19-20 - Game Theory Strategic Reactions in Sports Flashcards
What does game theory study?
The mathematical study of strategic behavior—where an individual’s outcome depends not just on their choices, but also on the choices of others.
What is meant by ‘strategic behavior’?
Decision-making that accounts for the likely actions of others, rather than assuming the world responds passively.
What’s the difference between game theory and standard decision theory?
Decision theory involves solo optimization, while game theory requires strategic interaction between multiple decision-makers.
Give an example of a simultaneous vs. sequential sport in terms of strategy.
Simultaneous: 100m sprint
Sequential: Track cycling sprint or curling.
What are the three core elements of a strategic game?
Players, Strategies/actions for each player, Payoffs for each strategy profile.
What extra features are needed in dynamic or imperfect information games?
The timing of moves, What each player knows at different decision points.
How does game theory apply to sports?
It helps model strategic interactions like deception, timing, and counter-strategy between opponents (e.g., pitcher vs. batter, kicker vs. goalie).
What are the strategies and players in the doping game?
Players: Two athletes
Strategies: Honest or Dope.
What’s the outcome if both athletes are honest?
Each gets a payoff of 2.
What’s the dominant strategy for both players?
Dope — because it yields a higher payoff regardless of the opponent’s choice.
What is the Nash equilibrium in this game?
(Dope, Dope) — even though both would prefer (Honest, Honest), they each have incentive to deviate.
For each athlete, for any given action of the other athlete, it is always preferrable to Dope.
What kind of game is the ‘two friends choosing sports’ scenario?
A coordination game, where mutual choice matters more than individual preference.
What are the two pure-strategy Nash equilibria?
(Baseball, Baseball) and (Soccer, Soccer).
What does this game demonstrate about equilibrium selection?
That multiple equilibria can exist, and communication or expectations may determine which is chosen.
What does it mean for a choice to be a ‘best response’?
It’s the strategy that maximizes a player’s payoff, given the opponent’s choice.
How do you find a Nash equilibrium using best responses?
Identify each player’s best response to every possible action of the other player. The intersection of best responses is the equilibrium.
Why is (Dope, Dope) a Nash equilibrium in the doping game?
Because each player is doing the best they can given the other is doping — neither has incentive to deviate.
What is a dominant strategy?
A strategy that yields a better payoff than all others, no matter what the opponent does.
Why are dominant strategies rare in sports?
Because they make games predictable and eliminate the need for strategic interaction — reducing competitiveness.
Why are games more interesting when there’s no dominant strategy?
Because players must adapt, predict, and respond to others — increasing depth and balance.
Why is rock-paper-scissors a balanced game?
Because no strategy dominates — each can be beaten by one and beats another, forcing randomization.
What is the Nash equilibrium in rock-paper-scissors?
A mixed strategy equilibrium where each player plays each move 1/3 of the time.
What happens when games lack a pure strategy equilibrium?
Players may resort to mixed strategies, randomizing across options.
What is a mixed strategy?
A strategy where a player randomizes across two or more pure strategies with specific probabilities.
