In our previous work on non-zero sum games we started with the matrix representation of the game. Thus the players' strategies, the possible outcomes of the game, and the utilities which the players assigned to these outcomes are predetermined. In this discussion, we would like to analyze situations which we can be modeled by non-zero sum games. To construct a game for a situation, we will have to determine strategies, outcomes and utilities for the players in order to develop the matrix representation of the game. Once we have constructed the matrix for the game, we can begin to analyze the games and, hopefully, increase our understanding of the original situation.
Exercises Describe each of the following situations as a non-zero sum game.
You should explain the strategies that are available to each player and the utilities that each player assigns to each outcome. You should then construct the matrix representation of the game. Using the matrix representation, find any Nash equilibria and all Pareto optimal outcomes. Two people, Rose and Colin, are suspected of committing a robbery together. The prosecution has enough evidence to prove they were involved in the robbery, but suspects that one of them was carrying a weapon making them liable to the charge of armed robbery.