Question

Distinguish between the following terms:

i. Simultaneous and sequential move games.
ii. Pure and mixed strategy.
iii. Nash equilibrium and dominant strategy equilibrium.

Answer 1

Simultaneous move games involve decisions made without knowledge of the opponent's decision, while sequential move games involve decisions made in a specific order. Pure strategy is a specific decision, while mixed strategy involves randomly selecting different options. Nash equilibrium is an optimal solution given other players' decisions, while dominant strategy equilibrium involves players having a best strategy regardless of the opponent's actions.

Step-by-step explanation:

1. Simultaneous move games: In simultaneous move games, each player makes a decision without knowing the opponent's decision. Examples include rock-paper-scissors and chess.
2. Sequential move games: In sequential move games, players make decisions in a specific order, taking into account the previous player's decision. Examples include chess and tic-tac-toe.
3. Pure strategy: A pure strategy is a specific decision that a player makes in a game. For example, choosing to always play rock in rock-paper-scissors is a pure strategy.
4. Mixed strategy: A mixed strategy is when a player randomly selects different pure strategies with certain probabilities. For example, choosing to play rock, paper, or scissors with equal probabilities is a mixed strategy.
5. Nash equilibrium: A Nash equilibrium is a solution concept in game theory where each player's decision is optimal given the decisions of other players. It is a stable solution that neither player has an incentive to deviate from.
6. Dominant strategy equilibrium: A dominant strategy equilibrium is a specific type of Nash equilibrium where each player has a dominant strategy, which is the best strategy regardless of what the other player does.