Behavior and Biased Choice: A Pitcher’s Problem

Abstract

A game-theoretic model can not incorporate behavioral attitudes. For more effective prediction, the model can be augmented with the reflection of irrational choices. Pitcher’s problem of baseball can be a useful example to show association between strategic choice and behavioral attitude. On mound, the pitcher should encounter great risk of possible unwanted outcome. Confronting the risk, he might be inclined to choose the comfortable strategy, which can reduce possibility of trembling hand. The pitcher’s decision can be explained in two-dimensions: rationality and irrationality. In this paper, we will consider a situation that mixed strategy can be chosen. Intuitively, behavioral attitude is believed to generate some bias on probability distribution assigned for the strategies. That is, likeliness of choosing one pure strategy can be biased depending on behavioral attitude of the individual. Understanding the individuality of the player can contribute to anticipating how he would make a choice.