21 – Game Theory: Strictly Competitive Games Flashcards
What change in kicker ability alters the equilibrium in the penalty kick game?
The kicker becomes stronger on the Left, scoring with certainty if the goalie dives Right.
What happens to the equilibrium when the kicker’s Left side is stronger?
The goalie dives Left more often (60%), and the kicker shoots Left less often (40%).
Why does the kicker shoot Left less, despite being stronger there?
Because the goalie responds strategically, covering Left more — forcing the kicker to mix unpredictably.
What is the key takeaway from changing payoffs in strategic games?
Small changes in payoffs can significantly alter optimal mixed strategies, often in non-intuitive ways.
What happens when the kicker is stronger across all options?
Both the goalie and kicker adjust: goalie dives Left more, kicker shoots Left more — reflecting nuanced shifts in equilibrium.
What might you suspect if someone always beats you in rock-paper-scissors?
That you may be missing part of the game — i.e., the opponent knows something you don’t, or is cheating.
What does the Houston Astros scandal teach about strategy?
Strategic cheating only works if others are unaware — outcomes that deviate from equilibrium signal unawareness or a rigged game.
How can unusual outcomes help detect cheating or unawareness?
If results consistently deviate from equilibrium predictions, it suggests that players may not be playing the same game or have unequal information.
What is unawareness in game theory?
When a player doesn’t know the full set of actions or rules, creating asymmetric strategic environments.
What is maxminimization?
A strategy where a player chooses the action that maximizes their worst-case payoff — i.e., ‘playing it safe.’
In the example matrix, which strategy does Player 1 choose using maxmin?
Strategy C, which guarantees at least a payoff of 2, the highest worst-case outcome.
Why might maxmin seem odd in general games?
Because it ignores probabilities and may leave value on the table — but it’s a good conservative strategy under uncertainty.
Why is maxmin useful in sports?
Sports are strictly competitive — your loss is your opponent’s gain, so minimizing loss is a strong defensive strategy.
What is the maxmin outcome in the T/B vs. L/R matrix example?
Player 1 chooses B to ensure a minimum payoff of 1, instead of risking a 0 payoff with T.
What defines a strictly competitive game?
A game where one player’s gain is exactly another’s loss, and no mutual improvement is possible.
What is a zero-sum game?
A strictly competitive game where the sum of both players’ payoffs is always zero.
What is a constant-sum game?
A game where the sum of payoffs is always the same constant, even though individual payoffs vary.
How do strictly competitive games relate to constant- or zero-sum games?
All zero-sum games are constant-sum. All constant-sum games are strictly competitive. But not all strictly competitive games are zero- or constant-sum.
What is an example of a strictly competitive game that’s not zero-sum?
A matrix where one player gains 5 while the other loses 1 — net payoff isn’t zero, but one player’s gain still hurts the other.
Why is maxmin completely reasonable in strictly competitive games?
Because your opponent’s gain = your loss — preparing for the worst-case outcome is strategically sound.
What is the relationship between Nash equilibrium and maxmin in strictly competitive games?
The Nash equilibrium strategy is exactly the same as the maxmin strategy — they coincide.
How does this help in solving complex sports games?
You don’t need to search for all equilibria — just find the maxmin, and you’ve found the optimal strategy.
Why is maxmin favored in computationally hard problems like chess?
It’s often impossible to compute full equilibria, so algorithms like IBM’s Deep Blue used maxmin heuristics to beat human players.
What is second-mover advantage?
A strategic edge that comes from being able to observe your opponent’s move first, and respond optimally.
