3 of 22

Homo economicus�

How would you characterize a homo economicus individual?

Perfectly rational
Maximizes expected utility
Cares only about monetary incentives
Selfish (self-regarding preferences)

4 of 22

The “standard” model�

5 of 22

Behavioral Game Theory

6 of 22

What is a game?�

Game: A situation where a group of people is affected by the choices made by other individuals within that group

Essential elements of a game:

Set of players (at least two)
Set of actions for each player
Preferences over the set of actions
Strategies – a complete plan of actions

Strategy:

A strategy is a part of the mental skill needed to play well
How best to make a choice that will maximize utility, anticipating the choice of the opponent

7 of 22

Example: Tennis�

crosscourt

down-the-line

8 of 22

Game theory�

Game theory: A mathematical approach to modeling behavior by analyzing the strategic decisions made by interacting rational players

Standard game theory (Nash 1950) assumes:

Players are homo economicus

Recall, homo economicus:

Perfectly rational
Maximizes expected utility
Cares only about monetary incentives
Selfish (self-regarding preferences)

9 of 22

Why game theory is important?�

Games are a convenient way to model the strategic interactions among economic agents:

Labor: Your chance of receiving a promotion depends not only on your effort but also on efforts of others
Industrial organization: Price strategy depends not only on your output but also on the output of your competitor
Public goods: My benefits from contributing to a public good depend on what everyone else contributes

Game theory outside economics:

Political science: Elections, voting, conflicts, wars
Computer science: Multi-agent systems, algorithms
Sports: NFL, NBA
Law: Arbitration, litigation
Biology: Animals fighting for dominance

10 of 22

Example: Prisoners’ Dilemma�

Two suspects held in separate cells are charged with a major crime. However, there is not enough evidence. Both suspects are told the following policy:

If neither confesses (NC, NC) then both are convicted of a minor offense and sentenced to 1 month in jail
If both confess (C, C) then both are sentenced to jail for 6 months
If one confesses but the other does not (C, NC) (NC, C), then the confessor is released but the other is sentenced to jail for 9 months

-1 , -1	-9 , 0
0 , -9	-6 , -6

Prisoner 1

Prisoner 2

11 of 22

Dominated strategy�

Dominated strategy: There exists another strategy which always does better regardless of other players’ choices

A rational player never chooses a dominated strategy

Is there a dominated strategy in Prisoner Dilemma game?

Prisoner 1: Not confess (NC) is always dominated by confess (C) disregarding what the other player chooses, so
Prisoner 2: Not confess (NC) is always dominated by confess (C) disregarding what the other player chooses

-1 , -1	-9 , 0
0 , -9	-6 , -6

Prisoner 1

Prisoner 2

12 of 22

Iterated elimination equilibrium�

Iterated elimination equilibrium (IEDS): Equilibrium obtained by eliminating dominated strategies

Often it is called the IEDS equilibrium (iterated elimination of dominated strategies)

Solving games using dominated strategy method:

If a strategy is dominated, eliminate it
The size and complexity of the game is reduced
Then eliminate any dominated strategies from the reduced game
Continue doing so

13 of 22

Example: Guessing game�

Each person in a group is asked to choose a number between (and including) 0 and 100 simultaneously. Communication is not allowed. The person whose number is closest to, but not exceeding, 2/3 of the average (called the target number) earns $10, while the rest earns $0.

Guessing game is also called the “beauty contest” game:

Beauty contest: a newspaper contest in which people guess what faces others will guess are most beautiful
Keynes (1936, p. 156): “It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree, where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth, and higher degrees.”

14 of 22

Example: Guessing game�

Solving the game using dominated strategy method:

Choosing any number above 66 is a dominated strategy, since the highest possible target number is 100 × 2/3 = 66.6 and you can always do better by choosing a number lower than 66
If everyone is rational, then nobody will choose more than 66
Similarly, choosing any number between 44 and 66 is a dominated strategy, since the highest possible target number is 66 × 2/3 = 44
If everyone is rational, then nobody will choose more than 44
This process will continue…

Deleting dominated strategies iteratively leads us to the IEDS equilibrium in which everyone chooses 0

This outcome is also called a Nash equilibrium – a situation in which no player can do better by unilaterally deviating from the decided plan of actions

15 of 22

Experiment #10 results�

Class experiment:

Guessing game

Class average

Nash equilibrium

16 of 22

Example: Centipede game�

The centipede game was first introduced by Rosenthal (1981)

It is a sequential move game in which two players take turns choosing either to take a larger share of a slowly increasing pot, or to pass the pot to the other player
The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes the pot on the next round, one receives less than if one had taken the pot on this round

We can illustrate the game in the following way:

C’

2, 0

1, 3

4, 2

S’

17 of 22

Subgame perfect equilibrium�

Subgame perfect equilibrium (SPNE): Equilibrium obtained by backward induction

Often it is called the SPNE equilibrium (subgame perfect Nash equilibrium)

Solving games using backward induction:

Start from the very end
Find the best response (i.e., the strategy that gives the highest payoff)
Refine the game, taking into account the results from previous steps
Continue until you cannot refine the game

18 of 22

Example: Centipede game�

Solving the game using backward induction:

The SPNE equilibrium is (S, S’) with payoffs of (2, 0): player 1 stops (S) at the first round and player 2 stops (S’) at the second round

What if the game is longer?

The SPNE equilibrium is (SS’’S’’’’, S’S’’’S’’’’’) with payoffs of (2, 0): player 1 stops in each round and player 2 stops in each round

S’

C’

2, 0

1, 3

4, 2

S’

C’’’

C’’

C’

2, 0

3, 5

1, 3

4, 2

C’’’’’

C’’’’

5, 7

8, 6

6, 4

S’’’

S’’

S’’’’’

S’’’’

19 of 22

Experiment #11 and #12 results�

Class experiment:

Centipede game

20 of 22

Limitations of IEDS and SPNE�

People are not perfectly rational:

Make mistakes
Not good at backward induction
Need time to learn

People are not perfectly selfish:

Other-regarding preferences

21 of 22

Behavioral game theory�

Behavioral game theory: Extends standard game theory by taking into account that people have limited strategic abilities and they care about payoffs of others

Behavioral game theory (Camerer 2003) assumes:

Players are bounded rational
Players care about payoffs of others
Players have difficulty learning

Typical games:

Ultimatum game
Dictator game
Trust game
Prisoners’ Dilemma
Cooperation game

22 of 22

References�

Dhami, S. (2016). The Foundations of Behavioral Economic Analysis. Oxford University Press.
Camerer, C.F. (2003). Behavioral Game Theory: Experiments in Strategic Interaction. Princeton: Princeton University Press.
Nash, J.F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36, 48-49.
Rosenthal, R.W. (1981). Games of perfect information, predatory pricing and the chain-store paradox. Journal of Economic Theory, 25, 92-100.