
- merge if both minimum local merging cost

- Complete Linkage: max minimal path length
- Single Linkage: min minimal path length

- iterative
- Splitting (Division): refine by splitting (top down)
- iterative
- split if yields minimal global cost
- split cluster with minimal local splitting cost
- split cluster yielding minimal global cost

- cut function
- S(V) (default)
- S_ratio
- S_balanced
- S_conductance: argmin inter. decoh.

- iterative
- Shifting
- actions
- move node between clusters
- make node singleton (C with k=1)
- swap cluster nodes

- potential function phi: genetic algorithm
- each step: seek C' with phi(C') > 0
- usage as refinement of existing clustering

- actions
**Newman Girvan**Method: Centrality based Splitting + Modularity- iterative
- calc edge betweenness
- remove edge with max betw.
- repeat

- Modularity as intra. coh.
- Edge centralities
- SPB (best avg)
- RWB

- iterative

- k clusters -> $k\times k$ matrix e
- $e_{ij}$: fract edges between communities
- $\mathrm{Tr\ } e = \sum_i e_{ii}$: fract edges in community
- $a_i = \sum_j e_{ij}$: fract edges connecting to $C_i$
- random network ($a_i$ fixed): $$e_{ij}^{\text{rnd}} = a_i^2$$
- f: real vs rnd.: $\mathrm{Tr\ } e - ||e^2||$

- node profiles
- personal data
- contextual personal data

- edge profiles
- avg data
- temporal / contextual data

- (non-)exclusive
- crisp <-> fuzzy
- (non-)hierarchical

- optimize objective function
- optimize intra coh. as MSE of obj. func
- Description of cluster with abstract prototype $\mu_k$ (barycenteres of clusters)
- Determining cluster for patterns $x_n$ with nearest neighbor
- Algorithm
- Compute $\mu_n$
- Assign cluster members
- repeat until convergence

- iterative search for optimal K through quality measure (metric)
- Dunn-Index
- Entropy based indices

- disadvantages
- favors spherical clusters
- need to know K
- no notion of noise

- parameters minPt, $\epsilon$
- search for unseen patterns in $\epsilon$-neighborhoods of density >= minPt
- disadvantages
- guess minPt, $\epsilon$
- parameters are fixed

- $r_{nk}$ membership of pattern $x_n$ in $C_k$
- obj func: membership matrix: sum over $(r_{nk})^m||x_n-\mu_k||^2$
- m: fuzziness parameter: 1 = crisp, $m\to\infty: r_{nk}\to 1/K$

- linear combination of gaussians (normal distribution)
- $p(x|\theta) = \sum_k \pi_k N(x|\mu_k, \Sigma_k)$ likelihood
- $\mu_k$: means vector
- $\Sigma_k$: covariances matrix
- need of iid data (identically independently drawn)
- goal: find best $\theta$ for data
- 1 of K representation: $p(z) = \prod \pi_k^{z_k}, z_k \in {0,1}, \sum_k z_k=1, p(z_k=1)=\pi_k$
- $\gamma(z_k) = p(z_k=1|x)$ responsibilities

- mean avg path length
- issue: counts 0 distances from i to i, solution: use inverse

- clustering coeff.
**Watts-Strogatz**: C = C^(2) = 1/n sum of C_i- C^(1) = 3 * # of triangles / # connected triples
- C_i = # triangles with i / # triples with i
- Real world NW: C^(1) ~ O(1), n->inf
- Random NW: C^(1), C^(2) ~ O(1/n) n->inf

- degree distribution
- cumulative distr.: P_k, sum over p_k (fraction nodes having deg. k)
- power law: $p_k \sim k^{-\alpha}$: WWW, citation NW
- exponential: $p_k \sim e^{-k/K}$: power grid, railway
- mix of both: Movie co-actors NW

- max degree
- polynomial distr.
- prob of k being highest deg: $h_k = (p_k+1-P_k)^n - (1-P_k)^n$
- $k_{\text{max}} = \sum_k kh_k$
- power law: $k_{\text{max}} \sim n^{1/{\alpha-1}}$

- resilience: effect of node removal
- mixing patterns
- assortative (Homophily): attach nodes to similar ones, e.g Social NW
- disassortative (Hererophily): n-partite behaviour, e.g ISP <-> end user
- measurement
- analogous to modularity
- degree correlation: assortative -> mean deg of neighbors higher
**Pearson**correlation: cov(X,Y) / deviation(X)deviation(Y)

- Poisson Graph
- poisson prob of node having deg k
- threshold func for phase transitions q(n)
- $S= 1-e^{-zS} = 1 - u$ fraction of graph occ. by giant component X
- random mixing
- not navigatable
- no community structure

- Watts-Strogatz Model
- L nodes, D-dim lattice, vert connected to vertices of max distance k
- rewiring prob p
- total num edges = L*k
- variants
- rewire both ends
- only add shortcuts, no rewiring

- avg path length: calc very hard

- reproduce properties of real world NW
- Price Model
- rich get richer
- Matthew effect
- iteratively add vertices
- power law
- acyclic graph -> not realistic for SN

- Barabasi-Albert model
- Price, but undirected
- fixed deg nodes added
- edge prob proportional to current degree
- p_k ~ k^-3

- percolation
- assign randomly: occupied vs not occupied, analyze seperately
- remove small fraction of high deg nodes -> destroys giant component
- measure resilience (existance of giant compo)

- epidemiology
- nodes: susceptibles (prob $\beta$), infective, recovered (prob $\gamma$)
- SIR Model, "fully mixed"
- investigate dissociation into components

- search & navigate
- Authority: high in from high out
- Hub: high out to high in
- in-degree: x
- out-degree: y
- $Ay = \lambda x, A^T x = \mu y ~ \to ~ AA^Tx = \lambda \mu x$
- local crawls instead of one big crawls
- good in decentralized scenario
- BFS, with
**Adamic**variant: yes OR no, but i have k neighbors

- homophily principle: closeness to similar entities
- heterogenity necessary
- Milgram
- nodes early in path: geographic proximity
- nodes late in path: similarity of occupation

**Kleinberg** Model

- Variant of Watts-Strogatz, respecting spatial distance
- Grid of nodes, manhattan distance ($r(i,j)=\Delta x + \Delta y$)
- connections to neighbors w/ distance <= q1 (regular local contacts)
- additional q2 long range edges, prob: $P(j) \sim r(i,j)^{-\alpha}$
- $\alpha = D$ clustering exponent, for D dimensions necessary for efficient delivery
- $\alpha = 0$ = Watts Strogatz
- $\alpha > D$ bias smaller distances
- $\alpha < D$ bias larger distances
- local (decentralized) knowledge
- only adjacent nodes
- grid structure
- target node
- long range contacts in previous message path

- applications in P2P systems
- friendship as func of distance: $\alpha \approx 1$
- geographic density not uniform
- modify Kleinberg: Rank based friendship, multiple people at node
- random expectaion includes random choice of target node

- Part of human behaviour modeling
- exploitabilty of social behaviour rules by social behaviour models

- short term social context
- Social science: qualitative models
- Process training sensor data
- train general quantitative models
- measure current sensor data
- instantiate quantitive model

- social signal processing
- preprocessing
- data capture
- person detection

- soc. interaction analysis
- behav. cue extraction
- signal understanding
- => social behaviours

- preprocessing
- audio processing
- speaker diarization (who talks when)
- segmentation speech / non-speech
- Generate features
- binary classifiers

- dection of speaker transitions
- split in 2-3s segments
- analyze using statistics

- clustering of segments & classification of speaker
- hierarchical bottom up
- Gaussians
- Dendogram

- segmentation speech / non-speech

- speaker diarization (who talks when)
- video processing
- Face detection
- pixel based
- relative skin batch positions
- feature detection (AdaBoost)

- (Face recognition)
- Eigenfaces (via PCA)

- Human figure detection
- histograms of directions of detected edges

- Face detection

- signals from and to humans & agents
- Multi agent systems
- function with fellow agents
- optimize own utility

- Social signal processing for useful services
- function with humans
- optimize human's utility

- Socially smart environments
- smart home (short term indiv. ctx.)
- availability management (short term soc. ctx.)
- e learning

- Socially smart services
- recommender systems (short term ind. & soc. ctx.)

- analyze human behaviour
- derive models for e.g. prediction
- focus on mobile sensors

- Behavioural cues: timeseries of physiological activity (µs - s)
- context dependent
- conveyed messages
- affective, attiduinal, cognitive state
- emblems (culture specific signs)
- manipulators / adaptors (subconscious)
- illustrators (gestures)
- regulators (turn taking, conversation mediation)

- Social Signals: composed of behav. cues (µs - s)
- Social Behaviour: composed of soc. signals (min - h - inf)
- halo effect: beauty = good

- 90% of gestures: speech
- honest signals: unconscious mind
- Posture
- very reliable cue about social attitude
- classification axes
- inclusive <-> exclusive
- relative body orientation
- (in-)congruence (mirroring)

- OCEAN (Big Five)
**o**penness**c**onscientiousness**e**xtraversion**a**greeableness**n**euroticism

- Facial Action Coding System (FACS)
- action units (muscles)
- 9 upper face
- 18 lower face
- 11 head position
- 14 additional descriptors

- detection of
- emotions
- cognitive states
- psych. states
- soc. behav. aspects
- pers. traits
- soc. signals

- FACS + classifier -> better detection than humans
- modeled via Dynamic Bayesian Networks (DBN)
- detection: integrative methods based on optical flow
- motion pattern of picture elements
- representation: vector field of intensity velocities V(x,y,t)
- $\frac{\partial I}{\partial x}V_x + \frac{\partial I}{\partial y}V_y + \frac{\partial I}{\partial t} = 0$ optical flow equation, solved numerically

- action units (muscles)
- Voal behaviour
- voice quality (Prosody): pitch, tempo, energy
- linguistic vocalizations (Segregates): äääähm
- non-ling. vocalizations: laughter
- silence patterns
- hesitation silence
- psycholinguistic silence
- interactive silence

- turn taking patterns

- interpersonal distances (
**Hall**)- 0-0.5m: intimate zone
- 0.5-1.2m: casual-personal
- 1.0-2.0m: socio-consultative
- 2.0-inf: public

- social context: architectural env, socio-petal/-fugal forces (
**Watson**) - body angles:
**Kendon**: F-Formations### Applications

- prediction of dyadic interaction outcome
- Eigenbehaviours
- Interaction analysis, role structures, user interest

- outcome in discrete state space $\Omega$
- Players only two actions (strategies): C, D
- env. behav. given by state transformer function $\tau(player1, player2) \mapsto \Omega$
- utility function (gain for player to play action), notation: payoff matrix
- $s^*$ set of outcomes when playing s
- Nash equilibrium (NE): no player incentive do deviate from equilibrium strategy
- Theory of focalness
- Risk dominance / Pareto optimality ((9,9) pareto dominates (7,7))

- strict competititveness: $\omega \succ_i \omega' \iff \omega' \succ_j \omega$
- zero sum: $\forall \omega\in\Omega: u_i(\omega)+u_j(\omega)=0$
- always strictly competitive
- negative utility for loser
- strictly zero sum only in games, only perceptual in reality

- prisoners dilemma
- defect better than cooperate
- infinite repeated games (shadow of the future): cooperate better (small losses irrelevant)
- in real situations: n (repetitions) unknown -> virtual shadow of the future, cooperation rational
**Axelrod's**tournament- strategies
- ALL-D
- RANDOM
- TIT-FOR-TAT (winner of tournament)
- TESTER: reactive TIT-FOR-TAT / CCD
- JOSS: TESTER with deviation probability 0.1

- rules afterwards
- Do not be envious
- Do not be first to defect
- Reciprocate C and D
- Don't be too clever

- strategies

- Stag Hunt
- JJ Russeau
- (C,C)(NE) > (D,C) > (D,D)(NE) > (C,D)
- naked party show up

- Game of Chicken
- James dean film
- hero, gangster frontal car driving

- structure is common knowledge
- pure strategy: set of actions
- mixed strategy: probability distribution over strategies
- iterated strict dominance
- A knows what B should play
- B knows that and plays accordingly
- A knows that ...

- pure strategy $s_i$ strictly dominated, if $\exists ~ \sigma_i': u_i(\sigma_i', s_{-i}) \ge u_i(s_i, s_{-i})~\forall s_{-i}\in S_{-i}$
- Game Theory <-> Decision Theory
- Decision Theory: nature only decision maker, maximize own utility
- Game theory: many decision makers, interdependent decisions

- Vickrey Auction: iterated dominance
- over-/underbidding

- each finite strategy form game has mixed strategy NE
- mixed strategy NE $\iff q^\ast(p) = p^\ast(q)$, indifference condition!

- order of choices relevant
- Stackelberg equilibrium: $(q_1^\ast, r_2(q_1^\ast))$
- Backward Induction: solve optimal choice of last player, then backwards

- Cournot equilibrium: $(q_1^c, q_2^c)$
**Selten**: Subgame Perfection: generalization of backward induction- each history entry: strategic form like subgame -> compute NE

- perfect information: each stage only one player has non trivial action set
- rationality decreases with more stages
- subgame-perfect EQ: $\forall ~ h^k:$ restriction $s|h^k$ to $h^k$ on $G(h^k)$ is NE of $G(h^k)$