SITUATION: BOXED-PIGS GAME
While this book aims to show how game theory can be used to understand human behavior, it can explain the behavior of lesser animals as well (which we explore more fully in Chapters 16 and 17). Let’s consider an experiment in which two pigs—one large and one small—are placed in a cage. At one end of the cage is a lever and at the other end is a food dispenser. When the lever is pressed, 10 units of food are dispensed at the other end. Suppose either pig incurs a utility cost of 2 units (measured in food) from pressing the lever. How the 10 units of dispensed food is divvied up depends on both who gets to the food dispenser first and a pig’s size. If the large pig is there first, then it gets 9 units and the small pig gets only 1 unit. The large pig not only has heft, but also positioning. (Imagine Shaquille O’Neal posting up against Michael Jackson on the basketball court.) If, instead, the small pig is there first, it gets 4 of the 10 units, as it con- sumes some before the large pig arrives to shove it out of the way. If both pigs get there at the same time, the small pig is presumed to get 3 of the 10 units (per- haps mostly from eating the food that falls out of the large pig’s mouth).
Each pig decides whether to press the lever or wait at the dispenser. Those are the two strategies in their strategy sets. Assuming that a pig’s payoff is the number of units of food consumed less any disutility from pressing the lever, the strategic form of the game is shown in FIGURE 3.14.
FIGURE 3.14 The Boxed-Pigs Game
1,5 �1,9
4,4 0,0 Small pig
Large pig
Press lever
Wait at dispenser
Press lever Wait at dispenser
Does the large pig rule the room by being the one that gets to wait at the dispenser? Actually, no. In this setting, “weakness is strength,” as it is the large pig that presses the lever while the small pig waits at the dispenser to start consuming the food. How does that outcome emerge?
Key to the outcome is that the small pig has a dominant strategy. If the large pig presses the lever, it is preferable for the small pig to wait at the dispenser, since it gets more food then and avoids the disutility from pressing the lever; its payoff is 4 from waiting at the dispenser, compared with 1 from also press- ing the lever. If, instead, the large pig waits at the dispenser, then the small pig doesn’t get enough food to justify the bother of pressing the lever. It gets only 1 unit of food, and the cost of pressing the lever is 2 units, so its payoff is �1. It
*Don’t get sidetracked on such matters as whether rationality—a concept intended for Man—is applicable to God, or how Man can play a game against someone he’s not sure exists, or whether the result is blas- phemous because it says that Man should not or will not believe in God. This example is just intended to be a thought-provoking application of game theory.
would prefer not to press the lever and get a zero payoff. Thus, if the small pig is rational (that might sound a bit odd) then it waits at the dispenser regardless of what the large pig does.