Game Theory Slides

Imagine that the government adopts a new policy (or changes an existing

policy) and you don’t like it. What can you do?

• Exit – when you opt to leave without trying to fix the situation (you move somewhere else, or

you buy a different product from a new company)

• Voice– when you speak up (protest, lobby) to try to prompt a change in policy to make it better

• Loyalty– when you accept the policy even though you don’t like it.

Which response you choose depends on what you expect will happen to

you with each option – how you think the state will respond

Will the state listen, ignore you, punish you?

We can model how citizens & the state

interact as a game

• Because it is a strategic situation

• A rational player “does what she believes is in her best interest given

what she knows at the time of choosing” (Clark, Golder & Golder

2009: 62)

When will the state respond positively to

the citizen? (Clark, Golder & Golder 2009)

When:

1) the citizen has a credible exit threat (E > 0)

2) the state depends on the citizen (e.g., for taxes) (L > 1)

Both conditions are necessary

E = citizen’s exit payoff

1 = value of benefit taken from the citizen by the state

L = state’s value from having a loyal citizen who does not exit

c = cost of using voice

How will a citizen react to a negative change in

her environment?

• The government increases taxes

• The government imposes a ban on handguns.

• The Supreme Court rules that prayer in public schools is

unconstitutional.

• The quality of peaches at your local fruit stand declines.

Exit: Accept the negative change but alter one’s behavior to

optimize in the new environment.

Voice: Do not accept the negative change and seek to ‘persuade’

the government to reinstate the original environment.

Loyalty: Accept the negative change and make no change to one’s

pre-existing behavior.

So, how should the citizen react to the negative change

in her environment?

Much presumably depends on what the citizen

thinks the government will do.

Respond: Respond positively and reinstate the

original environment.

Ignore: Ignore the citizen and maintain the new

environment.

Game Theory

a fundamental tool for analyzing strategic

situations.

In a strategic situation, the choices of one actor depend on the

choices made by other actors.

We can think of the decisions to be made by the citizen and the

state as a game.

a game

a situation in which an individual’s ability to achieve her

goals depends on the choices made by other actors.

Games have players and rules about how decisions are made.

The basic rule is that players choose to do what they believe is in

their best interest.

The payoffs in a game

indicate how the players value each of the

possible outcomes.

Players prefer outcomes with higher payoffs.

Two common ways of modeling strategic interactions:

Extensive Form Games → sequential choices.

Normal Form Games → simultaneous choices

An extensive form game consists of choice nodes linked in a

sequence.

A choice node is a point in the game at which a player must

choose an action.

The initial node is the place where the game begins.

The branches represent the actions that can be taken at the choice

nodes.

A game tree is the entire specification of choice nodes, branches,

and payoffs.

The exit, voice, and loyalty (EVL) game

Prehistory . . .

• There has been a negative shock resulting in a transfer of

some benefit from the citizen to the government.

• The negative shock might be a tax increase.

Citizen must decide whether to exit, use voice, or remain loyal.

Solving the EVL game

A rational player does what she believes is in her best interest

given what she knows at the time.

A subgame perfect equilibrium is an important solution concept for

extensive form games in which all actors do the best they can at

every point where they could possibly make a decision

Subgame perfect equilibrium

can be found using a method

known as backward induction.

Backwward induction

the process of reasoning backward, from the

end of the game or situation to the beginning, in order to

determine an optimal course of action.

Evaluating the EVL game

The government responds positively to voice only if

1. the citizen has a credible exit threat

and

2. the government is dependent on the citizen.

Think about what this means for your life!

Why would a dependent state ever take a benefit away from

citizens with credible exit threats?

It wouldn’t