Experimental games and economics Ilkka Leppänen Systems Analysis Laboratory Aalto University, Finland

Let’s do one experiment now

The Beauty Contest Nagel (1995) Game theory predicts: everyone chooses 0 – Solution to the equation (2/3)*x = x Most often people choose in the range of 20…35 Belief hierarchy: – 0 th step: choose randomly – 1 st step: others are 0 th – 2 nd step: others are 1 st – …

Purpose of experiments In economics there has been over-reliance on theory building – “Empirical realism of a theory’s assumptions is not a basis for the theory’s critical evaluation” (Milton Friedman) In natural sciences experiments are used to falsify or validate theories – Theories must produce testable hypotheses and be falsifiable

History Market experiments to test how prices are formed (1940s – ) – Nobel prize: Vernon Smith 2002 Game experiments to test behavior in abstract games (1950s – ) Judgement and decision making under uncertainty (1960s – ) – Nobel prize: Daniel Kahneman 2002

What are games? Taxonomy of strategic situations – “A rough equivalent for social science of the periodic table of elements in chemistry” (Colin Camerer) Analytical game theory uses mathematical rules to study what players possibly do in games Experimental/behavioral game theory provides evidence for what players actually do

Equilibrium The Nash equilibrium is the centerpiece of game theory (Nash, 1951) Nash equilibrium predicts that players end up into a situation in which no-one has incentive to deviate from their decision The subgame-perfect Nash equilibrium considers sequential decision making in games

Prisoner’s Dilemma (PD) Models the problems of cooperation – Both cooperating would give best mutual payoffs – Unilateral defection gives best individual payoffs – Both defecting is the unique Nash equilibrium The Public Goods Game (PGG): PD with 3 or more players CD C2 / 20 / 3 D3 / 01 / 1 Player 2 Player 1 Payoffs: Player 1 / Player 2 C = cooperate D = defect

Battle of the Sexes (BoS) Models the problem of coordination – Player 1 prefers M and Player 2 prefers B, but they do not want to choose different actions than the other Two Nash equilibria: both choose M and both choose B – Finding out which one will prevail is “perhaps the most difficult problem in game theory” (C. Camerer) MB M2 / 10 / 0 B 1 / 2

Ultimatum Game (UG) Models a simple bargaining situation Game theory predicts that Player 1 offers the smallest amount possible and Player 2 accepts this Player 1Player 2 Offer x € from 5 € Reject: both get 0 € Accept: Player 1 gets 5−x €, Player 2 gets x €

Dictator Game (DG) Player 2 has no choice available Game theory predicts that Player 1 keeps all the money to himself Player 1Player 2 Offer x € from 5 €

Experimental evidence on PD Subjects cooperate ~50% of the time Increasing the unilateral defection payoff decreases cooperation rates Pre-play communication between the subjects increases cooperation rates CD C2 / 20 / 30 D30 / 01 / 1 “I will play C”

Experimental evidence on PGG Subjects contribute ~50% of their endowment Fehr and Gächter (2000) Cooperation rates increase if subjects can “punish” non-contributors When they play repeatedly with new opponents, contribution rates deteriorate

Experimental evidence on BoS Subjects generally fail to coordinate Pre-play communication by one player improves coordination (Cooper et al. 1989) Relabeling the choice alternatives improves coordination by making one equilibrium more salient MMMMb 2 / 10 / 0 b 1 / 2

Equilibrium refinements Results from PD, PGG and BoS can be explained by “refining” the Nash equilibrium – The subgame-perfect Nash equilibrium – Literature on learning (Roth & Erev 1995): players in repeated games gradually adjust their choices so that they are in equilibrium – In BoS one equilibrium can be “focal” and become selected more often than the other

Experimental evidence on UG The subgame-perfect Nash equilibrium requires “backwards-induction” – Player 1 deduces the optimal choice by first evaluating Player 2’s choices and then own choices Güth et al. (1982) wanted to find out the ability to use backwards-induction – Subjects were able to use it in other games – … but they still offered almost equal splits in the UG Modal offer: 50%

Experimental evidence on UG and DG Forsythe et al. 1994

Experimental evidence on UG Sanfey et al. (2003) were the first to use fMRI When rejecting unfair offers, activity in deep emotional brain parts

Game theory refinements in UG? If players have the capacity to play in the UG as game theory predicts, why don’t they? This points to novel phenomena that Nash equilibrium or its “refinements” cannot take into account – Repeating the UG does not lead to the game theory prediction

Other-regarding behavior The literature on other-regarding preferences: players see games differently than the theorist – The best individual utility does not result from the Nash equilibrium but from a fair payoff allocation – See Cooper and Kagel (2013) UG and DG evidence conform to this idea – Most Player 1’s propose fair splits – Most Player 2’s accept fair splits and reject unfair splits Reciprocity: some players are conditional cooperators by nature – Intentions matter: computer proposals are accepted, human proposals rejected

How to use experiments Experiments can be used to: 1.Refine existing theory (the Nash equilibrium refinements) 2.Characterize novel phenomena (the models of other-regarding preferences) Third way is to stress test and demonstrate games before they are used by policymakers and firms – If a theory does not work in an experiment, it certainly does not work in real life

Stress testing theory with experiments UK government asked game theorists to design auctions for five 3G licenses Reported in Binmore and Klemperer (2002) and Abbink et al. (2005) They used experiments and found their theoretical design to be quite efficient – Subjects were from companies and the government – The experiments were useful in communicating the design to non-specialists

Methodological considerations Conduct pilot experiments Ensure anonymity and “blindness” – Single-blind: subjects do not know the research question – Double-blind: experimenters do not know the research question Test that subjects understand the instructions before they play the game Make sure others can replicate your results – Report every detail of the experiment Ideal: write the paper before you collect the data

Use performance-based payments Money is not only a reward for participating It is used to make the experiment a real-life decision making situation – Align monetary payment to success in the task – Student subjects earn generally about 20 € for an hour’s work in the laboratory “Induced valuation” (Vernon Smith 1976)

Deception of subjects Strictly forbidden in experimental economics – Subjects read the research papers and find out they have been deceived – Deception by one laboratory can contaminate the subject pool with false beliefs about how the experiment works – Economics journals do not publish experimental papers that use deception In experimental psychology and neuroscience deception is not a problem and even encouraged

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