simple version of the ultimatum game in which Player 1 could only select one of two possible splits between the two players. In one game (call this game 1), the first player could propose that both would walk away with $5 or that the Player 1 would receive $8 and Player 2 would receive $2. In this game, 44 percent of those playing the role of Player 2 rejected the offer if the proposed split was $8 and $2. But in another game (call this game 2), Player 1 could only choose between a split in which Player 1 receives $8 and Player 2 receives $2, or a split in which Player 1 receives $2 and Player 2 receives $8. Only 27 percent of those playing the role of Player 2 rejected an offer that gave them only $2 in this game, though it was exactly the offer that induced 44 percent to reject in game 1. Note that if Player 2’s preferences display inequality aversion as presented in equation 15.1, then rejecting the offer in game 1 means U2, 8 = 2 − α8 − 2< 0 = U0, 0. But accepting the split in game 2 implies U2, 8= 2 − α8 − 2 > 0 = U0, 0. Here, it appears that the particular options that were available to Player 1 changed the calculation of what was fair in the eyes of Player 2. In other words, the motives of Player 1 matters as well as the particular split of the money that is realized.

Holding Firms Accountable in a Competitive

Marketplace

Customers and employees hold firms to a standard of fairness that has sore implications. For example, in 2011 Netflix Inc., a firm that provided streaming movies and DVD rentals through the mail, chose to nearly double the prices for subscriptions at the same time that they limited their customers to either receive DVDs through the mail or to download—but not both. The customer backlash was strong, leading the CEO to apologize several times and provide explanations about how the profit model was changing, and eventually capitulating to incensed customers by allowing both DVD rentals and downloads.

Daniel Kahneman, Jack L. Knetsch, and Richard Thaler used surveys of around 100 people to study how we evaluate such actions by firms. For example, 82 percent of participants considered it unfair for a firm to raise the price of snow shovels the day after a major snow storm. Similarly, 83 percent considered it unfair to reduce an employee’s wages even if the market wage for that occupation has declined. It is acceptable, according to 63 percent, however, to reduce the wages of a worker if the firm abandons one activity (e.g., software design) for another in which the going market wages are lower (e.g., software support). Thus, it is okay to cut salary if it is associated with a change in duties.

In general, economists have found that consumers consider it fair for a firm to raise its price to maintain profits when costs are on the rise. However, it is considered unfair to raise prices simply to profit from an increase in demand or to take advantage of market power (e.g., due to a shortage). In other words, raising prices is considered unfair if it will result in a higher profit than some baseline or reference level. This principle is described as dual entitlement. Under dual entitlement, both the consumer and the seller are entitled to a level of benefit given by some reference transaction. This reference transaction is generally given by the status quo. Hence, if costs rise, the seller is allowed to increase prices to maintain the reference profit. However, the seller is not allowed to increase his profit on the transaction if costs do not rise, even if there are shortages of the item. To do so would threaten the consumer. Similar effects can be found in the labor market considering the transaction between an employer and employee. This leads to three notable effects in both consumer and labor markets.

Markets Might Not Clear When Demand Shifts

When increases in demand for a consumer product occur and producer costs do not increase, shortages will occur. This leads to waiting lists or other market-rationing measures because the price is not allowed to rise enough to reduce the quantity demanded. In labor markets, a reduction in demand for outputs generally does not lead to a reduction in wages. Rather, firms maintain wages but reduce the number of employees. Maintaining the same wages but reducing the number of employees generally leads to labor markets that do not clear, resulting in unemployment.

Prices and Wages Might Not Fully Reflect

Quality Differences

If a firm offers two variations of an item that cost identical amounts to manufacture but that differ substantially in value to the consumer, consumers will consider it unfair to charge prices that differ by too much. For example, a majority of football fans might value tickets to the big rivalry game more than when their home team faces other opponents. This should lead to much higher ticket prices for the big game. But fans’ opinions about fairness can limit the increase in price, leading to more fans being willing to purchase tickets for this game at the listed price than there are seats in the stadium. For example, the University of California charged $51 for most of their home games in 2010. However, they charged $66 for a seat at the game against Stanford, their primary rival. This game was sold out, as is the case every year when the two play. Clearly they could charge a much higher price and still fill the stadium. Similar effects are found with peak and offseason prices for hotel rooms.

With regard to wages, this leads to a case where more-productive workers are not paid quite as much as they are worth relative to other workers in the same firm and occupation. For example, many universities pay professors of the same rank similar salaries regardless of their field and level of productivity. This commonly leads to a situation where the most productive faculty are also the most undervalued and thus the most likely to leave for more lucrative work elsewhere. Universities often cannot increase the pay of the most productive faculty to the market rate because it would be perceived as unfair by others who are less productive or less valuable in similar positions.

Prices Are More Responsive to Cost Increases than Decreases

Because consumers are willing to allow producers to increase prices to maintain a reference level of profit, producers are likely to take advantage of this quickly. Alternatively, they may be slow to advertise when costs decline, leading to higher profits. They would only lower prices in response to the potential impact it could have on their competitive position in the market. Producers also have incentives to use temporary discounts to consumers rather than actual price decreases. Price decreases can alter the reference transaction in favor of the consumer, whereas discounts will be viewed as a temporary gain by the consumer. Although there is some evidence that prices respond asymmetrically, there is also some substantial counterevidence.

On the other hand, there is substantial evidence the wages are slow to decline and quick to increase. This is often referred to as wages being “sticky downward.” The slow decline can lead to prolonged periods of unemployment when market wages decline. This happens when many are willing to work at the going (lower) wages but cannot find employment. Employers will not hire, preferring to keep a smaller workforce at higher salaries rather than being perceived as unfair by cutting salaries of the currently employed. Additionally, employers may be inclined to give workers a portion of their pay in the form of a bonus in order to allow flexibility to reduce pay without being perceived as unfair.

Fairness

Important to note in the case of American Airlines executives and flight attendants is how key the perception of deception was to the flight attendants’ union. Even without the bonuses, it is clear that the outcome would be lopsided. The 10 executives would still be receiving salaries that could not be dreamed of by even the most senior flight attendants. The motive for dropping the agreement wasn’t to create a more-equal sharing of the rewards. The motive was to punish executives who were now perceived to be greedy and deceptive. The perception was that the executives had not negotiated in good faith. The perception of their duplicity drove the flight attendants to drop an otherwise acceptable labor agreement.

Matthew Rabin proposes that people are motivated to help those who are being kind and hurt those who are being unkind. Thus, he suggests that people are not motivated simply to find equal divisions (and sacrifice well-being in order to find them) but that they are also motivated by the intent and motivations of others. When people are willing to sacrifice in order to reward the kindness of others, or to punish the unkindness of others, we refer to them as being motivated by fairness. Rabin proposes that people maximize their utility, which is a sum of their monetary payout, and a factor that represents their preferences for fairness.

Formally, consider any two-player game in which Player 1 chooses among a set of strategies, with his choice represented by the variable a1. Player 2 also chooses among a set of strategies, with his choice represented by a2. As with all games, a strategy represents a planned action in response to each possible decision point in the game. The payoff to each player is completely determined by the strategies of both players, and thus the payout to Player 1 can be represented by a function π1a1, a2, and the payout to Player 2 can be represented as π2a1, a2. The Nash equilibrium is thus described as a1, a2 where Player 1 selects a1 so as to maximize π1a1, a2 for the given a2 and Player 2 maximizes π2a1, a2 for the given a1. Let us suppose that these payout functions represent material outcomes, such as the money rewards generally employed in economic experiments like the ultimatum game. If players are motivated by fairness, their total utility of a particular outcome will depend not only on the material outcome but also on the perception of whether the other player has been kind and whether the decision maker has justly rewarded the other player for his kindness or lack thereof. To specify this part of the utility of the decision maker, we thus need to define a function representing the perceived kindness of the other player and the kindness of the decision maker.

Let b1 represent Player 2’s beliefs about the strategy that Player 1 will employ, and let b2 represent Player 1’s beliefs about the strategy of Player 2. These perceived strategies will help define whether, for example, Player 1 believes Player 2 is being kind or cruel. We can then define a function f1a1, b2, called a kindness function, that represents how kind Player 1 is intending to be toward Player 2. This kindness function can take on negative values, representing the notion that Player 1 is being cruel to Player 2, or positive values, representing the notion that Player 1 is being kind to Player 2. Note that how kind Player 1 is intending to behave is a function of his own strategy, a1, and the strategy he believes the other player is employing, b2. Rabin’s model also assumes that both players agree on the definition of kindness, and thus this kindness function also represents how kind Player 2 would perceive the strategy of a1 by Player 1 to be in response to the strategy a2 = b2 by Player 2. Similarly, Player 2 has a kindness function given by f2a2, b1 defined analogously.

Finally, let c1 represent what Player 1 believes Player 2 believes Player 1’s strategy is and let c2 represent what Player 2 believes Player 1 believes Player 2’s strategy is. This can begin to sound a little tedious. These values are used to help determine if, for example, Player 1 believes that Player 2 believes that Player 1 is being kind or cruel. We can then define the function f 2b2, c1, which represents Player 1’s belief about how kind Player 2 is being. Note that this perception is a function both of Player 1’s belief regarding Player 2’s strategy, b2, and Player 1’s belief about what Player 2 believes Player 1’s strategy is, c1. Again, this function takes on negative values if Player 2 is perceived to be cruel, and it takes on positive values if Player 2 is perceived to be kind. Similarly, we can define payer 2’s belief about how kind Player 1 is, f 1b1, c2. With these functions in hand, we can now define Player 1’s utility function as

The first term represents Player 1’s perception of his material payout for playing strategy a1 given that Player 2 employs strategy b2. The second term represents the utility of fairness. If Player 2 is perceived to be cruel, f 2b2, c1 will be negative, and Player 1 will be motivated to make f1a1, b2 more negative by choosing a strategy that is also cruel. Alternatively, if Player 2 is perceived as being kind, f 2b2, c1 will be positive, leading Player 1 to choose a strategy that will make f1a1, b2 more positive by being more kind. Player 2’s utility function is defined reciprocally as

We can then define a fairness equilibrium as the set of strategies a1, a2 such that a1 solves

as the kindness function describing how kind the wife is attempting to be toward her husband. If she believes the husband is going to choose opera, the wife must be trying to be cruel if she decides to choose boxing. To do so costs her one unit of payout to reduce the husband’s payout by 0.5. Hence, we assign this a −1. Similarly, if she believes her husband is going to choose boxing, she must be cruel if she decides to choose opera. In this case she gives up 0.5 in payout to reduce the payout she believes her husband will receive by 1. Thus we assign a −1 to this outcomes also.

The value 0 is assigned to the outcome of (opera, opera) because in this case, the wife is maximizing her payout given that she believes the husband will choose opera. Maximizing your own payout is considered neither kind nor cruel, because the wife is not sacrificing her own well-being to hurt or help her husband. Similarly, we assign a 0 in the case she believes the husband will choose boxing and she chooses boxing, because again she is maximizing her own payout. The husband’s kindness function is defined reciprocally as

which represents how kind the husband is intending to be toward his wife.

We can also define the set of functions that yield each player’s perception of whether the other player is kind or cruel. We will define f 2b1, c2 = f2c2, b1, or in this case, bWife, cHusband = fHusband cHusband, bwife, where the latter function is as defined in equation 15.11. Thus, the wife perceives the husband to be kind or cruel using

the same measure as the husband himself uses to measure his own kindness or

husband uses the same functions to assess his wife’s fairness as does the wife to assess her own fairness. In this case, all players agree on the definition of fairness. The fairness

rewrite the game in terms of total utility rather than just material rewards, where substituting into equation 15.7

For example, consider the potential strategy pair in which the wife decides to play the strategy aWife = Boxing and the husband decides to play the strategy aHusband = Opera. To see if this pair of strategies can be a fairness equilibrium, we must see if it is a Nash equilibrium given bWife = cWife = Boxing and bHusband = cHusband = Opera—in other words, where both believe that the wife will choose boxing and the wife believes the husband believes she will choose boxing, and where both believe that the husband will