Question

Suppose a manager and a worker interact as follows. The manager decides whether to hire or not hire the worker. If the manager does not hire the worker, then the game ends. When hired, the worker chooses to exert either high effort or low effort. On observing the worker's effort, the manager chooses to retain or fire the worker. In this game, does "not hire" describe a strategy for the manager? Explain.

Short answer

Yes, "not hire" is a strategy for the manager as it dictates a complete response in the game.

Step-by-step solution

Understanding the Game

The setup of the game involves a sequence of actions between a manager and a worker. The manager must initially decide whether to hire or not hire. If the worker is hired, they then choose their level of effort (high or low). Depending on the worker's effort, the manager decides to retain or fire the worker. The game ends if the manager decides not to hire the worker or after the retain/fire decision.

Defining Strategy Concept

In game theory, a strategy is a complete plan of actions a player will take given the set of circumstances they could face within the game. It includes all possible situations and appropriate responses.

Analyzing the Manager's Choice

When considering the manager's options, not hiring is one of the first decisions made. This choice effectively ends the game, preventing further interactions like the worker's effort decision or the manager's retention decision.

Conclusion about Not Hiring

Since the manager's decision to "not hire" explicitly defines a complete action in the context of the game — leading to the game ending — it qualifies as a strategy according to game theory definition. It dictates a full response to the situation presented to the manager (decide to hire or not) even though no further actions are consequent.

Key concepts

Strategy

In game theory, a strategy refers to a complete and detailed plan of action that a player will follow throughout the game. It encompasses every possible situation the player might encounter and specifies the actions to be taken in each scenario. The goal of a strategy is to anticipate outcomes that maximize a player's utility or benefits, considering the possible decisions of other players.
In the context of the manager-worker game, the manager's strategy includes the decision on whether to hire or not hire the worker. Even the choice "not hire" is a valid strategy because it encapsulates a specific and predetermined response to the game's starting situation. The choice foresees ending the interaction entirely if the hiring does not take place, thereby covering the full scope of potential outcomes inherent in that decision.

Decision-Making

Decision-making in game theory involves selecting optimal actions based on the expected actions of others. Each decision should consider both the current scenario and the possible future scenarios that each choice opens. This process is central to formulating a strategy.
For the manager, the initial decision to hire or not hire is crucial. It affects the immediate outcome and the continuation of the game. If the decision is to "not hire," the game concludes. On the other hand, hiring leads to subsequent decisions related to the worker's effort and the retention or firing choices by the manager. Every decision is inherently linked, requiring careful analysis of the potential consequences of each choice.

Manager-Worker Interaction

The interaction between the manager and the worker is a dynamic sequence of decisions that can significantly affect the outcome for both parties. Beginning with the manager's decision to hire, if followed through, the interaction develops further based on the worker's effort level.
This interaction highlights the intricate balance of accountability and expectations where the manager must predict and respond to the worker’s chosen effort level. The worker, in turn, must consider the manager's likely reaction to their effort. Thus, the interaction is characterized by dependency and strategic thinking on both sides, ensuring that each understands the potential influence their actions have on the entire process.

Effort Levels

Effort levels in this game signify the two choices available to the worker once hired: providing either high effort or low effort. This decision is essential as it directly impacts the manager's subsequent decision to retain or fire the worker.
If the worker chooses a high effort level, they may increase their chances of retention, expecting that the manager will perceive the high effort positively. Conversely, low effort might increase the risk of getting fired, assuming the manager reacts unfavorably to poor performance. As such, the worker's selection of effort level is a strategic choice that profoundly influences the manager's eventual reaction and the overall outcomes of the game. Therefore, effort levels are a critical component in evaluating the worker's strategy within this interactive decision-making process.