3.1

The citizen-state dilemma is difficult because the citizen's decision is based on what she believes the state will do, and the state's decision is based on what it believes the citizen will do. Politics is defined by this strategic component of social relations. Game theory is a basic technique used by political scientists to analyze these sorts of strategic scenarios in which one actor's decisions are influenced by the actions of others.
The way decisions are made in games is governed by rules. The main guideline is that participants must pick what they feel is best for them. The payoffs associated with each potential game outcome reflect the interests of the participants. Players favor higher-payoff outcomes over lower-payoff outcomes. A game can be represented by either a game tree (expanded form games) or a reward matrix (normal, or strategic, form games).

3.2

What are your expectations for the players in this game? This is an unfair question since you can't fully answer it without first knowing how much each participant values the various outcomes. The payoffs for the participants associated with each of the five potential outcomes are listed in Table 3.2.

If the state is allowed to keep the benefit that it transferred from the citizen in the game's early stages, it will get a payout of 1. We might have picked any number other than 1, but for presentational purposes, 1 is the most convenient. If the city decides to remain loyal, the state receives a loyalty payoff (L), which is greater than zero.
We can now combine these payoffs to understand what each of the five possible outcomes means for citizens and the state. The payoffs in Table 3.2 are as follows. The citizen's payment in outcome 1 (O1) is E since she departs, but the state's payoff is 1 because it keeps the benefit is obtained from the citizen. The citizen's payout in outcome 2 (O2) is 0 since she remains faithful, but the state's reward is 1 + L because it keeps the advantage it took from the citizen while keeping a loyal citizen.
We're getting to the point where we can figure out what the citizens and state will do in this game. However, one more assumption must be made before we proceed. In particular, we assume that E 1 – c. Consider the implications of this premise for a moment. This assumption argues that the value a citizen receives from departing is less than the value a citizen receives from effectively exercising her voice and reclaiming a benefit stolen by the government.

We present a basic model in this chapter that encapsulates what we believe are the main elements of many political situations. 1) Our approach is a reformulation and expansion of an argument made by Albert Hirschman in his book Exit, Voice, and Loyalty: Responses to Decline in Firms, Organizations, and States, published in 1970. 2) Unlike Hirschman, who focuses on the power connection between customers and businesses, we are interested in the power relationship between citizens and governments.
It's important to note that while some individuals will dislike these changes and perceive them as negative, others will see them as positive. When the state raises the tax rate, for example, individuals who must pay more taxes will be upset, while others who get state benefits may be better off.
Let's assume you've noticed a shift in your surroundings that you don't like. What options do you have? In general, you have three options: you may leave, use your voice, or exhibit allegiance.

The citizen-state dilemma is difficult because the citizen's decision is based on what she believes the state will do, and the state's decision is based on what it believes the citizen will do. Politics is defined by this strategic component of social relations. Game theory is a basic technique used by political scientists to analyze these sorts of strategic scenarios in which one actor's decisions are influenced by the actions of others.
The way decisions are made in games is governed by rules. The main guideline is that participants must pick what they feel is best for them. The payoffs associated with each potential game outcome reflect the interests of the participants. Players favor higher-payoff outcomes over lower-payoff outcomes. A game can be represented by either a game tree (expanded form games) or a reward matrix (normal, or strategic, form games).

What are your expectations for the players in this game? This is an unfair question since you can't fully answer it without first knowing how much each participant values the various outcomes. The payoffs for the participants associated with each of the five potential outcomes are listed in Table 3.2.

If the state is allowed to keep the benefit that it transferred from the citizen in the game's early stages, it will get a payout of 1. We might have picked any number other than 1, but for presentational purposes, 1 is the most convenient. If the city decides to remain loyal, the state receives a loyalty payoff (L), which is greater than zero.
We can now combine these payoffs to understand what each of the five possible outcomes means for citizens and the state. The payoffs in Table 3.2 are as follows. The citizen's payment in outcome 1 (O1) is E since she departs, but the state's payoff is 1 because it keeps the benefit is obtained from the citizen. The citizen's payout in outcome 2 (O2) is 0 since she remains faithful, but the state's reward is 1 + L because it keeps the advantage it took from the citizen while keeping a loyal citizen.
We're getting to the point where we can figure out what the citizens and state will do in this game. However, one more assumption must be made before we proceed. In particular, we assume that E 1 – c. Consider the implications of this premise for a moment. This assumption argues that the value a citizen receives from departing is less than the value a citizen receives from effectively exercising her voice and reclaiming a benefit stolen by the government.