21 - Game Theory Strictly Competitive Games x Flashcards
What is a strictly competitive game?
A game where one player’s gain is exactly the other player’s loss — typically structured as a zero-sum game.
How does a strictly competitive game differ from other strategic games?
It involves pure conflict — there is no possibility for mutual gain, unlike coordination or prisoner’s dilemma games.
What are common real-world examples of strictly competitive games?
One-on-one sports (e.g., tennis, fencing), penalty kicks, bidding/auctions, political debates, military standoffs.
What is the goal of each player in a strictly competitive game?
To maximize their own payoff while minimizing their opponent’s payoff — a win-lose setup.
What is the relationship between the players’ payoffs in a strictly competitive game?
Their payoffs are perfectly negatively correlated — one player’s increase = the other’s decrease.
What is a best response in game theory?
A strategy that gives a player the highest possible payoff, given the strategy their opponent is using.
How does the concept of best response apply in strictly competitive games?
Each player must anticipate and counter their opponent’s optimal strategy, seeking to secure the best worst-case outcome.
What is a best response equilibrium?
A pair of strategies where each is a best response to the other — i.e., neither player would benefit from changing their strategy unilaterally.
Why are best response strategies critical in strictly competitive games?
Because they are the foundation for identifying Nash equilibria in both pure and mixed strategies.
What happens if neither player plays their best response?
At least one player is leaving value on the table, and the outcome is not stable or optimal.
What is the value of the game in a strictly competitive setting?
The equilibrium payoff each player can guarantee themselves, assuming both play optimally.
What is a maximin strategy?
The strategy that maximizes the minimum payoff a player can guarantee themselves, regardless of what the opponent does.
What is a minimax strategy?
The strategy that minimizes the maximum payoff the opponent can earn, acting as defensively as possible.
When do the maximin and minimax values match?
When the game has a Nash equilibrium — the value of the game is equal for both concepts.
Why are maximin/minimax strategies especially useful in sports?
Because athletes often need to hedge against the opponent’s best possible move, especially when information is imperfect or risk is high.
What is a mixed strategy?
A strategy where a player randomizes between multiple actions with certain probabilities, instead of always choosing one.
Why are mixed strategies important in strictly competitive games?
Because pure strategies often don’t yield an equilibrium, especially when no action strictly dominates others.
What is the condition for a player to use a mixed strategy?
The player must be indifferent among the pure strategies they are mixing over — each must have equal expected payoff.
What’s the mixed strategy equilibrium in Rock-Paper-Scissors?
Each player chooses Rock, Paper, and Scissors with 1/3 probability — making the game unpredictable.
What is the outcome of a mixed strategy Nash equilibrium?
A stable strategy profile where no player can improve by unilaterally changing their probability mix.
