Social Gaming Zusammenfassung

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.

1. Digital Games

Ludology

Methods
- empirical
- design science
- deductive
Influences
- psychology, sociology, socio-psychology
- economy
- informatics, CS, mathematics
- arts

Play

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

Game

Salen & Zimmermann
- system
- players engage
- artifical conflict
- rules
- quantifiable outcome
Hunicke
- systems building behaviour via interaction
- components (MDA)
  - Mechanics
  - Dynamics
  - Aesthetics
Juul:
- three levels
  - game (system)
  - player(s)
  - world (context)
- transmedial
Frasca: properties
- social
- performance measurement and value

Types of games

online
mobile
- context (sensors)
  - spatio-temporal
  - social
  - physical
  - medical
  - personal
- location based games
- mobile context != mobile UI
simulations
social
hardcore
casual
- Juul
  - characteristics
    - instant play
    - quick play
    - common play
  - design principles
    - Fiction
    - Usability
    - Interruptibility
    - Difficulty & Punishment
    - Juiciness
- 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
serious
- useful side effects (Susi)
  - education
  - training
  - information
- Games with a Purpose (GWAP)
  - human-based computing
  - crowdsourcing (Captcha)

Genre critique (Järvinen)

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)

Motivation

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)
  1. Physiological
  2. Safety
  3. Belonging-Love
  4. Self Esteem
  5. Self Actualisation

Emotions

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

Engagement

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

Flow

conditions
- challenge, appropriate level
- clear proximal goals
- immediate feedback
models
- 3 channel (Nakamura & Csikszentmihalyi)
- 4 channel (Novak)
- 8 channel (Nakamura & Csikszentmihalyi)

Emotional contagion (Hatfield)
- mimic & sync. expressions
- converge emotionally with other person
Performance: Hawthorne effect

Player communities

Macro: all players
Meso: guilds
Micro: teams

Web 2.0 (O'Reilly)

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

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

Communication

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
- ...

Context

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

Clustering coefficient

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

Centrality

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|))

Vertex -> edge graph

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

Vitality

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)

Random Walk (RWB) / current flow

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: $k_j^{-1}[M_t^r]_{js}$

Feedback centrality

centrality depends on adj. centrality
Hubbell index
Page rank

4. SNA: Dense subnetworks

Groups

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

Clique

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

N-cliques, N-clubs, N-clans

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

N-Plex

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

N-Core

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

LS-Sets

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

Lambda-Sets

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

Cohesion

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

5. SNA: Graph Clustering

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

Quality measures

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

Clustering Algorithms

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
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.
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
Newman Girvan Method: Centrality based Splitting + Modularity
- iterative
  1. calc edge betweenness
  2. remove edge with max betw.
  3. repeat
- Modularity as intra. coh.
- Edge centralities
  - SPB (best avg)
  - RWB

Modularity

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.: $\mathrm{Tr\ } e - ||e^2||$

6. Data Mining: Metric Clustering

Profile data

node profiles
- personal data
- contextual personal data
edge profiles
- avg data
- temporal / contextual data

Types of clusterings

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

K-means

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

DBSCAN

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

Fuzzy K-means

$r_{nk}$ 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, $m\to\infty: r_{nk}\to 1/K$

GMM (Gaussian Mixture models)

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

7. Real world Networks: Properties & Models

Properties

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)

Random Graph models

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

Models of network growth

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

Processes on Networks

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

Processing chain

short term social context
1. Social science: qualitative models
2. Process training sensor data
3. train general quantitative models
4. measure current sensor data
5. instantiate quantitive model
social signal processing
1. preprocessing
  1. data capture
  2. person detection
2. soc. interaction analysis
  1. behav. cue extraction
  2. signal understanding
    - => social behaviours
audio processing
- speaker diarization (who talks when)
  1. segmentation speech / non-speech
    - Generate features
    - binary classifiers
  2. dection of speaker transitions
    - split in 2-3s segments
    - analyze using statistics
  3. clustering of segments & classification of speaker
    - hierarchical bottom up
    - Gaussians
    - Dendogram
video processing
1. Face detection
  - pixel based
  - relative skin batch positions
  - feature detection (AdaBoost)
2. (Face recognition)
  - Eigenfaces (via PCA)
3. Human figure detection
  - histograms of directions of detected edges

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 aware computing

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.)

Reality Mining (Alex Pentland)

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

Definitions

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

Gestures & Posture

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)

Personality Traits Encoding Systems

OCEAN (Big Five)
- openness
- conscientiousness
- extraversion
- agreeableness
- neuroticism

Face & Eye Behaviour

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
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

Space & Environment

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

10. Game Theory

Basics

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

Symmetric 2x2 Games

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
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

Strategic Form Games

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!

Multi Stage Games

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 $G(h^k)$

Social Gaming