Psychological Profile of a Player 11
and their associated utilities—such as Table 1.3—is known as a utility func- tion. A person’s utility function captures all of the relevant information about the person’s preferences.
Writing down a person’s preferences begs the question of where they come from. Why does someone prefer rock and roll to opera? cats to dogs? stripes to solids? pizza to General Tso’s chicken? Preferences could be determined by genes, culture, chemicals, personal experience, and who knows what else. Where preferences come from will not concern us. We’ll be content to take preferences as given and explore what they imply about behavior.
1.4.2 Beliefs In many situations, the utility received by a person depends not just on the choices the person makes, but also on the choices of others. For example, many cell phone providers have designed their plans to create an interdependence be- tween the choices that people make. For most plans, the price charged per minute is lower if you are calling someone on the same network (i.e., someone who has chosen the same provider) than if you are calling someone on another network. What this means is that the best provider for someone may well de- pend on the providers used by the people whom they call.
With this in mind, consider Grace’s deciding on a cell phone plan, knowing that she spends most of her time calling her best friend Lisa. Although Grace really likes AT&T (because then she can have an iPhone), it is most critical to her that she choose the same network as Lisa. A utility function consistent with these preferences for Grace is shown in TABLE 1.4. Note that Grace’s most preferred provider is always the provider that Lisa chooses. If Lisa chooses Sprint, then Sprint yields the highest utility for Grace. (Compare 6 from Sprint, 5 from AT&T, and 3 from Verizon.) If Lisa chooses Verizon, then Verizon maximizes Grace’s utility. Given that Grace really likes AT&T, her highest utility comes when both she and Lisa choose AT&T.
To make the best choice, Grace will need to form beliefs as to which plan Lisa will choose. This condition leads us to the second key personal attribute
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