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Interaction Models & Social Networks: Game Theory and Cooperation - Prof. Barrera, Appunti di Sociologia

Università di Torino (UNITO)Sociologia
Prof. Davide Barrera

A comprehensive overview of models of interaction and social network analysis (sna), delving into game theory, cooperation problems, and the structure of social networks. it explores concepts like nash equilibrium, pareto optimality, and the significance of network structure in shaping behavior and resource distribution. the text also examines the role of social capital, both bonding and bridging, and its relationship to cooperation and competition. furthermore, it discusses the influence of network structure on individual behavior and the implications for social transmission and intervention strategies. Valuable for understanding the interplay between individual actions and social structures.

Tipologia: Appunti

2024/2025

Caricato il 24/05/2025

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MODELS OF INTERACTION AND SOCIAL NETWORK ANALYSIS
INTRODUCTION
HUME´S GUILLOTIN
Hume didn´t meet with no proposition that is not connected with an ought, or an ought not. For as this
ought, or ought not, expresses some new relation or affirmation, it´s necessary that it should be observed
and explained; and at the same time that a reason should be given; for what seems altogether inconceivable,
how this new relation can be a deduction from others, which are entirely different from it.
TYPOLOGY OF SCIENTIFIC EXPLANATIONS
- Statistical explanations: phenomena are explained by means of statistical relationships between
variables. They are based on the observed relationship that links (statistically) an input variable and
an putput variable.
- Mechanism-based explanations: phenomena are explained on the basis of a theory of action in
which actors, interactions, restrictions and opportunities are explicated. The explanation accounts
for how individual actions aggregate and produce collective outcomes.
COLEMAN´S BOAT
THEORY OF ACTION
- The complexity of social phenomena can be broken down to simpler, smaller units: actions and
interactions.
- At the core of a theoretical explanation lies always some theory of action.
- Older sociological approaches stressed socialization and norms vs: Goal-oriented theories of action.
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INTRODUCTION

HUME´S GUILLOTIN

Hume didn´t meet with no proposition that is not connected with an ought, or an ought not. For as this ought, or ought not, expresses some new relation or affirmation, it´s necessary that it should be observed and explained; and at the same time that a reason should be given; for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it. TYPOLOGY OF SCIENTIFIC EXPLANATIONS

  • Statistical explanations: phenomena are explained by means of statistical relationships between variables. They are based on the observed relationship that links (statistically) an input variable and an putput variable.
  • Mechanism-based explanations: phenomena are explained on the basis of a theory of action in which actors, interactions, restrictions and opportunities are explicated. The explanation accounts for how individual actions aggregate and produce collective outcomes. COLEMAN´S BOAT THEORY OF ACTION
  • The complexity of social phenomena can be broken down to simpler, smaller units: actions and interactions.
  • At the core of a theoretical explanation lies always some theory of action.
  • Older sociological approaches stressed socialization and norms vs: Goal-oriented theories of action.

EXPERIMENTAL METHOD

CAUALITY AND EXPERIMENTAL METHOD

  • Causal effect = Individual Treatment Effect (ITE) = on the same unit, at the same time, where is the outcome obtained for the untreated unit and is the outcome obtained for the treated unit.
  • Fundamental problem of causal inference: It is impossible to observe simultaneously, for the same unit, the value of when the unit is exposed to the treatment and when it is not (Holland 1986).
  • There is a scientific solution to the problem (typical of natural sciences) and a statistical one (typical of the social sciences, but not only, also medicine, biology, etc.). SCIENTIFIC SOLUTION: When one of two assumptions can be adopted (unprovable but plausible):
  • Assumption of equivalence (NB between units): o Causal effect (ITE) = on different units at the same time (e.g. of neighbouring fields, one treated and the other not with fertiliser).
  • Assumption of invariance: o (ITE) = on the same unit at different times. Requires:  Temporal stability: replaceable with (detected at a previous time)  Ininfluence of the detection: the value of is not affected by the previous detection of (on the same unit)
  • In the social sciences the assumption of equivalence is implausible, but the assumption of invariance can be plausible in some situations.
  • When the assumption of invariance is plausible -> Within Subject Design STATISTICAL SOLUTION:
  • For a single individual equivalence is an implausible assumption, but for a group the assumption of equivalence (statistical) is plausible if the process of group formation is random -> randomization (Fisher 1925)
  • Average Causal Effect (Average Treatment Effect) ATE = on two randomized groups.
  • The average effect estimated by comparing two groups obtained by randomization: Between Subjects Designs
  • Randomization is essential to make two groups identical in expectation on all variables not considered -> important implications in cases where randomization is not entirely controlled (Quasi- experiments, policy evaluation studies, natural experiments) THEORY AND EXPERIMENTAL DESIGNS:
  • Model driven experiments: o The design is a replication of the model o The results can be compared with the predictions of the model o In principle only one condition is sufficient (e.g., Henrich 2004, interaction models as tools for measuring social preferences
  • Theory/Intuition driven experiments:

COOPERATION GAME THEORY

THE LOGIC OF EMPIRICAL RESEARCH:

TIPOLOGY OF SOCIOLOGICAL PROBLEMS:

  • The rationalization problem
  • The problem of social order (cooperation problems)
  • The problema of inequality INTRODUCTION TO GAME THEORY
  • Games = a taxonomy of strategic interactions.
  • Theory = set of rules and assumptions used to “solve games. TERMINOLOGY:
  • Cooperative game: communication is possible Non cooperative game: communication is impossible
  • One-shot game: interaction occurs only once Repeated game: interaction is repeated, i.e., there is a common future
  • Simultaneous: normal form Sequencial: extended form MOVES AND STRATEGIES
  • A strategy is a set of rules or instructions that determine what an actor should doat any point in the game o In one-shot simultaneous games a strategy corresponds to a single decision or move
  • Given a one-shot noncooperative game involving two actors:
  1. The strategy X of actor A is a best reply against strategy Y of actor B if strategy X maximses A’s payoff in case B chooses strategy Y o Using a best reply is consistent with the model assumptions (goaldirected action) if actor A expects actor B to choose strategy Y.
  1. The strategy X is a dominant strategy if it is the unique best reply against all possible strategies of actor B (i.e. if X maximizes A’s payoff whatever strategy B chooses) o Goal-directed action implies that an actor chooses a dominant strategy if one is available; some games have no dominant strategy
  2. NASH EQUILIBRIUM: o A combination of two strategies (XY) (i.e., a possible outcome of the game) is a Nash Equilibrium if X is the best reply of actor A against the strategy Y chosen by actor B and Y is B’s best reply against the strategy X ––chosen by actor A.  If A anticipates that B will choose strategy Y and B anticipates that A will choose strategy X the Nash equilibrium is consistent with goaldirected action.  John Nash (Nobel laureate 1994) demonstrated that all finite games have at least one Nash equilibrium (not necessarily in ‘pure’ strategies).  A game may have more than one Nash Equilibrium
  3. PARETO OPTIMALLY: What is collectively better? a. .A combination of strategies (X, Y) (i.e., an outcome of the game) is Pareto-optimal if it is not possible to improve the payoff of (at least) one of the players – moving to one of the other possible outcomes – without decreasing the payoff of the other player. b. A combination of strategies (X, Y) (i.e., an outcome of the game) is Pareto-suboptimal if there is one other possible outcome whereby at least one of the players is better off (i.e., gets a higher payoff) and the other player is not worse off (i.e., does not get a lower payoff).
  4. Hypotheses: a. H1: Actors will chose a best reply, given their expectations concerning the choice of the partner b. H2: If an actos has a dominant strategy, she will use it c. H3: The choices of the two players will form a Nash Equilibrium A game in which the Nash Equilibrium (that is the predicted result) is Pareto-suboptimal is sometimes called a social dilemma.

PUBLIC GOOD GAMES

Dilemas with n players: provisions of public godos:

  • Welfare
  • Environmental problems, etc A MODEL OF A COOPERATION PROBEM WITH N (>2) PARTICIPANTS:
  • A group with N players
  • Every player has an initial endowment of resources Y.
  • Every player can choose to invest a fraction X of her endowment Y (or keep the whole endowment).
  • The investment X grows by a factor M (1<M<N) and subsequently the sum of all (grown) contributions is divided equally among the group members.
  • As M<N, keeping everything (X=0) is the dominant strategy.
  • However, if everyone contributed with the whole endowment (X=Y), all players would be better off. THEORY BUILDING:
  • In real cooperation problems defection (deserción: el hecho de no cooperar) sometimes can be punished.
  • However, sanctions are typically costly.
  • 2nd order free rider dilemma THE PROBLEM OF “SELFISH PREFERENCES” In defence of selfishness:
  • As a normative model it is tractable and useful as a benchmark (homo economicus)
  • It is consistent with the theory of evolution (selfish gene).
  • Limits of alternative models:
  1. Anything can be explained with ad hoc preferences.
  2. “Non-selfish” preferences require qn explanation, too (e.g., homo sociologicus?) THE BPC MODEL Human behavior depends on:
  • Beliefs: relative to the situation or to the expected behavior of others.
  • Preferences: assumed to be transitive (if A>B and B>C then A>C), but NOT homogeneous.
  • Constraints: characteristics of the interaction, possibility to use sanctions, distribution of preferences. BPC AND DBO MODEL Human behavior depends on:
  • Beliefs: relative to the situation or to the expected behavior of others.
  • Desires: assumed not homogeneous and not even transitive.
  • Opportunities (specular to constrains): characteristics of the interaction, possibility to use sanctions, distribution of preferences Solution? Why do actors use punishment and cooperate when sanctioning opportunities are available? Actors have heterogeneous preferences: conditional reciprocators force free riders to cooperate when punishment is possible, free riders force conditional reciprocators to defect when punishment is not posible.

o Emerging properties o Complex is more than complicated The sociological outlook: consequences and causes.

  • Borgatti´s typology:
  • Theories on tie formation TERMINOLOGY
  • Path: a sequence of nodes connected with each other – without crossing any node more than once
  • Walk: any sequence of nodes connected with each other – possibly also crossing one or more nodes more than once
  • Cycle: ring-shaped structure, a path including at least 3 nodes whereby the first and the last node coincide
  • Connectivity: a graph “connected” if every possible pair of nodes is connected by at least one path A disconnected graph is divided in components, i.e., connected subsets lacking paths between subsets
  • Distance: the length of a path corresponding to number of steps (edges) required to go from the first to the last node SOCIAL NETWORKS: DATA The unit of analysis is the combination of 2 sets consisting of actors (nodes, indicated as points or vertices) and relationships (edges, indicated as lines, arcs or ties). Leve lof análisis
  • Ego-centered networks (aka egocentric networks): they contain information about individual relationships of the research participants, and sometimes also information about relationships between the respondents contacts. At this level a network is analogous to a respondent’s set of attributes. They are generally studied using standard surveys.
  • Complete networks: information about all possible relationships inside a given group defined by “natural” borders, for example school classrooms or organizational units.
  • Cognitive networks: a full map of the network as perceived by each one of its members
  • Big data: digital traces of intrinsically relational activities (example, facebook, whatsapp, twitter, phone calls etc)

MEASUREMENT PROPERTIES AND GRAPHICAL REPRESENTATION

A relationship can be intrinsically symmetric (e.g., neighborhood, friendship etc) but the resulting tie can be (and often is) measured as a directed tie, by asking separately A about her relationship to B, and B about her relationship to A. HOMOPHILY The tendency to form relationships preferably with similar others (similar with respect to either acquired or ascribed characteristics, or both). Here homophily is meant descriptively. Possible causes?

  1. Sometimes on preferences (The P in the BPC model) → transmission/influence/selection.
  2. Sometimes on constrains (the C in the BPC model or the O in the DBO model) → environmental adaptation.
  3. Sometimes on both → diffusion of technological innovations

TERMINOLOGY:

  • Embeddedness: most commonly used as a generic term, however embeddedness (of a tie, or of two nodes) can be formally defined as the number of contacts shared by the two nodes connected by the tie.
  • Neighborhood overlap (of nodes A and B): number of contacts shared by A and B divided by the total number of contacts of A + those of B.
  • Structural holes (informal definition): the empty spaces between sets of nodes whereby the sets are connected only by a local bridge; advantages: 1) information, 2) creativity, 3) gatekeeping or brokerage SOCIAL CAPITAL:
  • Social Capital (micro): resources that can be obtained through relationships, they can be material or symbolic resources. o Ties carrying material resources are called instrumental ties o Ties carrying symbolic resources are called expressive ties (Nan Lin).
  • Connectivist approach: network closure leads to trust and cooperation = bonding social capital (J Coleman)
  • Social capital = number of contacts + tie strength + resources owned by the contacts (H Flap).
  • Structuralist approach: structural holes = bridging social capital (Ron Burt)
  • Corollaries: It is possible to invest in the creation of social capital, on the basis of a reciprocity norm, e.g., doing a favor creates a credit in social capital Social capital embedded in relationships grows slowly, but it can be destroyed quickly COOPERATION AND COMPETITION Structural holes produce advantages in competitive contexts but… Network density favors cooperation thorugh reputation mechanisms (e.g., the diamonds merchants in New York) What favors innovation: Ideally a mixed network:
  • Bridges and structural holes help in the creative pase.
  • Dense and cooperative networks help in the implementation pase INSTRUMENTS TO MEASURE SOCIAL CAPITAL:
  • Name generators (example: With whom do you discuss personal matters).
  • Position generators (example: Do you know someone that is a: medical doctor, lawyer, accountant etc...).
  • Resource generator (example: do you know someone that ... Can help you dealing with complex administrative tasks, such as filling a tax declaration form?) STRUCTURAL CAPITAL: EXCLUSION AND POWER

MEASURING SOCIAL NETWORKS