Questions

1. Inequity aversion has been used to explain why outcomes
in the ultimatum and dictator games deviate so
distinctly from the selfish outcomes generally predicted
in economic theory.
(a) Derive the predictions of the inequity aversion
utility function found in equation 15.1 for Kahneman,
Knetsch, and Thaler’s experiment in
Example 15.4. Assume α=β =0.5. Remember
that utility is now a function of each player’s
monetary outcome.
(b) Derive the predictions of inequity aversion in the
prisoner’s dilemma.
(c) Often, political arguments are made in terms of
inequity aversion. For example, in September
2011, thousands of protesters occupied Wall Street
and other venues, protesting what they claimed
was an unfair economy. Their targets were clearly
those making mass amounts of money in investing.
Which theories of social preferences would best
describe the actions of such protesters? What might
these theories say about the response by investors,
investment firms, or the government?
2. Consumers often impose rules of fairness on the firms
that sell them goods, leading to the failure of markets to
clear. Several theories suggest that when markets clear,
we achieve a desirable outcome in terms of market
welfare (the sum of consumer and producer surplus).
Suppose a disaster occurs, causing a severe decline in
the amount of gasoline on hand in the affected region.
Standard economic theory would suggest the price of
gasoline should rise to eliminate shortages. Suppose
that because of the perception of consumers, firms do
not let prices rise. What is the impact on consumer and
producer surplus? Who wins and who loses? Why
might firms comply with this rule?
3. Consider again the prisoner’s dilemma. Use the kindness
functions defined in equations 15.14 and 15.16 to
determine a fairness equilibrium for the game.
Describe how the motivation for fairness could lead to
such an equilibrium. Use the same functions to derive
the fairness equilibrium for the dictator game. Does
fairness appear to explain the outcomes commonly
found in experimental implementations of either of
these games?
4. Consider the game represented in Figure 15.7, often
referred to as Chicken. This game is intended to represent
the decisions in a game of chicken where two
drivers drive their cars directly at each other on a
narrow road. The drivers can either dare to continue
driving straight, or chicken out and turn off the road.
Daring to stay on the road while the other chickens out
will yield a big reward. However, if both dare to stay
on the road they will both almost certainly die. Solve
this game for the fairness equilibria using the kindness
functions defined in equations 15.14 and 15.16. How
do the equilibria depend upon the value of x? Provide
an interpretation of this result.
5. Consider the extensive form psychological game
described by Figure 15.8 in which Player 1 first can
choose either Down, resulting in a reward of 0 for both
players, or Up, resulting in a node in which Player 2
can choose either Up or Down. If Player 2 chooses Up,
Player 1 receives a reward of − p, where p is Player 1’s
belief regarding Player 2’s belief of the probability that
Player 1 will choose Up. Solve for all the psychological
equilibria. Which of these equilibria are subgame
perfect?