Normal Form Games

Traditionally in game theory textbooks, a game is described by a matrix which shows the agents, strategies, and payoffs. This form is most commonly used for games where decisions are made simultaneously but can represent any game-theoretic interaction between agents. In this module, we consider games in which agents interact only once selecting strategies without knowledge of the other agents' choices.

Elements

1. 3.1.aInterpret Games

   The ability to select the correct payoff given a set of actions in strategic form games: a matrix of payoffs for a single agent indexed by combinations of strategies by the agents and in bimatrix form games: the matrix includes sets of payoffs, one for each agent.

2. 3.1.bBest Response

   The ability to compute and select the strategy with the highest payoff given an opponent's action.

3. 3.1.cDominant Strategies

   The ability to select strategies that provide a greater payoff than any other strategy, no matter what the other agents do. I.e., strategies that are a best response to all possible strategies.

4. 3.1.dAvoidance of Dominated Strategies

   The ability to avoid strategies that are never best responses.

5. 3.1.eIterated Removal of Dominated Strategies

   The ability to systematically eliminate dominated strategies. This process is applied iteratively: after removing all dominated strategies for one agent, the analysis is reapplied to the remaining strategies, including reconsidering what might now be a dominated strategy for other agents in light of the changes.

6. 3.1.fPure Nash Equilibrium

   The ability to play a best response strategy when given knowledge that another agent is also best responding (i.e., is rational). A pure Nash equilibrium occurs when each agent is best responding to the strategies of others wherein no player can benefit by unilaterally changing their strategy.