Lecture 57 Introduction of Behavioral Games

When we are not always driven by self-interest… also concert for others and preference for fairness

Behavioral vs Standard Game Theory¶

Many of the analytical behavioral theories actually have no behavioral aspects

Occur when people don't take adequate account for effects of their decisions on others (positive/negative)
Developed nations: strict global control on carbon emissions. Others: No!
Traffic jam:
- Individuals contribute by not carpooling (driving alone), and not accounting for their contribution to the congestion
Antibiotics
- antibiotic-resistant bacteria
- harmful effect on many others

The tragedy of the Commons¶

Garrett Hardin
Control access… else would be exploited…
Fishermen as a group would be better off by not catching too much tuna.
Free riders

Greek storyteller Aesop = the mouse who will bell the cap… few lives lost, but will save other lives

Altruism¶

willingness to bear the cost in order to help the larger society.
The mouse

Present day global environmental problems

When individual don't just care about themselves but also about others… they have social preferences
even if they have lower payoff for themselves
Suppose there are $n$ players in a game… has extensive form representation. At any end node, player $i$ has direct utility $u_{i}$ ($i = 1,2,\dots, n$)
Each player has a type characterized by altruism coefficient, $a_{i} \in (-1,1)$
- Individual is spiteful: $a_{i}\lt 0$
- Self-regarding: $a_{i}=0$
- Altruistic: $a_{i}\gt 0$

$$
v_{i} = u_{i} + \sum_{j\neq i} \dfrac{a_{i}+\delta a_{j}}{1+\lambda} u_{j}
$$
where $\lambda \in [0,1]$. The right hand addend is the altruism-adjustment component.

The specification was given by Levine in 1998.

When $\lambda = 0$, $v_{i} = u_{i}+a_{i}u_{j}$
- And when $a_{i}=0$, $v_{i}=u_{i}$ (self regarding)
Spiteful behavior = flip side of altruistic
- imposes a cost on others, while also has a cost on the person behaving such
- Punishing those who throw litter out of their car, by yelling at them = Spiteful behavior. (May help to enforce valued social norms),
  - yelling (anger/frustration) is the cost
  - feeling like you contributed to the society (satisfaction) is a benefit
- Confer benefits that are non-material or psychological

Examples of Altruistic behavior¶

tipping
charity
voluntary unpaid work
monopolies not raising prices during shortages

Behavioral Game - Ultimatum Game¶

1982: Guth Schmittberger, & Schwarze
Format
- One "Proposer" divides/splits
- One "Responder" accept… reject then nothing.
By rejecting, the responder will get nothing… so he should always accept… as it gives a positive amount.
Responders think much less than half is unfair
- willing to reject such small offfers to punish the proposer for behaving unfairly
"negative reciprocity" = reciprocate unfair behavior.
- harm the unfair person.
- at a substantial cost to themselves.
- provided, unfair proposer is harmed more.
Reciprocity = preference to be help the kind and withhold help from the unkind.
Fairness = way of evaluation an allocation based on one's conception of justice.

Where did the fairness preferences come from?

Evolution $\implies$ Become angry when pushed around… getting angry had survival value.
Culture $\implies$ Standards of fairness

Competition in Ultimatum Game¶

New version: two-way split
- If both Responders accept, one is chosen at random to receive the slit
- If no one accepts, no one including the Proposer gets anything
Proposers will make lower offers as they know respondents are more likely to accept.