Engineering Decision Making and Risk Management

Chapter 6Game Theory

Learning Objectives:

After studying this chapter, the reader will be able to do the following:

1. Analyze a two-player simultaneous, zero-sum game (Section 6.2).
2. Find each player's optimal mixed strategy (Section 6.3).
3. Formulate a resource allocation game as a two-player simultaneous, zero-sum game (Section 6.5).
4. Analyze a two-player, simultaneous, mixed-motive game and find dominated strategies and equilibrium points (Section 6.6).
5. Analyze a two-player Stackelberg game and find the each player's optimal strategy (Section 6.8).

When we consider games, we often think of activities such as chess or tic tac toe (noughts and crosses), where the players alternate their moves. Such games are relatively easy to analyze (unless the state space gets too large, as it does in chess), because, when a player needs to decide which move to make, they know everything that has happened and everything that could happen in the future.

In simultaneous games such as rock-paper-scissors, however, neither player is sure what the other one will do, but they have to act simultaneously. In the traditional case, each player knows what the other could do, and both players know the payoff matrix, which describes the reward (or penalty) that each player will receive (pay) given their joint decisions.

Games occur in engineering as well. For instance, engineering firms often submit bids for projects that are being funded by government agencies. Each bidder must submit documents that ...