Social Animals: Cooperation, Conflict, and Corruption

Angelo Romano - Social, Economic and Organizational Psychology

• Social, Economic and Organizational Psychology.
• Institute of Psychology | Leiden University.
• Email: a.romano@fsw.leidenuniv.nl
• Date: 02-04-2025

Angelo Romano - Assistant Professor

• SEO psychology.
• Office: 2A35.
• Email: a.romano@fsw.leidenuniv.nl.
• Research interests:
  • Human cooperation & conflict.
  • Cross-societal differences.
  • Ingroup favoritism.
  • Reciprocity.
  • Human-AI interaction.

Organizational Notes

• Course Manual on Brightspace.
• Attendance is important.

Lectures

• April 2
• April 9
• April 16
• April 23
• April 30
• May 7
• May 14
• (May 21) SA41

Key Questions

• When and why do humans cooperate or help others?
• How could cooperation evolve?
• Why do we sometimes fight and compete?
• How can we prevent conflicts?
• What is the role of rules in human societies?
• Why do we sometimes violate rules and norms?

Course Overview

• A Short Primer to Game Theory and Economic Games
• Main Psychological Frameworks of Cooperation and Conflict
• Games of Cooperation and Coordination I (the evolution of cooperation)
• Games of Cooperation and Coordination II (cooperation and discrimination)
• Games of Conflict and Competition
• Cheating, Dishonesty & Norm Violations

Today's Focus: Game Theory

• Social situations: how to formalize them? (matrix)
• What actions to take? Nash equilibrium (pure, mixed)
• How to study them in practice? Economic games

Questions About Social Interactions

• Can I trust them or not?
• Can I outcompete them?
• Should I help or no?
• Should I lie or tell the truth?
• Should I cooperate or defect?
• Why social animal?

Game Theory

• Decisions are intrinsically social.
• In social situations:
  • Decisions not only influence own outcomes but can affect others (consequence for others).
  • Decisions of others likewise can influence own outcomes (consequence of others).

Formalizing Social Situations

• Social situations can be formalized as playing games.

The Game Analogy

• Examples include games like Monopoly and Risk.

Formalizing Simple Social Interactions

1. Identify the actors.
2. Identify the actions of each actor.
3. Identify the outcome for each action/action pair.

Prisoner's Dilemma

• A game where individual rationality leads to a suboptimal outcome for both players.

• Example payoff matrix:

  	Player 2 (P2) Wash	Player 2 (P2) Not Wash
  Player 1 (P1) Wash	2	0
  Player 1 (P1) Not Wash	3	1

• Higher scores in the prison example relate to worse outcomes

Matching Pennies

• A game with no pure strategy Nash Equilibrium.

• Example payoff matrix:

  	Player 2 (P2) Left	Player 2 (P2) Right
  Player 1 (P1) Left	1	0
  Player 1 (P1) Right	0	1

Stag Hunt

• A game that represents a coordination problem.

• Example payoff matrix:

  	Player 2 (P2) Stag	Player 2 (P2) Hare
  Player 1 (P1) Stag	2	0
  Player 1 (P1) Hare	0	1

Chicken Game

• A game that models situations of conflict.

• Example payoff matrix:

  	Player 2 (P2) Swerve	Player 2 (P2) Straight
  Player 1 (P1) Swerve	0	-2
  Player 1 (P1) Straight	2	-5

Rational Choice in Social Games

• Rationality: payoff maximizer.
• Rationality here refers not to:
  • being reasonable instead of emotional.
  • having a central nervous system or a bigger brain.
  • being educated or ‘intelligent”.

Nash Equilibrium

• A set of strategies where no player can unilaterally change their strategy and get a better payoff.
• In a Nash equilibrium, no player has anything to gain by changing only their own strategy; a player will be worse off by changing their strategy.
• John Nash (1928-2005).

Pure Strategy Nash Equilibrium

• In two-player simultaneous games.
• A state in which all players play the best response to each other’s strategy.

Prisoner's Dilemma Example

• Payoff matrix:

  	Player 2 (P2) C	Player 2 (P2) D
  Player 1 (P1) A	3	0
  Player 1 (P1) B	4	1

• B is a strictly dominant strategy → best action regardless of what the other player does.

• Pareto Optimal Outcome = state from which it is impossible to deviate, without making (at least) one individual worse off.

Stag Hunt Example

• Payoff matrix:

  	Player 2 (P2) A	Player 2 (P2) B
  Player 1 (P1) A	3	0
  Player 1 (P1) B	1	1

• Is there any pure equilibrium? yes

• Is there one strictly dominant strategy? no

Mixed Strategy Nash

• In two-player simultaneous games.

Matching Pennies Example

• Payoff matrix:

  	Player 2 (P2) Left	Player 2 (P2) Right
  Player 1 (P1) Jump left	1	0
  Player 1 (P1) Jump right	0	1

• No dominant strategy.

• Expected value of two actions is equal.

• If a player randomizes, there is nothing the other player can do to increase the own payoff.

Summary of Key Concepts

1. Social situations as games
2. Construction of a matrix
3. Pure vs mixed strategies

Economic Games

• Games used in experimental research.

Categories of Games

• Cooperation.
• Competition.
• Coordination.
• Generosity.
• Bargaining.
• Trust.
• Group cooperation.
• Asymmetric conflict.

Prisoner's Dilemma Game (Economic Game example)

• Illustrates cooperation vs. defection.
• Monetary incentives used in lab experiments.

Continuous Prisoner’s Dilemma Game

• Player 1 and Player 2 each have $10$ euro.

• Payoff matrix example:

  	Player 2 Cooperate	Player 2 Defect
  Player 1 Cooperate	$5+2=7$	$0+10$
  Player 1 Defect	$9+10=19$	$1+2$

• Generalized example with e1 and e2.

Public Goods Game

• Each member has resources (time, energy, money, effort etc.). In this example: 20 ‘resource points’ (RP).
• They simultaneously decide how much to invest to the Public good.
• Whatever is invested to the Public Good is multiplied by a factor $x$ (here: $3$; mimicking the efficiency gain of cooperation).
• The Public Good is then shared equally

Public Goods Game Example

• Initial resources: $20$ RP per member.
• Investments: Members invest $0$, $12$, $20$, and $0$ RP into the public good.
• Total investment: $0 + 12 + 20 + 0 = 32$ RP.
• Multiplication: The total investment is multiplied by $3: 32 \times 3 = 96$ RP.
• Distribution: The multiplied amount is shared equally: $96 / 4 = 24$ RP per member.
• Final Payoff: To calculate the final payoff, add the return from the public good to the remaining resources.
  • Member 1: $20 - 0 + 24 = 44$ RP
  • Member 2: $20 - 12 + 24 = 32$ RP
  • Member 3: $20 - 20 + 24 = 24$ RP
  • Member 4: $20 - 0 + 24 = 44$ RP

Real-World Examples of Prisoner's Dilemma & Public Goods Games

• Climate change.
• Public transport.
• Public health care.
• Refugee aid.

Dictator Game

• One player (dictator) decides how to split a sum of money with another player (recipient).
• The dictator can send any given amount:
  • $e$. Initial endowment of dictator
  • $g$. Given amount, where $0 ≤ g ≤ e$

Ultimatum Game

• One player (proposer) decides how to split a sum of money with another player (responder).
• The responder can either accept or reject the offer. If rejected, both players receive nothing.

Ultimatum Game

• Proposer offers a split.
• Responder either accepts or rejects.
• If responder rejects, both get 0.
• Example in job interviews.

Trust Game

• Investor (trustor) decides how much to invest with a trustee.
• The investment is multiplied, and the trustee decides how much to return to the investor.
• Calculations:
  • Investor sends amount $g$, where $0 ≤ g ≤ ei$. $ei$ = initial endowment of the investor
  • Trustee receives $g*m$, where $m$ is typically $3$
  • Trustee returns $r$, where $0 ≤ r ≤ g*m$

Trust Game - Example

• $10$ euro example, showing how trust and returns are calculated.

Trust Game - Real World Examples

• eBay.
• Peer markets.
• Baby sitting.

Attacker-Defender Game

• Models situations of conflict and defense.

• Payoff matrix:

  	Defender C (Peace)	Defender D (Defend)
  Attacker C (Peace)	2	0
  Attacker D (Attack)	1	1

Common Features of Games

• One-shot vs. repeated.
• Simultaneous vs. sequential.
• Symmetric vs. asymmetric.

Synthesis of Games

• Coordination: Stag hunt

• Competition: Chicken game

• Cooperation: Prisoner’s dilemma

• Generosity: Dictator game

• Trust: Trust game

• Asymmetric conflict: Attacker-defender game

• Group cooperation: Public good

• Bargaining: Ultimatum game

• Simplified models of reality!

Do People Play Rationally?

• NO!
• Deviations from rational benchmarks are common in Prisoner's Dilemma, Ultimatum Game, Dictator Game, and Trust Game.
• Cooperation is widely observed.
• Very common to offer $50\%$ and reject below this threshold in the ultimatum game.
• Very common to give at least something in the dictator game.
• People trust and return trust to others.

Next Time

• Main psychological frameworks:
  • Person, situation, culture.
  • Interdependence theory.
  • Social value orientation.
  • Socio-cultural ecological approach.

Further Literature

• Ken Binmore (2007). Game Theory: A Very Short Introduction.
• van Dijk, E., & De Dreu, C. K. (2021). Experimental games and social decision making. Annual Review of Psychology, 72, 415-438.
• Nagel, R. (1995). Unraveling in Guessing Games: An Experimental Study. The American Economic Review, 85(5), 1313-1326.
• Rapoport, A. (1962). The use and misuse of game theory. Scientific American, 207(6), 108–119.
• Kollock, P. (1998). Social dilemmas: The anatomy of cooperation. Annual review of sociology, 24(1), 183-214.
• Dawes, R. M. (1980). Social dilemmas. Annual review of psychology, 31(1), 169-193.
• Van Lange, P. A., Joireman, J., Parks, C. D., & Van Dijk, E. (2013). The psychology of social dilemmas: A review. Organizational Behavior and Human Decision Processes, 120(2), 125-141.