12.2 Experimental game theory and empirical findings

Experimental game theory bridges the gap between theoretical predictions and real-world behavior. It uses controlled lab experiments to test game-theoretic concepts and uncover systematic deviations from rational self-interest. This approach reveals fascinating insights into human decision-making in strategic situations.

These experiments have uncovered key findings like cooperation in social dilemmas, fairness concerns in bargaining, and limited strategic reasoning. They challenge standard assumptions and inspire new models that incorporate social preferences, bounded rationality, and psychological factors to better explain observed behavior.

Principles and methods of experimental game theory

Experimental methods and design

Top images from around the web for Experimental methods and design

• 

  Frontiers | Trust Game Database: Behavioral and EEG Data From Two Trust Games View original

  Is this image relevant?

• 

  Frontiers | Cooperative Behavior in the Ultimatum Game and Prisoner’s Dilemma Depends on Players ... View original

  Is this image relevant?

• 

  Frontiers | Trust Game Database: Behavioral and EEG Data From Two Trust Games View original

  Is this image relevant?

• 

  Frontiers | Cooperative Behavior in the Ultimatum Game and Prisoner’s Dilemma Depends on Players ... View original

  Is this image relevant?

1 of 2

Top images from around the web for Experimental methods and design

• 

  Frontiers | Trust Game Database: Behavioral and EEG Data From Two Trust Games View original

  Is this image relevant?

• 

  Frontiers | Cooperative Behavior in the Ultimatum Game and Prisoner’s Dilemma Depends on Players ... View original

  Is this image relevant?

• 

  Frontiers | Trust Game Database: Behavioral and EEG Data From Two Trust Games View original

  Is this image relevant?

• 

  Frontiers | Cooperative Behavior in the Ultimatum Game and Prisoner’s Dilemma Depends on Players ... View original

  Is this image relevant?

1 of 2

• Experimental game theory studies human behavior in strategic situations using controlled laboratory experiments to test game-theoretic predictions and identify systematic deviations
• Key principles include inducing valuations through monetary incentives, controlling the information structure, and randomly matching participants to implement one-shot interactions
• The strategy method elicits contingent responses for every possible decision node, enabling the study of counterfactual and off-equilibrium behavior
• Experiments often implement simplified versions of games like the Prisoner's Dilemma, Public Goods game, Ultimatum game, and Trust game to isolate specific strategic considerations

Types of experimental designs

• Within-subject designs expose the same participants to multiple treatment variations
  • Allows for direct comparisons of behavior across different conditions
  • Enables the study of individual-level heterogeneity in responses to game parameters
• Between-subject designs compare behavior across different participant groups
  • Each group is exposed to a single treatment condition
  • Mitigates potential order effects or spillovers that may arise in within-subject designs
• Statistical analyses test hypotheses about treatment effects, often employing non-parametric tests robust to distributional assumptions
  • Examples include Wilcoxon rank-sum tests for between-subject comparisons and Wilcoxon signed-rank tests for within-subject comparisons

Seminal experiments in behavioral game theory

Experiments on social dilemmas and cooperation

• In the Prisoner's Dilemma, a non-negligible fraction of participants cooperate despite defection being the dominant strategy, suggesting other-regarding preferences or bounded rationality
• Public Goods game experiments find positive contributions that decline over time in finitely-repeated play
  • Introducing punishment opportunities can sustain cooperation
  • Conditional cooperation strategies are common, where individuals contribute more when others are expected to contribute

Experiments on bargaining and fairness

• The Ultimatum game reveals that responders frequently reject low offers, contradicting subgame perfect equilibrium predictions, indicating fairness concerns or negative reciprocity
  • Proposers often make equal splits, anticipating the possibility of rejection
  • Cultural differences in rejection rates have been observed, with higher acceptance of unequal offers in some societies
• Trust game studies show that many players exhibit trust and trustworthiness, with the degree varying based on the social context and framing of the interaction
  • Higher trust and trustworthiness are observed in repeated interactions or when reputation is at stake
  • Communication and face-to-face interactions can enhance trust

Experiments on market entry and auctions

• Market entry experiments find excess entry relative to Nash equilibrium, especially with a small number of potential entrants, consistent with overconfidence bias
  • Providing feedback and experience can reduce excess entry over time
  • Introducing market selection can drive behavior closer to equilibrium predictions
• Experiments on common-value auctions document the winner's curse, where bidders systematically overbid and earn negative profits, suggesting a failure to account for adverse selection
  • The severity of overbidding is reduced with experience or when bidders receive additional information about the value of the object

Experiments on strategic reasoning and learning

• Centipede game experiments show that players often fail to backward induct, continuing to play even in the final rounds, implying limited strategic reasoning
  • Increasing the number of rounds or the stakes can lead to more unraveling
  • Introducing intermediate payoffs or incomplete information can sustain cooperation
• Experiments on learning in games find that players adjust their strategies over time based on feedback and experience
  • Simple reinforcement learning models capture some aspects of observed behavior
  • Belief learning models, where players form beliefs about others' strategies and best respond, provide a better fit in some cases

Standard vs. empirical game theory

Assumptions of standard game theory

• Nash equilibrium assumes rational self-interested agents with perfect information
  • Experimental evidence suggests that human players have bounded rationality and social preferences
  • Deviations from Nash predictions are common, particularly in one-shot or finitely repeated games
• Subgame perfect equilibrium requires credible threats at every decision node
  • Experiments reveal that incredible threats are sometimes carried out due to emotional reactions or fairness concerns
  • Forward induction reasoning is not always applied, as players may not perceive the full strategic implications of past actions
• Mixed strategy equilibrium predicts serially uncorrelated choices that are best responses to the opponent's equilibrium mixtures
  • Empirical studies find excessive switching and payoff-dependent mixtures
  • Players often exhibit a "gambler's fallacy" or hot hand beliefs, expecting positive or negative autocorrelation in random sequences

Empirical regularities and extensions

• Evolutionary game theory models the dynamics of strategy adoption in populations
  • Experimental tests identify the importance of noise, mutations, and the speed of the replicator dynamics
  • Behavioral strategies like tit-for-tat or win-stay-lose-shift can emerge and sustain cooperation in repeated interactions
• Standard theories abstract from the framing of the strategic interaction
  • Experiments manipulating framing find substantial effects on behavior, holding the game structure constant
  • Presenting a Prisoner's Dilemma as a "Community Game" rather than a "Wall Street Game" can increase cooperation rates
• Psychological game theory incorporates belief-dependent preferences like reciprocity, guilt, and surprise
  • Empirical evidence supports the relevance of these motivations in shaping behavior
  • Models of inequity aversion, where players dislike unequal payoff distributions, can explain deviations from standard predictions

Strengths and limitations of experimental approaches

Advantages of experimental methods

• Experiments allow for the controlled testing of game-theoretic predictions by manipulating specific variables of interest while holding other factors constant, strengthening internal validity
• The use of randomization and treatment-control comparisons enables causal inference about the effects of game parameters on behavior
• Experimental designs can implement novel institutional arrangements that are difficult to study using naturally-occurring data, expanding the range of empirical investigations
• Inducing valuations through monetary payments aligns incentives and encourages participants to make considered decisions, enhancing the reliability of the data

Limitations and methodological challenges

• Experiments face challenges in terms of external validity due to the abstract, simplified settings and the use of convenience samples like university students
  • The generalizability of findings to real-world contexts should be carefully considered
  • Field experiments or natural experiments can provide complementary evidence in more realistic settings
• The strategy method may elicit different behavior compared to "hot" decision-making in direct-response designs
  • The interpretation of results should consider these elicitation effects
  • Comparing outcomes under different elicitation methods can shed light on the robustness of the findings
• Experimenter demand effects can arise if participants infer the research hypotheses and modify their behavior
  • Careful experimental instructions and protocols aim to mitigate these concerns
  • Using neutral framing, double-blind procedures, or deception can help reduce demand effects
• The exclusive focus on behavioral outcomes limits insights into the underlying decision processes
  • Combining experiments with other methods like surveys, eye-tracking, or neuroeconomics can provide a more complete understanding
  • Eliciting beliefs, emotions, or strategic reasoning can shed light on the mechanisms driving behavior