Strategic SocialInteractions

Andreas DiekmannETH Zurich

Conference Social Interaction and SocietyETH Zurich, May 26 – 28, 2016

Sociologists on Strategic Interaction

Erving GoffmanStrategic Interaction, 1969

Raymond BoudonThe Logic of Social Action, 1981The Unintended Consequences of Social Action, 1982

Sociologists Gerald Marwell and Ruth E. Ames, 1979Inventors of the Public Good Game

Jessie Bernard, 1954

Strategic Interaction►Fundamental problems of sociological research are of strategic character

Examples: • The emergence of cooperation and social order• The dynamics of competition and conflict• Social norms and the problem of sanctioning• The impact of signals and signs on beliefs and behaviour• Inequality of power, status, resources• The emergence of institutions• Social exchange and the problem of trust• The development of protest movements• The dynamics of segregation, herding, “bubbles”• Social dilemmas and collective goods

Game Theory in Sociology

• Provides precise models of social interaction

• Neglected by most sociologists• Moreover, for a long time sociology

ignored its experimental tradition

Experimental Sociology?

British J. of Soc.

ASR AJS AER

0 %(0 of 75)

0,8 %(1 of 126)

2,7 %(3 of 111)

12,2(33 of 270)

Articles published 2005 to 2007

„Sociology as a nomothetic science, aiming at the exact description of functional and causal relations in the area of social phenomena, will sooner or later have to employ experimental methods for investigating its research problems“ (translated from German, Sorokin 1928).

Pitirim A. Sorokin in „Kölner Zeitschrift für Soziologieund Sozialpsychologie“, 1928

►Fortunately, for more than a decade a younger generationof sociologists in Europe, Japan, United States, etc.started to focus on both:

a) Applications of game theory (and behavioural gametheory) to solve sociological problems of strategicinteractions

b) Employing experimental methods, conducting field andonline experiments and exploiting new data sources

(digital data, using web crawler, smartphone apps, etc.)

Desires, Beliefs, Opportunities (DBO, Hedström 2007)Beliefs, Preferences, Constraints (BPC, Gintis 2007)

Preferences (aims, goals, desires)

Beliefs (assumptions about „nature“and likely choices of other actors)

Opportunities (budget, technology, institutions, social context)

Key elements of a theory of social action

Desires, Beliefs, Opportunities (DBO, Hedström 2007)Beliefs, Preferences, Constraints (BPC, Gintis 2007)

Preferences (aims, goals, desires)

Beliefs (assumptions about „nature“and likely choices of other actors)

Opportunities (budget, technology, institutions, social context)

Key elements of a theory of social action

But note: Elements are not a theory!

Desires, Beliefs, Opportunities (DBO, Hedström 2007)Beliefs, Preferences, Constraints (BPC, Gintis 2007)

►Key elements of a theory of social action

Preferences (aims, goals, desires)

Beliefs (assumptions about „nature“and likely choices of other actors)

Opportunities (budget, technology, institutions, social context)

ActionDecision and game theory combines the elements

1. Risk and uncertainty: Subjective expected utility, maximin, regret theory, bounded rationality,heuristic principles

2. Strategic interaction: Equilibrium strategies, refinement of eq. strategies, evolutionary stablestrategies, learning, adaptation, etc.

►Toolbox of behavioural decision and game theory

Decision Theory:Three Circles of Rationality

I. Homooecono-micus

II. Rational Choice

III. Bounded Rationality

I. Homo oeconomicus = selfishness,material interests (time, money),axioms of rationality (i.e. transitivepreferences etc.)

II. Rational choice: consistency with axioms of rationality (i.e. transitive preferences etc.) Note:no restriction on preferences!By definition “wide version” concerning preferences

III. Bounded rationality: Learning,heuristic principles, evolution

Decreasing restrictionson assumptions of decision theory

I. Homo oecon.

II. RC

III. Bounded Ratio.

Rationality (Definition): Consistency with axioms, e.g. transitive choices

Preferences (aims, goals, desires)

Beliefs (assumptions about „nature“and likely choices of other actors)

Opportunities (budget, technology, institutions, social context)

Action Strategic interaction

Beliefs and opportunities are not exogenousBeliefs and opportunities are dependent on the structure of

social interaction.

►Traditional rational choice models neglect strategic interaction

►Strategic interaction:

1. Opportunities are dependent on other actors‘ choices (Example: “Tocqueville paradox”)

2. Beliefs are dependent on other actors‘ potential and actual choices (Example: Signals of trust)(Endogeneous preferences: E. Fehr, Friday lecture)

3. Endogeneous beliefs and Evolution: Asymmetric volunteer’s dilemma (Asymm. VOD)

„Tocqueville Paradox“

Boudon‘s Competition Model Explains the Paradox

Payoffs: α > β > γ

Boudon 1982 [1977], Raub 1984, Hedström 2007, Berger & Diekmann 2015

►Frustrated loser

►Satisfied winner

Exogenous rise ofopportunities (k)

Increase ofinvestingactors (p)

Endogenous decline of individualopportunities(actor‘s winningchance)

►

Intuition:

Opportunities

►Stayer

Investment decision = participating in a costly competition

Level of frustration

}

TocquevilleParadox

Mixed Nash Equilibrium Strategy in the Competition Game

Raub 1984, Berger & Diekmann 2015

N = number of actorsk = number of positionsn = number of investors

p = probability to invest(decision variable)

►Three lab experiments with small groups (Berger & Diekmann 2015)►In progress: Experiment with larger group size using Amazon Mechanical Turk

k = 1 2 5

Investment

No InvestmentPlayer i

The gain of investment depends on other players‘ decisions: It is not a dominant strategy!

Beliefs about Trust

Trust Game with Asymmetric Information

►Proportion α of honest actors, 1 – α cheaters

►Belief about α is exogenous

► Classic rational choice theory: Place trust if:α > α*=(P – S)/(R – S)(“Coleman’s threshold”)Honest actors: R > T - c

When the threshold no longer holds and trustors encounter too many cheaters

α < α* ?

• Sanctioning institutions/repeated games/social embeddedness (Buskens/Raub 2013)

• Or signalling. Separating signalling equilibrium if ►signalling costs of honest trustees are smaller than (R – P) ►and signalling costs of cheaters are larger than (T – P)• Belief is α initially but will be updated by signalling • Beliefs are endogenous and conditional on signals!

„Marry Me“Yasushisi Takahashi travelled 7’164 km and traced his journey by GPS.

„Marry Me“Yasushisi Takahashi travelled 7’164 km and traced his journey by GPS.His bride said „yes“!► Apparently, a strong signal larger than T – P, and, hopefully,costs are smaller than R – P.

Beliefs are endogenous and dependent on signalling

►Car dealers voluntarily granting a warranty claim higher prices (1.5% according to the analysis of 41’359 VW Golf offers on Autoscout24. Besides: the impact of “Dieselgate” is measurable as a price reduction of 6.8%)

Siow/Tobler & Diekmann/Wehrli 2016 (preliminary results). All coefficientsare significant for p < 0.001.

Indep. Variable log (price) log (price) for Golf TDI

Age -0.008 -0.007

Mileage -0.028 -0.035

Horsepower [PS] 0.006 0.006

Warranty 0.015

Reputation 0.014

„Dieselgate“ (before/after Oct. 2015)

- -0.068

Constant 9.476 9.625

Adj. R2 0.898 0.918

N 41359

Data from more than 40‘000 offers of second-hand VW Golf cars werecollected from the platformAutoscout24using web crawlingSoftware.

Beliefs are endogenous and dependent on signalling

►Car dealers voluntarily granting a warranty claim higher prices (1.5% according to the analysis of 41’359 VW Golf offers on Autoscout24. Besides: the impact of “Dieselgate” is measurable as a price reduction of 6.8%)

►Trustors place trust more often when interacting with trustees who were observed as being generous (= signal) in a dictator game (Gambetta and Przepiorka 2016)

►Trustees invest in embeddedness (a costly signal) to convince trustors that they are honest (Vincenz Frey 2015)

►Reputation effects are observable on eBay and even on illegal markets in the “darknet”. Investing in reputation is a signal of being trustworthy

Seller‘s reputation6 out of 6 positive

Rating informsabout transactionprice!►Prevents„whitewashing“

Micro

Micro Macro

The game theory solution to the micro-macro problem:

• Micro: Individual preferences, beliefs, opportunities• Macro: A Nash equilibrium (or some refinement)

aggregates the individual actions

►In theory, an elegant solution. However, rationality theory often fails to predict the observed behaviour of human actors►However, RC by Evolution

Symmetric non-linear public good game: A single actor is sufficient to produce the collective good. A cooperative actor gains U on cost K and a free rider gains U. If all actors decide for free riding they get nothing (U > K > 0)

Asymmetric game: A “strong” player has lower costs K or higher gains U. A strong cooperative player receives Us – Ks , N-1 symmetric “weak” players’ get U – K whereby: Us –Ks > Uw – Kw > 0

► Mixed Nash equilibrium. Probability of cooperation:

However, there is an “asymmetric”, efficient (Pareto optimal) Nash equilibrium in pure strategies:

► s = (Cs, D, D, D, D, …,D)

►This is the rationality solution of the asymmetric game (in accordance withthe axioms of the Harsanyi/Selten theory)

►Moreover, the strategy profile s = (Cs, D, D, D, D, …,D) is an evolutionary stable equilibrium (ESS)

Asymmetric Volunteer’s Dilemma: Evolution of Rationality

PLoS one August 2014

► s = (Cs, D, D, D, D, …,D)

► strong player cooperates,weak players free rideis stable ESS

Endogenous Beliefs and Evolution: Asymmetry SolvesCoordination Problems

►The rate of cooperation is small in a symmetric volunteer’s dilemma due to “diffusion of responsibility” p(C)=𝑁𝑁−1 𝐾𝐾/𝑈𝑈►Asymmetry largely increases the probability of cooperation (a strong player has lower costs K or higher gains U from collective good production than other players) ►There is a tendency that Asymmetry mitigates the effect of “diffusion of responsibility”(but does not fully compensate for group size)►The asymmetric equilibrium is ESS. It should be approached by an evolutionary process (learning in repeated one-shot games, empirical work in progress)►Rationality by Evolution!

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Percent Cooperation in the Symmetric and Asymmetric Volunteer’s Dilemma by Group Size

Symmetric game Asymmetric game Diekmann & Przepiorka 2015a,b, 2016

0.88

0.47

0.73

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www.allgemeine-zeitung.de (12.9.15)

Strong player‘s coop

Strategic Interaction Models• Focus on key problems of sociology• Explain the mechanisms of collective outcomes: Social

norms, movements, institutions, etc. • in case of strategic interaction sociologists should apply

models of game theory (and behavioural game theory) • Take account of social preferences if necessary• Relax assumptions of strict rationality if necessary• Focus on evolutionary processes: Learning, adaptation,

bounded rationality• Work interdisciplinary: Psychology, Economics, Anthropology,

Political Science, Law …• Empirically testable predictions

►Elements of Sociological Science

Jim Walsh about Mark Mallman‘s song, Arts & Culture 3/4/16