ECO290E: Game Theory
Lecture 13: Behavioral Game Theory
Review of Lecture 13
In Bayesian games, one’s strategy is optimal if and only if it induces optimal actions for every possible types (against given other players’ strategies).
In the presence of information asymmetry, there might arise inefficiency which is absent if there were no private information.
In market for Lemon, only the worst quality goods are traded, under wide range of parameters.
Introducing certification may induce agents to voluntarily reveal their qualities. (full information disclosure)
Shortcomings (?) of Game Theory
Game theory is powerful, but it has shortcomings as a complete model of agents’ behaviors:
Players are not perfectly rational.
their beliefs about what other players will do may be consistently wrong or it takes time to become correct.
each player may not take best response given her belief.
Players are not motivated material self-interest only.
observable material payoffs are often different from the actual utilities that players would receive.
some people appear to be motivated in part by social concerns such as altruism, fairness, and prestige.
Behavioral Game Theory
Behavioral game theory incorporates limited strategic thinking (bounded rationality), equilibrating forces
(learning in games), and theories of social preference,
while retaining the mathematical formalism and generality across different games that makes game theory useful.
Hundreds of experiments show conditions under which predictions of game theory are sometimes approximately satisfied, or badly rejected.
Experimental economics
Beauty Contest Game
Players choose a number between 0 and 100.
The average of the numbers is computed, and multiplied by 0.7.
The player whose number is closest to 0.7 times the average wins a fixed prize.
⇒ Class room experiment! (You have to guess what other players will choose.)
Bounded Rationality
In (complex) games, equilibrium analysis may predict poorly what players will do.
Cognitive hierarchy theories of different limits on strategic thinking, e.g., “level k” theory
Players who do k steps of thinking anticipate that others do fewer steps.
Non-maximizing theories, e.g., quantal response equilibrium (QRE)
Players make mistakes by choosing strategies with higher expected payoff deviations less often.
(Voluntary) Contribution Game
Each member of a group receives a fixed number of tokens and is invited to contribute some or all of their tokens to a central pool.
After players decide contributions simultaneously, each player obtains her remaining tokens plus M times tokens in common pool where 0 < M < 1.
In essence, the voluntary contribution game creates a conflict between individual interests and collective
Contribution Game: Remark
Many players focus on their individual economic
incentives and give nothing while many others focus on collective interest and give all of their tokens.
Relatively few give something in between.
The overall contribution rate is usually around 30 – 50 percent, which is far from the theoretical prediction, i.e., 0.
Contributions get shrink as players become more familiar with the voluntary contribution game.
Threat of Punishment
Adding a second stage in which any player could punish any other player by giving up some tokens.
For example, it costs 4 tokens to reduce another players payoff by 30 tokens. Then, what will happen?
Note that group assignments (members) change each round.
Although the threat of punishments is NOT credible,
introduction of the second stage dramatically changes the players’ behaviors.
The contribution rate leaped to 40 – 65 percent.
Dictator Game
One player (dictator) divides a fixed prize, $10, between herself and another player (recipient) who is a passive participant.
This is not a game since only one player makes decision.
If people care only about their own monetary payoffs, every dictator should keep the entire prize for herself, but most subjects play differently.
In some experiment, 21% kept everything while the same fraction gave away half of the prize ($5). 17% chose $1, 13% chose $2, and 29% chose $3.
Dictator Game: Remark
Most studies have found evidence of significant generosity, even as subjects gained experience.
Results of the dictator game illustrate the potential importance of social motives.
Possible explanations include altruism, fairness, egalitarianism, etc…
Concerns about status may also play a role.
Indeed, dictators are considerably less generous when their anonymity is assured.
Ultimatum (Bargaining) Game
When the proposer makes an offer below 20%, the
recipient rejects it about half of the time. Higher offers are rejected but with lower frequency.
The threat of rejection results in larger offers compared to the dictator game, and recipients enjoy significantly higher payoffs on average.
Most of the proposer divide the prize equally.
Emotions such as anger and indignation may influence agents’ decisions.
Social Preferences
Some of game theory’s failures are attributable to faulty assumptions about agents’ preferences, rather than to fundamental problems with theory.
When analyzing strategic decisions, social motives such as altruism, fairness, and prestige may matter.
Well-known Theories:
Inequality aversion (Fehr and Schmidt 1999)
Players prefer more money and more equal allocations.
Neuroeconomics
Neuroeconomics (neuroscience + economics) studies the human neural system, including brain processes, with the object of discovering new principles of economic (game theoretical) decision making.
Some researchers believe that
neuroscience evidence can be used directly to falsify or validate specific hypotheses about agents’ behaviors.
neuroeconomics will eventually enable us to build better models of economic behavior, and perhaps develop a new unified theory of decision making.
Beauty Contest Game: Remark
Some players choose numbers scattered from 0 to 100, many others choose 35 = 0.7 • 50 (the average if others are expected to choose), and others choose 24 ≈ 0.7 • 0.7 • 50.
Most evidence suggests that 0-2 steps of iterated reasoning are most likely in the first period of play.
When the game is played repeatedly with the same
players (who learn the average after each trial), numbers converge toward zero.
